EP2158496A2 - Method and device for measuring magnetic fields - Google Patents

Abstract

The invention relates to a method which makes use of the Zeeman effect for measuring magnetic fields, by way of dark resonances. According to said method, a measuring cell (14) is exposed to the magnetic field (B) to be measured and contains the atoms of a measuring medium in a buffer gas, a radiation source (11) being provided for exciting the atoms by radiation and being connected to the modulation frequency generator and emitting electromagnetic radiation with different frequencies. A frequency detector (17) is mounted downstream of the measuring cell (14) and comprises a control loop (18) for the frequency tuning to a dark resonance frequency. The invention is characterized in that at least one modulator (22) for modulating a comparatively high first modulation frequency with a lower second modulation frequency, thereby producing a double sideband structure, is mounted downstream of the modulation frequency generator (24) to couple a plurality of dark resonances using the electromagnetic radiation (12) modulated therewith, substantially only one frequency being detected according to the magnetic field-dependent frequency shift.

Description

 Method and device for measuring magnetic fields

The invention relates to a method and a device for measuring magnetic fields based on the magnetic field dependence of the energy levels of atomic or molecular quantum systems (Zeeman effect) by means of dark resonance, according to the introductory parts of the independent claims.

Dark resonance is a resonance phenomenon that occurs through a quantum mechanical interference effect in atomic or molecular systems. A quantum mechanical system excited by resonant electromagnetic radiation is set in a destructive superposition state of the wave functions of the ground states of the quantum system. In this state, the quantum mechanical system is decoupled from the excitation process of the electromagnetic radiation. A medium consisting of such systems becomes transparent as a result of this phenomenon. The reduced absorption leads to a reduced fluorescence radiation for reasons of energy conservation. The medium appears darker, resulting in the term dark resonance. The observation of this effect requires the observance of certain conditions with regard to the electronic structure (so-called Λ-system). The linewidths of CPT resonances (CPT) may be very low, making these resonances suitable for precision measurements (e.g., CPT atomic clock, CPT magnetometer).

CPT dark states or dark resonances can be observed in the simplest case in a quantum mechanical system consisting of three energy levels. Prerequisite for the observation of the CPT dark resonances is the mutual coupling of the three energy levels by means of an electromagnetic radiation field (eg by several laser frequencies). This coupling can be made in the simplest case by exciting two of the three possible (energetic) transitions of the three-level system. The radiation field must then consist of two (spectral) components of different frequency (bichromatic electromagnetic field), ie a bichromatic electromagnetic field is used. In Fig. 1, this fact is shown graphically. The energy levels are generally determined by the quantum mechanical states | 1>, | 2> and | 3> described. This type of level designation is initially chosen arbitrarily. It can be replaced by the spectroscopic notation of the respective energy levels in a specific quantum mechanical system (eg the hyperfine structure of an alkali metal atomic vapor, as can also be present according to the invention). Behind the name of the energy levels is actually the corresponding quantum mechanical wave function. Knowledge of these wave functions can be gained from the theory of atoms (molecules). This information is known for all atomic levels mentioned here.

In Fig. 1, the two frequency components of a bichromatic electromagnetic field (eg laser field) with vi and v ₂ and M ₁ and CO ₂ (angular frequency) are characterized. The energy of the levels is given in Fig. 1 by the respective equivalent frequency Q ₁ = E ₁ / h (with i = 1 ... 3). 1, with the arrow configuration shown therein, it can be seen why this excitation scheme is called the "Λ system." The following (known per se) magnitudes are important in these excitation schemes and especially in the context of the dynamics of the dark resonances (see FIG. namely:

the two-photon detuning δ _L :

δ _L = (Q ₃ - Q ₂ ) - ω ₂ (1)

and the Raman-Detuning δ _R :

where Δ ₂ χ = Ω ₂ - Q _{2 is} the splitting frequency of the levels 11> and | 2>.

On the basis of these quantities, the behavior of the dark resonances at variable excitation frequencies (frequencies of the bichromatic electromagnetic field) can be discussed particularly clearly. The Raman detuning δ _R can be regarded as a frequency difference between the ground state hyperfine structure splitting Δ ₂ i = v _HFS (for the alkali metal _isotope ⁸⁷ Rb, the frequency v _HFs is approximately 6.8 GHz) and a microwave generator frequency v _RF . As can be seen from FIGS. 2A and 2B (where the dispersion D or absorption A of CPT dark resonances are illustrated (in arbitrary units)), the dark resonance occurs only in a very small frequency interval around δ _R = 0 Hz. The change in the energy (or, equivalently, the change in the frequencies cύi and ω ₂ in FIG. 1) of the atomic / molecular levels under the influence of external magnetic fields is reflected in the change of δ _R (see equation 2). Accordingly, the achievable sensitivity in the determination of the magnetic field is directly related to the frequency interval (by δ _R = 0) in which the dark resonance occurs. This property of the "sensitivity" of the dark resonances to a Raman detonation δ _R ≠ 0 is therefore an essential point.

Raman detuning is often controlled by a radio frequency (RF) or microwave generator that modulates a laser. In this frequency range, a setting accuracy of the generator of 0.1 ... 0.001 Hz is readily possible. The CPT resonance line can therefore also be "sampled" with this accuracy.

The frequency width (= linewidth) of the CPT resonance is largely determined by the so-called decay rate of ground state coherence, which is essentially a measure of the lifetime of the dark resonance. This rate of decay is generally composed of several factors which, in turn, can be classified into intrinsic (quantum dynamics derived) decay rates (e.g., the spontaneous transition of the population from level j 2> to level | 1>) and external decay processes.

In order to achieve the smallest possible line width of the dark resonances (and thus a high sensitivity of the magnetometer), the decay rate of the ground state coherence must be minimized. This is achieved by choosing the level arrangement of the quantum system such that the transition from level \ 2> to I 1> is a so-called dipole-forbidden transition. The decay rate of the ground state coherence is determined in this case as far as possible by external influences (eg by impacts of the atoms in the dark state with a vessel wall).

By using a so-called buffer gas, the impact rate with the wall is greatly reduced. With a suitably selected buffer gas pressure, the mean free path of the quantum systems pumped into the dark state is thus substantially reduced. A diffusion movement of the quantum systems is the result. The effect of time-of-flight broadening of dark resonance is therefore greatly reduced.

The described measures ultimately achieve effective lifetimes of ground state coherence of 1 ... 30ms. Consequently, this means that the frequency width of the dark resonance is significantly reduced. The sensitivity of the magnetometer therefore increases in the same way.

However, the requirement of the buffer gas is that the rate of decay of ground state coherence by this gas (and the resulting collisions) is not significantly increased. When

(Buffer) gases with the required properties are, for example, the noble gases or molecular gases such as nitrogen and methane, etc. in question. The electronic structure of these gases is such that only a slight overlap of the wave functions of the buffer gas with the wave functions of the ground states

I 1> and i 2> of the dark state quantum system is given. However, the overlap of these wave functions, albeit small, is responsible for a systematic frequency shift of the dark resonance, which depends on the buffer gas density and the temperature of the buffer gas. The origin of the influence of the dark resonance frequency in such a collision process lies in the interplay of Van der Walls forces and exchange interactions of quantum system and buffer gas.

This (unwanted) frequency shift significantly affects the accuracy and long-term stability of the magnetometer. A conclusion from the dark resonance frequency on the magnetic field (see equation 3 below) is no longer strictly given by the natural constant and the frequency value of v _HF s. In the presence of a buffer gas, these pressure and temperature-dependent frequency shifts of the undisturbed frequency ^v HFS are due to superimposed.

In contrast to the "sensitivity" of the dark resonances compared to the Raman-detuning, the insensitivity to the two-photon-detuning δ _L (see equation 1) is shown by a quantum-mechanical analysis showing that the line widths ^ frequency-widths) of the optical transitions between the Levels | 1> - | 3> and | 2> - | 3> (see Fig. 1) .Thus, the two-photon detuning δ _L may well have values of 10... 20% of the line width of this optical Transitions assume (eg 50-100 MHz when using atomic rubidium vapor as a quantum system), without losing the dark resonance significantly at signal height.

Therefore, no great demands are placed on the laser stability. Often a freewheeling, i. unstabilized, laser.

The behavior of the CPT resonances is discussed on the basis of the ⁸⁷ Rb-Di ~ line as a concrete quantum system (among many other possibilities). In addition to the possibility of realizing Λ-like excitation schemes, in Rubidium (as with all other alkali metals) the desired dipole-forbidden transition between the ground states occurs.

FIG. 3 shows the realization of a Λ excitation scheme within the ⁸⁷ Rb hyperfine structure of the D ₁ line. By the special choice of ground states | 1> and | 2> in the form of the two magnetic substates | 5 ² S _1/2 F = 1 m _F = 1> and 15 ² Si _{/ 2} F = 2 m _F = 1> the magnetic field dependence of the ground state splitting frequency is given by the known Zeeman Ef fect. Since these are ground states of the D-lines, the quantum-mechanical solution of the problem succeeds without disturbance calculation. The splitting can therefore be specified for "any" magnetic flux densities B. FIG. 3 shows schematically, with strong lines, magnetic field-dependent CPT dark resonances in the ⁸⁷ Rb-Di line: In FIG. 3, (F, m _F ) and (F ¹ , m ' _f ) give total Angular momentum quantum numbers or magnetic (sub-) quantum numbers of the ground state and of the excited state, v _B the frequency shift due to the Zeeman effect, v _ges the total frequency splitting in the magnetic field, V _HFS the frequency of the splitting of the ground state (without magnetic field ), v ₂ i and V _{22 are} the frequencies of the electromagnetic field that cause the excitation in the Λ-system with the number n = +2, and λ the center-of-mass wavelength of the transition 15 ² S ₁₇₂ > → 15 ² P _1/2 > ,

From Fig. 3, the dependence of v _ges = v _HFS + 2v _B is generally apparent. In the field of small fields (eg | B | <^ C ITesla), the well-known Breit-Rabi formula can be used in its linearized form (linear Zeeman effect). With the numbering of the CPT dark resonances by n = m _F1 + m _F2 and by the choice of Δm = m _r2 - m _F1, we obtain for v _ges (B - magnetic flux density [T]):

V _gea = v _HFS + ^ _{2 I} ^ ₁ ^ _h [n (g _J -g _I ) + 8 AiTLg ₁ ] B (3)

The quantities g _Jr g _x and I _k are given in Eq. 3 for the fine-structure LANDE factor (g _α ) or the Atmokern-LandE factor (g _τ ) and for the nuclear spin (I _k ), P _B denotes the Bohr magneton. These sizes are known and are tabulated.

The linearized form of the Breit-Rabi formula is given in the remainder of the text only for reasons of simpler notation of the equations. The described principles are also valid when using the exact form of the Breit-Rabi formula.

The frequency V _HF S corresponds to the splitting frequency of the ground states at B = O (see Fig. 3) and is very well known in the case of the alkalis. This splitting frequency v _HFS at ⁸⁷ Rb is, for example, 6.834 682 610 904 29 (9) GHz. The g _α factor depends on the respective electron configuration. From Equation 3 can be a shift coefficient for the ⁸⁷ Rb-D ₁ line

C = n-7kHz / μT can be calculated. It follows for the in

Fig. 3 illustrated ein system has a value of 2v _B / B = 14kHz / μT.

Magnetic fields can in principle (see, eg, WO 2004/051299;... And Peter DD Schwindt et al, "chip-scale atomic ^{magnetometer",} "Applied Physics Letters, Vol 85, No. 26, December 27, 2004, pp 6409-. 6411) are measured by the single Λ system shown in FIG. For generating the dark resonance, a circularly polarized, bichromatic radiation field with the frequency components V ₁ and v ₂ would be required here. The two frequency components of the laser field can be realized in the form of sidebands, which are produced by modulation of the laser.

If the frequency of the modulation generator is subsequently kept at (v ₂₁ - V ₂₂ ) ^~ v _ges = 0 by a control loop, Vmod = 1/2 (v ₂₁ - V22) can be applied to the frequency of the modulation generator according to Equation 3 Magnetic field B to be closed. The accuracy of the magnetometer is limited by systematic (error) influences that undesirably affect the frequency position of the CPT resonance. These systematic frequency shifts result, as already described, on the one hand from the interaction of the dark state quantum systems (eg atoms or molecules) with a buffer gas (see above) and, on the other hand, from the intrinsic accuracy of the frequency measurement with which the CPT resonances. frequency can be determined.

However, this means that the frequency v _HFS depends essentially on the buffer gas used, the buffer gas pressure and the ambient temperature. For example, the frequency of the dark resonance at a variable temperature may already shift by 5 Hz / K. If the buffer gas temperature changes from 1 K, this drift could not be distinguished from a change in the B field of 360 pT. This is a significant limitation given the otherwise achievable accuracy of ΔB «1 ... 10 pT. To avoid the temperature drift, a complex temperature stabilization of a measuring cell in which the quantum systems (eg rubidium, cesium) are located would be necessary. The required accuracy of the temperature stabilization would have to be in the example mentioned ΔT << 0.01 K in order to achieve the otherwise conceivable accuracies. The ability to compete with a system according to FIG. 3, magnetic fields with high accuracy and repeatability, lost despite thermalized cell because a hysteresis repeatability of Zellentem ^¬ temperature is technically impossible despite temperature stabilization.

Another source of error in the known magnetic field measurement with dark resonance is that the stability of the RF generator with which v _{ges is} determined also limits the accuracy of the B-field measurement. Common and still financially affordable generators have a long-term stability of Δv / v «" 10 ^"9 per month, with v _ges * V _HF S = 6.8 GHz resulting in a drift of approximately 7 Hz per month systematic drift of the magnetometer of 500 pt per month.

A modified measurement principle is in Article R. Lamb Egger et al, "A magnetometer Based on Quantum Interference Effects", 13 ^th International School on Quantum Electronics. Laser Physics and Applications, Proceedings of SPIE VoI 5830, Bellingham, WA, 2005, page 176 -180, (similarly: A. Huss et al., "Polariza- tion-dependent sensitivity of level-crossing, coherent-popu- lation-trapping resonances to stray magnetic fields", Sept. 2006, Journal of the Optical Society of America B (Optical Physics), Opt Soc. America, USA; AN 9057678; INSPEC / IEE Database and Vol. 23, pp. 1729-1736), the suitability of CPT resonances in a "Hanle" configuration is explained with respect to the application in a magnetometer, and wherein the measuring principle is geared to a level crossing, ie the CPT resonances occur if and only if the total magnetic field to which the atoms (namely rubidium atoms) are exposed, the Value B = O has. The applied magnetic field is thus determined in such a way that a compensation magnetic field is applied to the measuring magnetic field, and this compensation magnetic field is regulated in such a way that the CPT resonance occurs this only occurs at a magnetic field B = O, the magnetic field to be measured and the compensation magnetic field the same size, but opposite, be. The compensation magnetic field is generated by a solenoid, a long cylindrical coil, whereby the coil current of this solenoid ultimately determines the magnetic field to be measured. It follows that the measuring principle is based on a current measurement.

In the article E.B. Aleksandrov, "A new model of quantum magnetometer: a single-cell Cs-K tandem based on four-quantum resonance in <39> K atoms" Juicy 2000; Technical Physics; Vol. 45, No. 7; MAIK Nauka ; Russia; AN 6716360; INSPEC / IEE database, pages 931-936, discloses an optically pumped cesium-potassium (tandem) magnetometer, but such an optically-pumped magnetometer is fundamentally different from a CPT magnetometer Magnetometers rely on a modulated AC magnetic field to depolarize the alkali vapor, which is excited by an unmodulated laser or a spectral lamp, and such an excitation source would be insufficient to excite CPT dark resonances.

In the article Hwang Lee et al., "Quantum limit sensitive of cohesive dark-state magnetometers" May 19, 2002; Conference on lasers and electro-optics (CLEO 2002) .Technical Digest., Postconference edition, Long Beach, CA. , Trends in optics and photonics (TOPS); Washington, WAOSA, US; XP010606401; NPL / EPO database, pp. 36-37 (similarly to Brandt S. et al., "Magnetometry and frequency references with coherent dark states "17-21 June 1996; Proceedings of 20 ^th Biennial Conference on Precision Electromagnetic Measurements; Braunschweig, Germany; AN 5483666; INSPEC / IEE Database, p. 190) bases the theoretically achievable sensitivity limit of a conventional dark state magnetometer treated on the excitation of a single dark resonance, wherein in particular a "dark-state" magnetometer is shown with interferometric structure.

In the article Shirley JH et al. , "Zeeman coherences and dark states in optically pumped cesium frequency standards", June 27, 1994, Precision Electromagnetic Measurements, 1994 Conference on Boulder, NY, NY USA, IEEE; ON XP010123851; NPL / EPO Data Bank p. 150-151, deals with the avoidance of "trapped states" in the preparation region of cesium atomic-beam atomic clocks, with particular attention to the problem of atomic clocks, in contrast to magnetometers.

Similarly, US 2004/0202050 Al also deals with the operation of an atomic clock, in which, among other things, the Zeeman effect is exploited in order to lock both the atomic clock frequency and the magnetic field to defined values.

It is an object of the invention to provide a method and a device for measuring magnetic fields, wherein over long periods an accurate measurement even in extremely small magnetic fields, for example in the order of μG to a few G, is possible. In particular, the aim is to be able to carry out the measurement in such a way that the systematic error influences discussed above, which manifest themselves in the frequency of the ground state, ie the frequency v _HFS (p, T), are eliminated, and a sole measurement of only the Magnetic field-dependent size (see the second term in the above equation 3). It would be possible then one of the mentioned error influences, such as buffer gas, buffer gas temperature and pressure, free measurement of the magnetic field B.

To achieve this object, the invention provides a method and an apparatus for measuring magnetic fields as defined in the independent claims. Particularly advantageous embodiments and further developments are specified in the dependent claims.

In the measurement technique according to the invention, several dark resonances are coupled together, as will be explained in more detail below, wherein a polychromatic radiation is used as an electromagnetic field, in particular a light field or laser radiation with different frequency components. This polychromatic electromagnetic field can preferably be achieved by a multi-stage modulation process of a laser as a radiation source. Unlike the prior art, therefore, a second modulation or mixing process is used, preferably a ring modulator or ring mixer is used for mixing a low-frequency modulation signal with a first, high-frequency signal of a microwave generator. In this way, the desired frequency components result after the mixing process, in particular in the form of a double sideband structure, as will be explained in more detail below. In order to be able to detect only the magnetic field-dependent frequency components or to achieve a simultaneous training of all dark resonances of the system, the first modulation frequency, the high-frequency modulation frequency, equal to the splitting frequency v _{HFs is suitably} chosen, and then results for the second, low-frequency modulation frequency - After tuning to the resonance - a value v _B , this second modulation frequency can be treated completely separated from the first modulation frequency. The second modulation frequency is generated by a low-frequency generator, in particular a voltage / frequency converter or a Digital Data Synthesis (DDS) frequency generator, which is constantly adjusted via a control loop so that the Raman detuning for all Λ systems is equal to 0 (CPT condition). By using a ring modulator, there is virtually no restriction on the magnetic field to be measured (corresponding to the second modulation frequency). This advantage results from the generally very high bandwidths (GHz range) of such mixers. In the case of a direct control of the HF generator, on the other hand, the bandwidths of the generator-internal (PLL) phase locked loops would limit the maximum possible LF modulation frequency to approximately 100 kHz. In this way, magnetic fields could only be measured up to a maximum of 0.1 G. The use of a ring mixer, however, allows the full range (some gauss) of the CPT magnetometer to be exploited.

As a further advantage results from this type of modulation by means of ring mixer, that it is an amplitude modulation. In this type of modulation occur (regardless of the modulation index) only the first-order sidebands. This contributes to the multichromatic radiation containing only the desired frequency components. The direct control of the HF generator with the second modulation frequency, however, would mean a frequency modulation, wherein depending on the modulation index sidebands higher order occur, which can complicate the spectrum of dark resonances.

Moreover, in the described amplitude modulation of the ring mixer, a strapless operation can easily be achieved in which the RF modulation frequency is absent in the spectrum. This is an advantage for the measurement because the associated dark resonance (with the number n = 0) is not needed anyway. This dark resonance produces only a disturbing signal background, which would have to be removed with a phase-sensitive detection.

In order to enable a scan mode during measurement, it is favorable if the input of the voltage / frequency converter can be selectively connected to the output of a ramp generator. With this mode, the low frequency sidebands can be sampled and the dark resonances can be recorded. In the locked mode, with active servo loop, the LF sidebands are coupled to the dark states split according to the Zeeman effect.

As already mentioned several times, wxrd preferably uses a laser as the source of the electromagnetic radiation, and in particular the radiation source is formed by a VCSEL laser. This VCSEL laser can be assigned a temperature control loop for temperature stabilization.

The multiple modulation signal is expediently fed to the radiation source via an attenuator in order to be able to apply the modulation signal with the optimum energy to it.

In the case of the use of alkali metal atoms in the measuring cell, it has proven particularly advantageous if the modulation frequency generator generates a first modulation frequency in the range of several GHz, in particular 3.4 GHz or 6.8 GHz in the case of ⁸⁷ Rb, and the second Modulation frequency up to a few MHz, so that a measuring range of a few Gauss (G) is achieved.

The invention will be described below with reference to preferred embodiments, to which, however, it should not be restricted, and further explained with reference to the drawings. In detail in the drawing:

Fig. 1 is a basic, already explained above scheme for illustrating the known three-level system in which CPT dark resonances can be observed;

FIGS. 2A and 2B are diagrams showing the dispersion D or absorption A of CPT dark resonances (in arbitrary units) over the Raman detuning δ _R (kHz), for the parameters 2-photon tuning δ _L = 0 Hz, Rabi frequencies gi = g ₂ = 20 kHz, decay rate of the ground state = 100 Hz;

FIG. 3 shows the known scheme of the magnetic field-dependent CPT dark resonances in the ⁸⁷ Rb-D ₁ line, likewise explained above, for illustrating the frequency shifts v _B by the Zeeman effect in the various excitations in the Λ-system;

FIG. 4 shows a scheme comparable to FIG. 3, in which, however, according to the invention, the simultaneous coupling of a plurality of dark resonances is illustrated using the example of the ⁸⁷ Rb-D ₁ line, the formed Λ systems having the indices n = -2.0, 2 numbered;

5 shows a diagram of the total dark resonance amplitude in such a system with coupled dark resonances, namely with different RF oscillator detunings δv in units of the CPT line width Δv _CP τ, wherein the total dark resonance amplitude L _g = L _a - ₂ + L _{a + 2 is shown} for four different frequency detunings δ _^ ;

Fig. 6 is a graph for the same RF oscillator detuning as in Fig. 5, the respective curves corresponding to the 1st derivative of the total dark resonance amplitude;

Fig. 7 is a schematic diagram in the form of a block diagram for illustrating a preferred embodiment of the measuring device according to the invention;

8 a required for the coupling of the dark resonances, spectral composition of the signal at the output of the tunable frequency generator according to FIG. 7, consisting of carrier frequency and first and second order sidebands;

Fig. 9, in sub-figures 9A, 9B and 9C, a ramp signal (Fig. 9A) appearing at the output of the frequency generator of Fig. 7, a superimposed ramp and modulation signal (Fig. 9B) at the output of the adder unit of Fig. 7 and Figs correspondingly modulated output of the frequency generator (Figure 9C);

10 in sub-figures 10A and 10B, the input signal coming from the adder unit according to FIG. 7 and the high-frequency output signal (GHz range) of the mixer shown in FIG. 7, once without (FIG. 10A) and once with DC component E _D (Fig. 10B);

Figures 11 to 14 frequency modulation spectra (FM spectra) with different choice of modulation and resonance parameters of the coupled dark resonances (as will be explained in more detail below), in each case in the subfigures IIA to 13A detailed representations are given with corresponding parameter studies; and

Figures 15A and 15B show FM spectra of the coupled dark resonances for a general set of modulation and resonance parameters.

As already mentioned above, in the measurement technique according to the invention, the systematic error influences explained in the prior art with reference to FIGS. 1 to 3 are eliminated by determining the frequency of the ground state v _HFS which is dependent on external influences (such as on pressure, the temperature and the nature of the buffer gas) to the quantum system in the dark state, is formally split off from the term of equation 3 which depends on the magnetic field B. Accordingly, the frequencies v _HFS and v _B are generated separately, the sole measurement of the variable proportional to the frequency v _B (see the second part of Equation 3 above) makes it possible to determine the magnetic field B in which the aforementioned error influences are avoided. This can be seen by the scheme of FIG. 4, in which three Λ systems with a polychromatic electromagnetic field (light wave field) with the frequency components v_ ₂ i ... V _{22 are} shown. The Λ-systems formed are numbered in Figure 4 with the indices n = -2,0,2; the frequency components j of the electromagnetic field causing the excitation in the Λ-system with the number n = i are indicated by V _1J (j = 1,2 and i = -2,0, +2); v _iges denotes the total frequency splitting in the magnetic field of the ground states of the Λ-system with the number n = i. The meaning of the remaining symbols is identical to that of FIG. 3. The polychromatic field according to FIG. 4 can be technically achieved by a multi-stage modulation process.

According to a first modulation stage, the laser (laser frequency v _L ) is modulated by an RF (RF) signal having the frequency ^v modi - I ^V HFS. This results in a sideband structure of the laser radiation in the form of v _O i = v _L + v _mod i; v _L ; and V ₀₂ = v _L - v _modl ; This results in a total of three frequency components (the laser frequency is in the case of ⁸⁷ Rb as a quantum system about 377 THz.

If the RF generator frequency is assumed to be variable, then, with a tuning of the frequency v _mod i, only the dark resonance with the number n = 0 occurs at the position v _modl = 1 / 2v _HFs (δ _R = 0, see Equation 2 above). on. The Λ system n = 0 is thus formed by the sidebands v _O i = v _L + 1 / 2V _H FS and V ₀₂ = v _L - 1 / 2v _HFS . This dark resonance (n = 0) is "only" second-order dependent on the magnetic field due to known atomic physical conditions, so that the position of this dark resonance can be (initially) assumed to be independent of the magnetic field for the observations made here, but V _HFS = V _HFS (P _/ T), ie the dependence of pressure p and temperature T of the buffer gas is given.To now - in addition to the Λ system n = 0 - also the two vom systems dependent on the magnetic field B with the numbers n = -2 and n to form = 2, the additional frequency components need to FIG. 4 v. _2α, v. ₂₂ and V ₊₂₁ V generated _+22. This is accomplished by a second, still explained in more detail below with reference to Fig. 7 mixing process . In This mixing process, the RF signal, ie the first modulation frequency V ₁ - _OdI , again - preferably using a ring modulator (ring mixer), see. Fig. 7 - mixed with a second, low-frequency modulation signal v _mod2 . In this way, after the mixing process in the microwave range, the frequency components v_ _2RF = v _{motn -v mod2} , v _0RF = v _mod1 and V _{+ 2R} F = v _mod i + v _{mod2 -in} itself the way in which this modulation is achieved , not critical for the principle of operation, however, the use of a ring modulator offers significant technological advantages, as will be explained in more detail below.

Now, if the two mixing processes (as already stated, the first modulation process in the mere modulation of the laser, ie in a current modulation in semiconductor laser diodes) taken together in their effect, the result is a multichromatic electromagnetic field (laser field) with the following frequency components :

V ₂₂ = V _L - (v _mod i + V _mod2 ) V02 = V _L - V _modl v_ ₂₂ = v _L - (v _mod i - v _raod2 ) V _L = V _L

V-21 = V _L + (V _modl -V _mod2 ) V ₀ I = V _L + V _modl

V _2x = V _L + (v _modl + v _mod2 ) (4)

The comparison of these relationships with the excitation scheme of FIG. 4 shows that all the necessary frequency components for the excitation of all Λ-systems are present. A dark resonance, ie a change in the absorption of the alkali vapor considered here by way of example as a quantum system; see. also Fig. 2, occurs exactly when the condition δ _R = 0 is satisfied for one of the in-systems cited in Fig. 4. A simultaneous formation of all three dark resonances is thus given under the condition δ _R _ ₂ = δ _R0 = δ _{R + 2} = 0 (see Equation 2). In the case of a multichromatic radiation field of the type of equation 4, this condition is reached directly if:

^V modl ~ l ^V HFS - n -

[InKgj-gJ + ^β ΔmgjB

: S)

From these equations (5), it can be seen that the modulation frequencies v _modl and v _mod2 can be treated separately. Preferably v _modl = l / 2v _{HFS is} set and left so. The second modulation frequency v _moά2 is generated by a low-frequency generator, which is permanently adjusted via a control circuit so that δ _R - ₂ = δ _{R + 2} = 0 remains satisfied, that is, the CPT condition is given. As already mentioned, the specification of the linearized Breit-Rabi formula is only made for the sake of simpler notation of the equations. The measuring principle remains valid even when using the exact form of the Breit-Rabi formula.

In a technical realization, the magnetic field measurement according to equations 5 can be carried out by the much simpler determination of v _mod 2 (v _{mod2 ≦} MHz range). From this splitting results in terms of accuracy and stability of the magnetic field, a decisive advantage that makes this measurement principle extremely accurate and long-term stability.

For the generation of the RF signals v _modl (in the GHz range) can be a commercially available highly stable time base in the form of a temperature-stabilized quartz oscillator (OCXO - oven controlled crystal oscillator) with a stability of approximately Δv / v ~ 10 ^"9 are used per month. If done, the magnetic field by measuring the frequency of only one dark resonance using the RF-Si gnals, as is the case in the prior art, so a systematic drift resulted despite the high stability (= fictitious magnetic field) of about 500 pT per month (numerical values for ⁸⁷ Rb).

By the above described possibility of the separate determination of v _mod2 , the systematic errors, which are caused by the oscillator drift, are _reduced to ΔB _sysC = v _rood2 / v _HFS ^• ΔB ≤ 0.5 / 7000 in a magnetic field determination via v _mod2. 500 pT = 0.035 pT. (These numbers are for the case of a "Rb magnetome- For magnetic field measurements of the order of magnitude of 0.7G H v _mod2 * 0.5 MHz assumed (geomagnetic field "0.5 G).) The multistage modulation process is therefore a very significant reduction (eg factor 7000) due to the oscillator drift conditional systematic errors possible.

The division of the modulation in two stages allows the separate evaluation of the magnetic field B dependent frequency v _mod2 . By this measure, it is possible to eliminate the systematic (external) influences (eg by a buffer gas) to the frequency A ₁₂ (or v _HFS ) of the quantum system, since only the component v _B = v _{mod2 is} used to determine the magnetic field. A comparison of equation (3) and equation (5) shows that the frequency v _B = v _{mod2 is} not dependent on the possibly influenced (disturbed) frequency v _HFS . It is important that there is no influence of v _m odi on the position of the dark resonances (and thus also on Vn ₁ Od ₂ ). By this decoupling is additionally ensured that the systematic influences (by eg pressure and temperature of a buffer gas) on the position of the signal of the coupled dark resonances in a certain (depending on the width of the dark resonance (see equation 9 below)) range - even without active Correction by another control loop - can be eliminated. The systematic error of the B-field measurement due to temperature influences tends towards zero.

As will be explained below, from Equation (39) a signal can be derived which allows for active correction (with the aid of a control loop 43 in FIG. 7) of the frequency v _rood i. In this way, the maintenance of the decoupling explained above is no longer dependent on the line width of the dark resonance. The magnetometer can thus be operated with the highest resolution (ie with the smallest line widths of the dark resonances). Even systematic errors of size v _HFS -2v _mod i> Δv _C Pτ no longer matter.

For small values of Raman detuning δ _R _ ₂ , δ _{R + 2} ^κ 200 Hz «: Δv _hom == 6MHz and of two-photon detuning δ _L <§: Δ _doppler « 500 MHz, the frequency dependence of the absorption and the Frequency dependence of the dispersion of the medium (see also Fig. 2) by simple be described Lorentzfunktionell:

(6)

The index a means that it is a Lorentz function with absorptive character. The index -2 or +2 indicates the number n of the dark resonance. The quantity h _n , with n = -2 or +2, determines the height (signal strength) of the dark resonance with the number n. In the following considerations is with good approximation h-. ₂ = h ₊₂ assumed. This approximation is justified for dark resonances in buffer gas cells because the lifetimes of the excited states are greatly reduced by the buffer gas. Despite the optical pumping through the σ-polarized electromagnetic field (laser light), increased spontaneous decay in all m _F states produces an even distribution of the population (occupation) over all m _P states.

The further terms in the denominator of Equation 6 have the following meaning: The quantity Δv _CPT is defined as the full width of the dark resonance at half the signal height (FWHM - filling width at half maximum). Furthermore: are the corresponding Raman detunings of the dark resonances with the number n. The variable is the frequency difference between the dark resonance n = 0 (0-0 transition) and the RF oscillator frequency v _modl . For a perfectly matched RF oscillator, the value δv = 0 results.

Since both dark resonances are coupled via the multichromatic laser field, only the quantity L _g = L _a - ₂ + L _{a + 2 is} detectable. In a magnetic field measurement according to equation 6, the NF generator _frequency v _{mod2 is} the variable size. The _AF generator is tuned via a control loop so that v _{mod2 is} just at the frequency at which the total absorption becomes maximum (L _g (v _mOd2 ) = max.) _f matches. This is also shown in FIG. 5, in which the total dark resonance amplitude L _g = L _a - ₂ + L _{a + 2} is illustrated with different RF oscillator detunings δv (in units of the CPT line width Δv _CET ). For .DELTA.V ≤ V ^{3/6 •} .DELTA.v _CPT is 1 / 2C-B, where only a single global maximum at v = _mod2, which as Lockpunkt (locking point) for the LF-oscillator (v _mod2 the generated) is used. Further parameters in FIG. 5 are: magnetic field (in frequency units) CB = 10, single dark resonance amplitude h_ ₂ = h _{+ 2} = 1. (The numerical values of the parameters are freely chosen, so that the basic principle can be clearly illustrated.)

The quantity CB (unit of a frequency) is functionally related to the external magnetic field B due to the Zeeman effect (see equation 3); it is like δv a parameter in the equation of L _ς = L _a - ₂ + La + 2 •

The preservation of the accuracy is guaranteed if the maximum of the total dark resonance amplitude applies: , and this is true even if the detuning of the RF oscillator δv φ 0.

This can be verified by the formation of the first derivative of Equation 6, cf. also Fig. 6.

As can be seen from FIGS. 5 and 6, three real zeros result in the general case. The position of these zeros can be analytically achieved by the solution of the following equation:

dL "Δvc _PT (δv + CB-2v _mod2 )

^■ = h. dv +2 mod2

[17 (δv + CB-2v _mod2 ) ² + -ΔvL]

With the condition h ₊₂ = h_ ₂ (which satisfies very well, as stated ), the following positions of the zeros result:

v _N i, ₃ = ^ CB ± - ^ - 4δv ² + 4Vδv ² Δv ^ _τ + 4δv ⁴ -Δv ^ _PT

V ₁₁₂ = - CB (8)

The zero point v _N2 corresponds to a fixed point (see Fig. 6), the strict at lies. These zeros, which is a maximum of L _g at the point is independent of the RF generator detuning v _modl , independent of v _HFs ⁼ ^ _HFS (P _/ T) and independent of the CPT line width Δv _CPT .

In the technical realization, a suitable control edge is achieved by a phase-sensitive detection of L ₉ , which is a conventional lock-in technique. In such a detection method, the modulation of the modulation parameters-the NF generator is correspondingly modulated again-generates the first derivative of L _g (as shown in FIG. 6) with a suitable choice. Thus, only the point ^v mod2 ~ ^v N2 ~ ^~ ₂ ^^ as a clear lock point for the NF generator in question. However, a specific limit value for δv must not be exceeded. This limit is characterized by the disappearance of the second derivative of L _g at the position ^v mod2 ^{~ v} N2 ~ 1.CB.

Due to this, the condition for the RF generator detuning δv is as follows:

δv = (v _HFS -2v _raodl ) <^ - Δv _CPT ~ 0.289Δv _CPT (9)

For line widths of ΔV _C PT ~ 100 ... 200 Hz, a tolerable drift of the RF oscillator of approx. Δv * 30 ... 60 Hz results. However, this limit value becomes at an oscillator stability of Δv / v = 10 ^"9 at v _mod = v _HE . _Ξ = 3, 4GHz not exceeded.

By a control circuit (see control circuit 43 in Fig. 7) are frequency deviations of the oscillator (23 in Fig. 7) from the No- Minimum frequency actively corrected. This control loop can be operated with a high time constant, since the accuracy of the magnetometer is not influenced by a frequency drift δv ≠ 0.

In the presentation of the measuring principle, the CPT resonance with the number n = 0 was not considered. In the case of the phase-sensitive detection of the dark resonances with the numbers n = ± 2, only the LF generator is modulated at the frequency which is used as the mixing frequency in the demodulation of the photodiode signal. Consequently, only the signal of the dark resonance with the number n = ± 2 appears visible at the output of a lock-in amplifier, which is connected downstream of the photodiode (see FIG. The constant signal background generated by the dark resonance n = 0 can therefore be disregarded.

By a strapless operation of the ring mixer, moreover, the generation of dark resonance n = 0 as mentioned can be avoided at all.

The detection of the dark resonances is carried out with a phase-sensitive detection (lock-in techniques) in order to obtain a suitable zero-crossing control edge for the stabilization of the LF oscillator. The analysis shows that the stabilization point agrees with the line center of gravity as long as the frequency drift of the RF oscillator (and / or the drift of v _HFS ) does not exceed approximately 30% of the CPT resonance bandwidth achieved. Due to the typical CPT line widths ΔV _C PT ^% 100 ... 200 Hz and the typical drift of commonly available quartz oscillators of about 10 ^{~ 9} per month, it can be expected that the deviation of the RF oscillator frequency practically never verifies the allowed range - leaves. Since the frequency of the line center of gravity (= lock point) is linked by very well-known relationships with the external magnetic field, with the present technique of coupling multiple dark resonances a virtually drift-free magnetometer can be realized. In the extended analysis (explained below), a further control loop 43 (see FIG. 7) indicates a method by means of which arbitrarily large deviations of the oscillator frequency can also be compensated. Frequency measurements are among the most accurate and best researched measurement methods in physics and engineering. The measuring principle of the magnetometer is ultimately based on the determination of a difference frequency of two atomic (molecular) crossover frequencies. The measured frequency can thus be linked using exactly known quantum mechanical relationships with the external magnetic field acting on the quantum systems.

FIG. 7 diagrammatically illustrates in a block diagram an embodiment of such a CPT magnetometer as explained above in principle. The device shown

10 for measuring the magnetic field contains as a radiation source 11 for the emission of electromagnetic radiation, a laser device, in particular a VCSEL laser whose laser beam 12 via optical elements 13 (incl. ND gray filter, Ll lens and λ / 4-plate QW) by a measuring cell 14 and behind it is directed to a photodiode 15 via a lens L2. The VCSEL laser

For example, 11 has a frequency of approximately 377 THz (in the case of ⁸⁷ Rb). The measuring cell 14 is preferably filled with a buffer gas and contains the quantum systems to be excited, for example Rb or Cs atoms. The diameter of the laser beam 12 in the region of the measuring cell 14 is for example approximately 2-8 mm, whereby, as experiments have shown, sufficiently narrow dark resonances can be achieved with sufficient resolution of the magnetometer. The quarter wave retardation plate (λ / 4 plate) QW provided under the optical elements causes circular polarization. In this way, several dark resonances of different frequency (Zeeman effect) are brought about by paired σ-transitions. The photodiode 15 is a low noise photodiode; the signal / noise (SN) ratio is further influenced by temperature, length, pressure, etc. of the measuring cell 14, wherein it is possible to achieve a high S / N ratio with a corresponding tuning of these parameters and in particular when using Rb or to reach Cs in the measuring cell 14. It has been shown that the S / N ratio can be additionally increased by heating the measuring cell 14 to about 30 ° -60 ° C. Furthermore, although not shown in Fig. 7, a temperature stabilization for the measuring cell 14 is advantageous for this purpose.

The low-noise photodiode 15 is followed by a particularly low-noise amplifier 16, wherein the photodiode 15 and the amplifier 16 together belong to a detector unit 17 for the magnetic field B to which the measuring cell 14 is exposed.

The above-explained optical part of the device 10 can be made largely metal-free, so that this part does not cause its own magnetic fields; In particular, the measuring cell 14 can also be simply connected to multimode optical fibers.

The detector 17 is associated with a control circuit 18 with two lock-in amplifiers 19, 20, which serve for locking ("lock-in") on the detected dark resonance frequency, as will be explained in more detail below, and that of are conventional and therefore unspecified type.

The laser radiation is 12 (or the associated electrical signal) by means of a modulation unit 21 and a mixer 22 modulates a plurality of stages to be carried out for the measurement ^'. The modulation unit 21 contains a temperature-stabilized quartz oscillator 23 (OCXO - oven-controlled crystal oscillator), which is followed by an RF synthesizer (RF generator) 24 in order to control the first modulation frequency, for example to a value of 6.8 GHz in FIG Case of ⁸¹ Rb, at a frequency of the RF generator 24 of 3.4 GHz. The oscillator reference unit 23 is preferably a per se known, highly stable precision oscillator with low phase noise and with a short-term stability of ≤ 4 x 10 ^-13 and a drift of ≤ 10 ^-9 per month. The high-frequency first modulation signal thus obtained is fed to the mixer 22, which is in the form of a ring mixer, where the RF modulation signal is fed to one of a tunable (low) frequency generator 25 in the form of a voltage / frequency converter or a digital mixer. Data Synthesis (DDS) generator second modulated low-frequency modulation signal is modulated. The first, high-frequency modulation frequency of the oscillator 24 is as mentioned by the rule circle 43 to the frequency v ^^ v ₊ ^ + v ^ J ^ v ^ ^w ß ^ G / fc ^ e?), whereas the low-frequency second modulation frequency forms the measure of the frequency v _B and accordingly with the help of an even closer is tuned to explanatory electronic servo or control loop.

The thus modulated high-frequency modulation signal is transmitted via an attenuator 26 and via a so-called bias tee setting circuit 27 with an inductance 28 and a capacitor 29 of the radiation source or laser diode 11, i. as described above, so as to allow the desired coupling of at least two dark resonances, to the laser, as well as a temperature stabilization circuit 31 assigned.

To tune to, for example, two caused by an external magnetic Zeeman-split dark resonances is a servo circuit (electronic controller) 32, which is connected via a switch Sl, with the first lock-in amplifier 18. The output of the controller 32 is connected via an adder 33 to the tunable frequency generator 25, at the output not only - via a further adder 34 - the ring mixer 22, but also a frequency counter 35 is connected so as to measure the magnetic field B by using equation (5). The frequency counter 35 is further connected to the oscillator 23, to which also a modulation frequency generator 36 is connected, the output of which is connected to the lock-in amplifier 19 and, moreover, can be connected to the RF generator 24 via a switch S3, as further will be explained in more detail below. With this modulation frequency generator 36, a not further shown in Fig. 7 processor or computer is also connected, via which the measurement results, optionally after processing, for example, can be output on a display or on a printer.

The frequency counter 35 and the modulation frequency generator 36 are supplied with the frequency (10 MHz) of the oscillator 23 as the reference time base. In this way, a high stability ensured throughout the system. The modulation frequency generator 36 may also be a DDS (Digital Data Synthesizer) controlled by the PC or microprocessor (not shown) and forming the modulation source for the phase-sensitive detection via the lock-in amplifier 19.

For operation in a scan mode is also a ramp generator

37, which can be connected via a switch S2 to the adder 33, wherein in this mode, in which the switch Sl is open, the low-frequency sidebands sampled and the dark resonances can be recorded, as will be explained below. In the locked mode, in which the switch S1 is closed and the switch S2 is opened, the LF sidebands are coupled to the Zeeman dark resonances.

Finally, it can also be seen from FIG. 7 that the second adder 34 has a second input to a voltage source

38 is connected. Furthermore, the output of the mixer 22 is connected to the attenuator 26 via an isolator 39 having a termination resistor 40. The second lock-in amplifier 20 is connected to a frequency multiplier 41 and connected via a switch S4 with another servo circuit or regulator 42, to which the RF generator 24 is connected.

Subsequently, the operation of the measuring device according to FIG. 7 will now be explained in more detail. For reasons of systematics, reference should be made in advance to the signal at the output of the adder 33 that results from the modulation signal E _n , (t) of the modulation generator 36

E _a {t) ^ E _m exp [iω _m t} + cc (10)

on the one hand and from the signal E _Raπ , _{p of} the ramp generator 37 E _Raπ , _p or (depending on the position of the switches Sl and S2) from the control signal E _{st of} the electronic controller 32 composed. The resulting total signal

represents the modulation signal with which the tunable Frequency generator 25 is modulated. The term E (t) can be equated with E _Rarnp or E _st in equation 11, depending on the switch position of Sl and S2. To calculate the modulated output signal E ₃ (t) of the generator 25, the instantaneous phase must be formed by integration from the instantaneous motor frequency. For this output signal E ₃ (t), therefore, the relationship results: f Ke {E _M (r)} dr + φ ₀ )} + cc (12)

The angular frequency ω represents the center frequency of the generator 25 at E _m = 0; φ ₀ is the initial phase position at τ = 0.

In the case of closed loop 18 (switch S1 and switch S2 open) and assuming steady state conditions, the analytic form of the output of the tunable frequency generator 25 is (as integrating with equation 11 as integrand) as follows:

& z (t) e.τp i (ωot + β sm (ω _m t)) + cc

1 ⁺ °° (13)

= 2 ^E ° Σ ^J Λβ) ^ xp [i {ω ₀ + nuj _m ) t] + cc n - oo

In this equation (13), B _{n functions} ( _n ) are given by J _n (β). The size ß is the modulation index and here by the relationship ß Are defined. This quantity β is a measure of the maximum deviation of the instantaneous frequency from the center frequency related to the modulation frequency ω _m .

FIG. 8 schematically shows the spectrum of the frequencies at the output of the tunable frequency generator 25 under steady-state conditions (locked state). The arrow direction in the negative n-direction for the sideband ω _o -ω _ra symbolizes a phase shift of π relative to the carrier frequency ω ₀ . Side bands of the order n ≥ ± 2, ie ω ₀ ± 2ω _ra , are not taken into account in the further analysis because of their low amplitude.

In the following, for the sake of simplicity, it becomes a modulation index ß ≤ 1 assumed. In this range the signal-to-noise ratio is optimal. This approximation simplifies the mathematical derivation of corresponding expressions, since only the frequency components n = 0, ± l are taken into account. It should be noted that conclusions regarding the occurrence of the corresponding signals of the dark resonances at certain frequency values also remain valid for the case β> 1.

In the case of an open switch Sl and closed switch S2 results in a scanning operating mode, which allows the recording of the entire dark resonance spectrum. The ramp-shaped (or triangular) signal of the ramp generator 37, cf. 9A, in conjunction with the modulation signal of the modulation generator 36, cf. Fig. 9B, a temporally continuous increase (while wobbling) the instantaneous frequency of the tunable frequency generator 25. (The wobble with the frequency ω _m causes the modulation generator 36.) The analytical form of the output signal E ₃ (t) of the tunable frequency generator 25 is under these conditions:

E ₃ (t)

In Equation 14, the (real-valued) function E _Ramp with E _Ram p ( ^τ ) ^~ A-Ramp ' ^τ V τe [O.Tj gives a linearly increasing signal in the interval [0, T], which (periodically continued) the desired ramp-shaped waveform results, see. Fig. 9A.

The functional form of the signal E _Ramp (τ) is not limited to a (linear) ramp signal. However, the linearly increasing ramp signal simplifies the mathematical expression for the instantaneous frequency

ω (t) En _mιιρ {τ) dτ ⁽¹⁵⁾ of the tunable frequency generator 25. After the demodulation of the photodiode signal (see detector unit 17 in FIG the lock-in amplifier 19 can be made by the (temporally) linear member in equation 15, a unique relationship between the frequency of the sidebands n • ω _m and the current output signal of the ramp generator 37.

In Fig. 9 shows in detail the part-FIG. 9A shows the ramp signal of the ramp generator 37, FIG. 9B shows the sum signal consisting of the ramp signal and the modulation signal of the modulation generator 36, and FIG. 9C shows the output signal of the tunable frequency generator 25 in frequency modulation with the sum signal. The parameters (amplitudes, modulation index, time axis) are chosen so that a clear representation is given. The typical time scale in Fig. 9 is ms. The typical ratio of VCO (25) fundamental frequency / VCO modulation frequency is in the range of 5 ... 10,000.

Furthermore, in Fig. 10, in the part-FIG. 10A and 10B, the input signal E ₃ (t) and the output signal E ₄ (t) of the high-frequency mixer 22 with (Fig. 10B) and without (Fig. 10A)

DC voltage component E _{D shown} as a function of time. For a clear representation, the ratio of the frequencies ω _R / ω ₀ = 100 (instead of about 4000) was chosen. The characteristic time scale depends on the magnetic field to be measured and is approx. Ms ... μs.

From Fig. 4 and the accompanying description it is apparent that for the coupling of the dark resonances n = 0 and n = ± 2, the frequency components v _H Fs and v _{± 2} ges are required. These frequency components can be simultaneously generated by a mixing process of the output signal of the tunable frequency generator 25 with the signal of the radio-frequency synthesizer 24. This mixing process is a multiplicative operation performed in the high frequency mixer 22. By means of the adding unit 34 and the E _D voltage source 38, a DC component E _{D can be} added to the output signal E ₃ (t) of the tuning-frequency generator 25, s. also Fig. 1OB. This measure makes it possible, depending on the height of E _{D, to control} the amplitude of the carrier frequency ω _R = 2π ^· V _H FS / 2 in the microwave range. At the output of the mixer 22, therefore, the signal E ₄ (t) results as follows: 1 ^{+ o} ° 1

E ^ t) = -ME ₀ E ₂ Y] Jn (β) exp [i (ω _R ± (ω ₀ + nω _m )] t] + -ME _n E ₂ ezp [iω _R t] + cc (16) n = - oo

(Here, the size M takes into account the characteristics of the mixer 22)

If, for example, E _D = O is selected, s. Fig. 10A, the carrier frequency disappears. In this way, only the magnetic field-dependent dark resonances n = ± 2 are coupled by the frequency components v _{± 2} . This case is taken during the locked state (measurement operating state), ie when the switch Sl is closed and the switch S2 is open. The magnetic field independent dark resonance n = 0 is no longer excited due to the missing carrier frequency.

On the other hand, the choice E _D ≠ 0 allows the oscillator 24 to be _tuned exactly to the frequency Q _R = 2π · v _HFs / 2. In this operating state (and only in this), the oscillator 24 is still to be modulated by the modulation generator 36, that is, the switch S3 is closed. This operating state of the magnetometer is only assumed when the frequency of the oscillator 24 is tuned to the frequency ω _HFs .

The isolator (circulator) 39 is a transmission unbalanced 3-port having the property of passing the incident electromagnetic waves respectively to the next port (= port) (1-2-3).

The insulator 39 thus causes the reflected wave resulting from electrical mismatching of the VCSEL laser diode 11, as shown in FIG. 7, to be passed in the insulator 39 in the counterclockwise direction, in the direction of the arrow, to the terminating resistor 40, where it is completely absorbed , In this way, this reflected wave is prevented from reaching the mixer 22 where it interferes with the forward wave field (in the direction of the VCSEL laser diode 11) or with E ₃ (t).

At the node inductance 28 / capacitance 29 and VCSEL laser diode 11 occurs the necessary for the operation of the VCSEL 11 tion of the signal E ₄ (t) and the supply current (coming from the constant current source 30).

The necessary separation of the microwave signals and the supply current of the VCSEL 11 is achieved by the inductance 28 and capacitance 29 contained in the bias tee 27.

The capacitance 29 of the bias tee 27 protects the microwave signal path from the DC voltage at the VCSEL diode 11, which adjusts in operation by the impressed supply current. Saturation of the mixer 22 by this DC level is therefore counteracted. The inductance 28 of the bias tee 27 on the other hand ensures by a low-pass effect that no microwave signals can penetrate to the constant current source. The radiation of these microwave signals to the outside is therefore prevented.

The high-frequency modulation of the impressed supply current of the VCSEL diode causes i.a. As is known, periodic changes in the refractive index in the (not shown) laser medium in the laser resonator. As a direct consequence of these periodic changes there is an amplitude and frequency modulation of the emitted laser radiation:

I r f i

E ₆ (i) = -E _L exp i (ω _L t + L, / E _Λ (r) dτ) + cc

-fώo 4-cc 4-oc

1 2 ψ ^" >> Σ MC ⁾ ∞P PK + ^jω _a ^{) t} ] ^• II (Σ ^) ^ P [* ^« Ϊ]) _H + approx. L = -x

π: with

B _n - k ~, ßΛEaE- ₂ - Jn - (ß) ω "

Oj _n :

The vector of the electric field strength E _L (the laser radiation) indicates the polarization state. The magnitude of the modulation constant A ₇ depends on the operating point of the VCSEL.

The multi-chromatic laser field immediately after the VCSEL source is given by Equation 17 (except for the neglect of a small contribution of amplitude modulation by the non-linear characteristic of the VCSEL 11). In the approximation of small modulation indices (B _n , C <1), it can be better seen that with a suitable choice of the frequency ω _L (optical range) and the modulation frequencies (CO _R , ω ₀ and ω _m ) all the frequencies required for the coupling of the dark resonances are included in the equation 17. This approximation is also useful for a correct description of the real operating state of the magnetometer device, since the choice of B _n , C <1, the intensity of the non-resonant, higher harmonic frequency components (j, l ≥ ± 2) is largely avoided. (This does not apply to the modulation index β, for which higher harmonic components are also of importance (especially n = ± 2).) In this approximation, Equation 17 simplifies to:

In the operation of the magnetometer, a distinction is made between the pre-stabilization of the RF synthesizer 24 and the actual "measuring mode." In the first case (with the switch S3 closed), all coefficients B _n = 0 are obtained by E ₀ = 0 j ^• ω _R (see Equation 17) around the frequency of the optical transition ω _L including the sidebands n ^• ω _m arranged around ω _L + j • ω _R (I j |> 0) The sidebands are used to generate the It should be noted that the additional modulation of the RF synthesizer 24 in this operating state is not included in the equation 17 for the sake of clarity, and a product term (see Equation 17) would be added to the mathematical structure.

This operating state will subsequently not be discussed any further. because this pre-stabilization occurs only when the RF synthesizer 24 has an (actually unacceptable) deviation.

When measuring external magnetic fields, the parameters E _n = 0 and C = 0 are set (switch S3 is open, switch S1 is closed). Equation 18 is therefore simplified again to:

It can be seen particularly clearly from equation 19 that both the frequency components ω _L + ω _R + (ω _o + nω _m ) and ω _L - ω _R Ψ (ω ₀ + nω _m ) (where n = 0) for coupling all the dark resonances and all the frequency components ω _L + ω _R ± (ω _o + nω _ra ) and ω _L - ω _R T (ω ₀ + nω _m ) (where n ≠ 0) for the phase-sensitive detection by the lock-in amplifier 19 are.

The transverse mode structure of the electromagnetic field E _{6 of} a VCSEL corresponds to the Gaussian OO mode due to the geometrical dimensions of the active medium. The transverse intensity profile thus follows a Gaussian function. The laser field can be clearly assigned a polarization state. In the case of a VCSEL laser, the emitted electromagnetic wave is largely linearly polarized. The electromagnetic field E ₆ of Equations 17-19 may be in the form of a Jones vector

be set. For example, a largely linear polarization state of E ₆ (t) with the plane of polarization 45 ° to the x direction is characterized by E _x = E _y and φ = n -TΓ, WeN ₀ (see last expression in Equation 20). The formation of Λ-shaped excitation schemes (see Fig. 4) and their coupling is possible with a linear, circular or generally polarized E ₆ -FeId. The desired polarization state of E ₅ during operation of the magnetometer is set by the position of the main axes of the λ / 4 plate (QW in FIG. 7) relative to the components of E ₆ .

The transmission property of the λ / 4 plate QW is given by a 2x2 Jones matrix T with (Φ _τ = ± π / 2):

^B FrM ⁽ O.T ^T -P -P ^B ₁ I ⁽ I ^I l ⁾ - (I ₀ ¹ ^ ° \ ) (I ^ ^& 'Wy - I ( ₀ ' _ü °) M ( _B ^{£ fa} W ^ I ^

Circularly polarized light E ₇ is generated (using Equation 19) when linearly polarized light (E ₆ ) with the polarization plane at 45 ° to the principal axes radiates onto the λ / 4 plate.

In contrast, linearly polarized light E ₇ occurs when the polarization plane of E ₆ coincides with one of the major axes of the λ / 4 plate. For example, for E _x = E _L and E _y = 0 (Φ = arbitrary), polarized light is again obtained in the x-direction:

At an arbitrarily chosen angle of the polarization plane of the linearly polarized wave field E ₆ (t) with the principal axes of QW, on the other hand, an elliptically polarized, electromagnetic field E ₇ (t) results. Mathematically, this fact becomes apparent when in Equation 21 E _5x ≠ E _6y and ψ - π-τr. neN _{0 are} set.

By selecting the angle of the main axis of the λ / 4 plate QW relative to the polarization plane of the linearly polarized electromagnetic wave E ₆ (t), the corresponding desired polarization be set state of E ₇ (t) (linear, circular, elliptical). Which polarization state is the most suitable depends on the angle of any preferred direction of the (magnetic) magnetic field to be measured and on the propagation direction of E ₇ (t).

The maximum sensitivity is achieved, for example, at a magnetic field B in (normal to) the propagation direction of E ₇ (t) when a circular (linear) polarization of E ₇ (t) is selected.

In the measuring cell 14, the interaction of the electromagnetic field E ₇ (t) with the atomic ensemble occurs. In order to describe the quantum mechanical processes of a (statistically distributed) atomic ensemble (eg alkali-atomic vapor), the semi-classical approach (no quantized electromagnetic field) is chosen via the so-called density matrix formalism. In order to account for the spontaneous decay mechanisms (eg relaxation from the excited state into the ground state, relaxation by collisions, etc.), phenomenological additional terms R (t) (called the relaxation operator) are added in the density matrix equations:

In this equation 24, the Hamiltonian Η = H _Q + V (i) is composed of the Hamiltonian Ji _{0 of} the undisturbed atom and of a time-dependent (disturbance) term V (t) describing the interaction with the electromagnetic fields. This interaction term in the dipole approximation rBohr) '

V (t) = -a-E (t) ₍₂₅₎

The size ά refers to the considered dipole moment of the atomic transition. The coupling of the ensemble's atomic system with the electromagnetic field is done according to Equation 25 when E (t) = E ₇ (t) is set.

For N-levels, equation 24 in component form reads: d 1 ^N

- _PlJ {t) = -iω _υPυ (t) + ^ Σ [VAt) PxAt) - PAWkAt)] + Rυit)

The dipole operator V (t), through which the coupling with the multichromatic laser field (equation 17 or equation 21) is produced, is in this component illustration:

The differential equation system (equation 26 with the dichroic-chromatic laser field E ₇ (t) according to equation 27) represents a very complicated system in the general case, which usually has more than 250 unknown quantities within the alkali D lines. The solution of this mathematical problem can only be done numerically in this generality.

One way to obtain yet approximate analytical expressions for the quantities p _{υ is} to assume that the linewidth of the dark resonances is small compared to the splitting of the Zeeman sub-levels. Under these circumstances, the degeneration of the various levels is abolished. The atomic levels (equation syst. 26) are decoupled with respect to the excitation by the field E ₇ (t) such that an excitation scheme results in the manner of FIG. 4, wherein additionally a single-photon transition between 5 ² Si _{/ 2} F = 2, m _F = -2 → 5 ² Pi _/ 2F '= 2, i% = -1 occurs. In this way, it becomes possible to reduce the complicated system of Equation 26 to three Λ systems which are "only" coupled via the incoherent process of spontaneous decay (via i ((0).

The solutions of the density matrix equations in the conventional RWA (Rotating Wave Approximation) approximation are known for Λ-systems plus a loss level describing the remaining incoherent coupling.

The quantity p _nn (t) indicates the (percentage) portion of the atoms of the statistical ensemble in the state n.

The Great _nm p (t) = σ _nm (t) exp [iω _nm] coherences can be mentioned. Of the The real part and the imaginary part of the coherences (p _nm (t) and σ _nm (t)) of the optical transitions are functionally related to the refractive index and the attenuation index of the medium (atomic ensemble).

As an example, the solution for the coherences σ _{13 of} the stationary density matrix is given. The solutions are given as a series of Lorentz functions £ f ' ^s and Cf ^ss .

Im (σi ₃ ) = )

The function Cf ' ^B (Cf **) is symmetric (skew-symmetric) with respect to the Raman detonation δ _R.

The parameters _i J ^ _k and _i β _k ⁱ depend on the field strength E ₁ and on the dipole matrix elements d _nm . The two-photon detonation δ _L in Equation 28 results in a deviation from a pure Lorentz function £ " ^ÄS (Cf" *). However, this influence is of a higher order {iΛ [δc / iΛl <1, <1 and for corresponding k, 1 5R -C 1), if 5 _L <δ _{d <ipp} ι _he «500MHz is maintained. The laser stabilization on the corresponding atomic transition results in a two-photon detonation of a maximum of | δ _L i≤10 MHz. The Raman detonation δ _R in Equation 28 is the actual magnetic field-dependent variable and can be identified with δ _R _ ₂ , δ _Ro and δ _{R + 2} , depending on the particular A system considered (n = -2.0, +2). A plot of Re (σ _i3 ) and Im (σ _i3 ) under the condition (δ _L <δ _dopp i _sr ) is given in FIG.

In order to produce these functional relationships between the coherences σ _nm and the real or imaginary part of the susceptibility X = X '+ "-λ" of the medium (= atomic vapor), results of the electrons trodynamics used:

P ( _Z , t) = JV " _« T _r (dp) ₍₂₉₎

P (M) = (χ '+ iχ ") E (z, t)

N _act refers to the molar density of the atoms in the gaseous state.

For concrete calculations, the polarization P (z, t) is decomposed into its components. To account for the Doppler effect correctly, the density matrix elements must also has all the speed classes ((with the weighting of the prevailing velocity distribution mostly Maxwell distri ^¬ lung)) are averaged.

σ.

Equations 29 and 30 make it possible to establish a connection between the microscopic (quantum mechanical) quantities and the observable macroscopic quantities (susceptibilities) (when considering a Λ-system):

The atomic vapor measuring cell 14 of the magnetometer operates, for example, in a temperature range up to about 50 ° C (rubidium). Under these operating conditions, the atomic vapor can still be considered as optically thin. In this range, only single scattering of photons at the atoms takes place, whereby the validity of the Beer-Lambert law of attenuation is given:

B (t, L) = - Σ Ej {t 0) exp [ύvjt] exp [% L (l + (^ { _Uj ) + tχ "( _Wj )) / 2)] + cc (32)

I ~ ι

In addition to exponential attenuation, due to the influence of X, a phase shift increasing linearly with the optical path occurs. This is an immediate consequence of of one different refractive index.

For easier handling of the equations and for better clarity, the functional correlations relevant for the propagation are summarized in a propagation operator Ε:

Ej (tL) = ^ E ₇ (i, 0) exp [i {kjL + ω ₃ t)] exp [* (χΗ) + .χV;)) / 2] + cc

= -F ₃ E ₁ exp [i (fc, L + u;, t)]] + cc

This operator has vector character with the components x and y and the spectral components F ₃ , which correspond to the respective ω-.

The propagation operator F ₃ thus describes the interaction of the electromagnetic fields with the atom ensemble. The index of the propagation operator refers to the spectral component ω-, to which the operator is applied. The size L indicates the (geometric) length of the optical path and here can be simultaneously with the length (in the cm range) of the spectroscopic measuring cell 14.

By applying the propagation operator F ₁ to the multichromatic wave field E ₇ (t) occurring at the input of the spectroscopic measuring cell 14, the multichromatic wave field E ₈ (t) immediately after the cell 14 is obtained as follows:

+ OO (C) exp [1 {ω _L + jω _R ) f]

2 yj F _j J ₃ f = - OO

; 34:

+ OO π F ₁ J ₁ (B _n ) cxp [i I ω "t]) + cc

/ nn = - oo (Σ This wave field. E ₈ (t) contains the full information resulting from the interaction with the atomic vapor.

In addition to the various functional dependencies of the above-mentioned parameters (cf., for example, Equations 17 and 34), the functional dependence on the frequency ω _{0 of} the tunable frequency generator 25 proves to be the most important. This frequency ω ₀ is variable in the sense that it is varied until the dark resonances n = -2.0, +2 coincide in a single (observable) dark resonance. This frequency effectively bypasses the splitting of the magnetic sublevels resulting from the Zeeman effect (see Equation 3). If the frequency ω ₀ coincides with the Zeeman splitting frequency, a level degeneracy is again formally established. The Λ-shaped excitation schemes are coupled under these circumstances. Therefore, the signal E ₈ (t, L) (the waveform in the time domain) depends substantially on the value of ω ₀ relative to the atomic sublevels from. Enables E _s (t, L) this information, so the control technical problem, namely to tune the tunable oscillator 25 exactly to this sub-level split can be solved. To achieve this, the general multichromatic wave field is converted by the photodetector 15 into an electrical signal. A photodetector is a so-called square element in which the electrical signal, the photocurrent ip _h (t), is proportional to the incident intensity (power) of the electromagnetic radiation:

Therein the size H _p h {\) is called photodiode responsiveness; Z _vac is the characteristic impedance of the vacuum.

The integration according to equation 35 is carried out over the entire intensity profile. The value of the constant G _L depends on the specific form of the intensity profile as a function of the (to the laser propagation direction transverse) spatial coordinates. In all considerations made here, therefore, the greatest value of the transversal profile can be set for the electric field strengths E _x (the location dependence is then contained in G _L ). The process of squaring represents the mathematical see analysis is a complication, since in addition to the infinite variety of frequency components mixed terms of the sums and difference frequencies occur.

However, a further simplification is achieved by taking into account the fact that the photodetector 15 used can not register time-resolved frequencies in the optical range (~10 "Hz). + const ₍₃₆ )

The second equal sign in Equation 36 is valid because the summands | - £ f | and | i5 | ² | periodic functions of the time with a frequency of 2ω _L ~ 10 ¹⁴ rad / s and the photodetector 15 registered only their mean value due to its low-pass effect. Due to the phase-sensitive detection of the photodiode signal further needs the (time) constant value const. not considered further. The evaluation of the mixed term 2E _& B _$ of Equation 36 provides a signal proportional to the photodetector current which is important for further evaluation. In the calculation of the mixed term, the multichromatic electromagnetic field in the form of equation 19 in conjunction with the propagation operator F is used.

E * (i, £) = 2J ₀ ² (C) jE ^ F ^* 1 + i Σ IS.M - 2 Σ I ^ W ∞β2SJ _n

+ ac + 3O

1 / N

2 Σ Σ BkB ₁ [R [P _{1 ^} F;) COs (UJk - LJ ₁ ) Y - ^Q [F _{1 ^} F ₁ ^* ] sm {iü _k - ωι) t J ₍₃₇₎ fc = - oo l ~ - c

_ I VZ ^ ZV ^ BkB ₁ (Jt [F _t F ₁ '] cos (ω _k + ω _t) t +% [F _k F] aN {ω _k + ω _t) t j k = - oc / - - oc

(In this case, J? [..] or Q '[..] is called the real part of [..] or the imaginary part of [..].)

The functional relationship (Equation 37) describes the total dark resonance spectrum (the coupled dark resonances) under the excitation of the multichromatic laser field in the approximation of small modulation indices (B _n , C <1) and assuming that the detector 17 contains the frequency components of the electric field, which are in the optical range, can not detect time-resolved. Equation 37 is the epitome of the principle of coupling the dark resonances in the measurement of magnetic fields with the aid of the CPT (Coherent Population Trapping) effect. From this composite signal, the most appropriate for magnetometer operation shares must be extracted.

Due to the power level of P = 1 ... 100μW, the unit 17 (photodetector 15 and amplifier 16) can register only frequency components of the signal i _Ph (t) up to a maximum of a few MHz in a time-resolved manner. The frequency components in the GHz range are therefore no longer present at the input of the lock-in amplifier 19.

At the output of the detector unit 17 is a proportional to the photocurrent of the photodetector 15 voltage

Mt) = Ü (ω) R _τ i _ph (i) = ψ ^ Ü (ω) R _τ G _L Εl {i, L)

given (the proportionality is produced by the transimpedance R _τ and the (total) transfer function U (ω) of the unit 17); in turn, this voltage is proportional to the signal E ₈ (t, L) (except for the high-frequency components (see above)). The task of the lock-in amplifier 19 now consists in the selection of suitable for the magnetometer frequency components of u _s (t). The pre-factors of the frequency components include the required information of the strength of the external magnetic field in the form of the refractive index (δ ₃ ) and the attenuation index (Φj) of the dark resonances. Based on Equation 37, the frequency components for magnetometer operation + α + ift + 2 <r ^{2Ä + 2 + 2 •} y ~ <L ₂ -3 + 5_ ₂ -i + <5 _{+ 2} -i-i - δ ₊ 2 + .3 j cosω _m i

+ fl ₊ lo + 2 <r ^{'2ή + 2 + 2 •} (- + 2Φ-2-2 ^~ 2-1-Φ + Φ + 2 + S ^~ 2φ _{+ 2 + i} + (D _{+24. 3} J ShlüJ _m t

+ α _hl o _{+: J e} - ^{'u + a + 2 ■} (- 2 - (L ₂ -I - 2 ⁽ 5_ ₂ _ ₂ + <5_ ₂ - ₃ + ^ -2 + 1 - 2 ^ _{2 + 2} + (J ₊ a + s) cos 2ω _{t) 1} f

+ «+ I« _{+ Λ e} - ^{M + 2 + 2 •} (- ώ_2-3 - Φ-2-1 + 0 + 2 + 1 ^~ Φ + 2 + 3) mi 2ω _m t]

^V / (39) proved to be suitable, with Ü (ω) = 1 + Oj was selected for clarity. Corresponding spectral representations are shown in FIGS. 11 to 14. In Equation 39, other indices are used to allow a more compact notation of the equation. The indices ± 1, ± 2 and ± 3 of equation 39 refer to the frequency components: ω_ ₃ : = ω _R - ω ₀ - ω _m ω_ 2: = CUR - UJQ ω_i: = ω _κ -w ₀ + ω _m

^ o: = ω _R

(40) ω ₊₁ : = ω _R + ω _Q - ω _m ω + 2: = ω _R + ω o

W ₊₃ : = ω _R + ω ₀ + ω _m

The indices n and j of δ _nj and φ ^ here refer to the nth dark resonance (n = -2, 0, +2), which is represented by the j-th frequency component (j = -3 ... +3). is produced.

The selection of the expressions ~ ω _m and ~ 2ω _m in Equation 39 is achieved by taking advantage of the orthogonality of trigonometric functions. The technical realization of this selection is accordingly carried out by the multiplication of u _a (t) with one (or more) sine / cosine oscillations having the frequency cω _ra (c = 1,2) and the phase C ^ _LOCMΠ . Subsequent filtering of all time-dependent components ~ 2ω _m of U ₉ (t) yields an electrical signal U ₉ (t) which is proportional to the precursors of sin (cωt) and cos (cωt) (c = 1,2) (s also Fig. 11 to 14). (The transfer function of the electronic filter (digital or analog) is designated Ü _L ).

u ₉ {t) = Ü _L u _s (tyu _LockM sm {c _{-ω m} t + φ _Lockι ") ₍₄₁₎

Whether this multiplication by digital circuits (digital lock-in amplifier 19) or, as sketched in Fig. 7, realized in an analogous way, is of minor importance. Both methods are state of the art in their own right and essentially lead to the same end result. FIGS. 11 to 15 show the individual components of the signal U ₉ (t). These signals agree with the pre-factors of the terms sin (cω _m t) and cos (cω _m t) of Equation 39 except for an additional factor stemming from the characteristic of the multiplication process. In these examples, the parameters of the line width are .DELTA.V = 50 Hz (s. Equation 28) and the frequency of the modulation frequency generator 36 so selected (v _m = ω _m / 2π = 2kHz) to correspond to the typical values of a real magnetometer.

The independent variable is in all cases the frequency ω _{0 of} the tunable generator 25. This frequency is finally used by measurement by means of the frequency counter 35 - and corresponding conversion - for the determination of the magnetic field B. The control circuit 18 of the magnetometer structure of Fig. 7 is such (see below) that ω _o / 2π = v _B = C • B is ensured (see Equation 5). In FIGS. 11 to 15, this point coincides with the origin of the respective coordination system. The frequency zero point of the images was therefore expediently placed in the point v _B = C • B, which coincides with the position of the dark resonance in a specific magnetic field measurement.

The amplitudes of the individual components are normalized to 1. It follows that the magnitude of the maxima of the total signals is ≥ 1. The frequency values on the abscissa of Figs. 11 to 15 are indicated in kHz.

Specifically, Fig. 11 shows the frequency modulation spectrum of the total absorption signal (pre-factor to cosω _m t; s equation 39) of the coupled dark resonances, where the detuning of the microwave generator 24 is δv = 0 Hz. In Fig. IIA, an enlarged region thereof is shown, wherein this detuning δv = 0, 10, 25 and 50 Hz and accordingly four graphs are shown.

FIG. 12 shows the frequency modulation spectrum of the total dispersion signal (pre-factor to sinω _ra t; s, equation 39) of the coupled dark resonances, wherein the detuning of the micro-resonance Wave generator 24 δv = 0 Hz. The illustration in FIG. 12A once again shows an enlarged range, again showing four curves for which detunings δv = 0, 10, 25 or 50 Hz.

In Fig. 13, the frequency modulation spectrum of the entire pre-factor signal to cos2ω _m t (see Equation 39) of the coupled dark resonances is illustrated, the detuning of the microwave generator 24 being δv = 0 Hz. In Fig. 13A, an enlarged area is again shown, with four curves for which detunings δv = 0, 10, 25 and 50 Hz, respectively.

From Fig. 14, the frequency modulation spectrum of the entire signal of the pre-factor to sin2ω _m t (see equation 39) of the coupled dark resonances can be seen, wherein the detuning of the microwave generator 24 δv = 0 Hz.

The spectra according to FIGS. 11 to 14 result on the condition that the width of the dark resonance is smaller than the modulation frequency, ie Δi / <! / ". This circumstance is clearly illustrated by the fact that the individual peaks, the distance of which is always 2ω _m , appear clearly separated from one another in the in-phase spectrum of FIG. In the illustration according to FIG. IIA, the right-hand part of the in-phase spectrum is shown enlarged. The various individual graphs of this representation correspond to different deviations ΔV = V _HFS ~ 2V _{R of} the current frequency of the radio-frequency synthesizer 24 from the desired target frequency v _{HFS of} the atomic transition between the ground states of the atoms located in the measuring cell 14. The extended system analysis shows that the introductory qualitative considerations concerning the splitting of the dark resonances with the dependence on Δv are also correct analogously for the important case Au <C v, ". However, the line center of gravity of the in-phase signal (the in-phase spectrum is proportional to the absorption signal (~ χ ") of the CPT dark resonance) of the dark resonance by the frequency amount + v _m m with respect to the center frequency ω ₀ (or v ₀ ) of the frequency generator 25 is shifted.

The in-phase signal of the coupled dark resonances under the Condition Au <C v _m is less suitable as a control signal for the frequency generator 25, since it (in addition to the unwanted frequency offset) has no point symmetry with respect to its line centroid, cf. also Fig. 11.

The frequency modulation spectrum of the dispersion signal, s. Fig. 12 is in the case Δz> - <C v- _m . however, as a control signal for the tunable frequency generator 25 well suited. The system analysis shows that the middle part of the spectrum is point-symmetrical with respect to the line center of gravity and thus can be used as an input signal for the controller 32. Furthermore, the line center of gravity (= zero) coincides with the frequency of the frequency generator 25.

With the switch S1 closed, the frequency of the frequency generator 25 is always stabilized by the action of the controller 32 to the frequency of the line center of gravity (= zero point). The lock point corresponds to the point V ₀ = 0 in FIG. 12. Since in this figure the frequency value v _B = CB corresponds to the origin, the frequency of the generator 25 V ₀ = V _B = CB (see also equation 5 and associated explanation) are used directly for measuring the external magnetic field B.

The servo block or controller 32 consists in the simplest case of an analog (or digital) sequential control system consisting for example of amplifier (P), integrating (I), and differentiating units (D) (PID controller). The implementation takes place in the case of an analog controller 32 constructed by discrete electronic components and in the case of a digital controller by the software-moderate implementation of the corresponding arithmetic operations (PID, etc.) in a digital processing unit.

Both realization options (analog and digital) of the controller 32 have in common that finding the lock point on the simultaneous fulfillment of the conditions

Amplitude = setpoint = 0

Sign of the rule slope = positive

he follows. (Whether the sign is positive or negative depends on - Al - the rule edge off. In Fig. 12, there is a positive sign. )

With regard to the simultaneous fulfillment of both mentioned criteria, the signal of FIG. 12 is unique. That is, with the switch S1 closed, the frequency γ _{0 of} the generator 25 is automatically and uniquely tuned to the point v _o = v _B = CB (origin of FIG. 12). The frequency V _{0 =} v _B thus automatically corresponds to the frequency splitting of the Zeeman sub-levels (= the splitting of the dark resonances). By measuring the frequency ω ₀ or V ₀ can therefore be closed directly to the outer (to be measured) magnetic field.

Both in the introductory qualitative analysis and in the system analysis expanded above (see also FIG. 12), it can be seen that the detuning of the microwave generator 24 does not influence the position of the line center of gravity of the signals according to FIGS. The accuracy of the magnetic field measurement, which takes place via the position of the line center of gravity, is therefore not influenced by a microwave generator drift.

The maximum permissible range of the microwave generator drift when using the signal from FIG. 11 as a control signal is not given by δv ≤ 0.289ΔV _C PT (with Δv _CPT = Δv), since in the case of Δι / <cv _m in the graphs of FIG 11 and 12 are two independent signals (~ χ 'and ~ χ "), which are defined separately from each other by Equations 28 and 31. Therefore, in the range Δi / <i /", the (weaker) condition δv ≤ 0 holds , 5ΔV _CPT .

In the case Δv S> u _nι , however, the assumption made in the introduction that the control signal corresponds to the first derivative of the absorption signal applies. These introductory considerations can therefore be taken over directly. Illustratively, this behavior can be imagined by assuming that the modulation frequency is becoming ever smaller. The two peaks in FIG. 11 of the absorption signal continue to converge in the sequence until finally, in the limiting case, the first derivative of the absorption signal results. The different signs produce a point-symmetric signal. Both generated sidebands (with variation of V ₀ ) finally coincide tig below the line profile of the dark resonance (compare also the pre-factor to term cosω _m t of equation 39).

FIG. 13 (or FIG. 15B) shows the signal component belonging to the pre-factor of the temas cos (2ω _m t), cf. also equation 39.

More specifically, Fig. 15A shows the frequency modulation spectrum in the case of v _m ~ Δv of the control signal component of the coupled dark resonances associated with the term ~ sin 2ω _m t, whereas Fig. 15B illustrates the corresponding spectrum of the correction control signal component associated with the term ~ cos 2ω _m t. also equation 39. In both illustrations, FIGS. 15A and 15B, the detuning of the microwave generator 24 is δv = 0, 10, 25 and 50 Hz, respectively, so that four curves are shown.

It can be seen from these figures according to FIG. 13 or 15B that in the adjusted state (switch S1 closed), the value of this signal at ω _{0 is} in direct functional relationship with the detuning δv = v _HFs -2v _{R of} the RF generator 24. This signal can therefore be used directly in the magnetometer to stabilize the frequency of the generator 24 to the value δv = 0. In this way, a drift of the generator 24 occurring during magnetometer operation can always be compensated. The steepness of the control edge achieved by this measure constantly their maximum value. The operating state of the control circuit 18 is constantly optimized, since always the greatest sensitivity (greatest signal / noise ratio) is achieved.

In a technical realization of the magnetoremitter, this signal can be generated by the synchronous demodulation of the signal of Equation 39 in the lock-in amplifier 20 in conjunction with the frequency multiplier 41 (see Fig. 7). Finally, at the output of the regulator 42, the signal component of FIG. 13 results for the case .DELTA.ι / <C v _nι or the signal component of FIG. 15B for the case .DELTA.f.sub.i / _m .

To complete this correction loop 43 of the generator 24 is the second lock-in amplifier 20 of the other Connected downstream of the servo circuit or regulator 42, which activates the generator 24 for the purpose of frequency correction and in accordance with amplitude (v _k ) = max (see FIG. 13) (o _R = 2πv _R ).

Dxe fact that the magnetic field measurement by means of V ₀ and the detuning of the generator 24 are decoupled, allows operation of this correction loop 43 with a large time constant. A simultaneous operation of both control circuits 18, 43 is therefore possible.

With these two control circuits 18, 43 the possibility is created that the magnetometer can work without further recalibration. At the same time, always the correct lock point of the signal of FIG. 12 for the magnetic field measurement is assumed. Due to the permanent correction of the frequency ω _R or v _R , the magnetometer always works with the maximum achievable signal / noise ratio.

The validity of the considerations regarding the advantages of the coupling of dark resonances by a multichromatic laser field is given for any modulation frequencies v _m (or for any ratios Δv / v _m ). In order to clarify this, the frequency modulation spectrums important for magnetometer operation are given for the regime v _m = Δv. In the following examples, the parameters are the same as those of FIGS. 11 to 14 selected.

For example, it can be seen from the graph of the dispersion signal of FIG. 15A that even in this regime a suitable control signal results, which ensures a clear locking of the generator 25. The tolerance range for a detuning of the RF synthesizer 24 from δvtal (2Δ.v corresponds approximately to the tolerance range valid for Ai / <g; v _m .) Similarly, a unique signal for the correction control loop can be taken from the frequency modulation spectrum of the second harmonic component (See also Fig. 13).

The principles outlined above are generally valid and thus independent of the use of digital or analog components. It should be noted, however, that Set of digital components, the corresponding connection lines of the block diagram of FIG. 7 are to be interpreted as data lines. Many of the units shown in FIG. 7 are in this case implemented by software in the program of a digital computer. The generator 25 can then be formed by a so-called digital data synthesis generator (DDS generator), which is controlled by digital data words. The frequency ω ₀ is then coded by a data word.

In a digital realization of the generator 25 by a DDS generator together with servo frequency counter 35 can also be omitted, since the frequency can be taken directly from the corresponding data word at the input of the "generator" 25. The data stream can now directly via a (digital) It should, however, be mentioned that this DDS generator 25 should derive its clock from the OCXO time base 23 in order to avoid stability and accuracy losses.

Claims

Claims:

1. A method for measuring magnetic fields (B) based on the Zeeman effect using dark resonances, wherein quantum systems, such as atoms or molecules, a measuring medium in a measuring cell (14) irradiated with electromagnetic radiation having different frequencies and excited with frequency coordination which causes frequency splitting with a frequency shift (V _B ) due to the Zeeman effect, causing reduced fluorescence radiation having a reduced absorption at a resonant frequency, the dark resonance, which is magnetic field dependent, and which the frequency tuning is determined in order to determine therefrom the magnetic field, characterized in that a plurality of dark resonances are coupled by using a polychromatic electromagnetic radiation (12) and thereby a dependent only on the magnetic field caused by the frequency shift frequency detection to Magnetf eld measurement is made.

2. The method according to claim 1, characterized in that the polychromatic electromagnetic radiation is generated by a multi-stage modulation of an electromagnetic fundamental radiation, in particular a laser radiation.

3. The method according to claim 2, characterized in that a first high-frequency modulation frequency (v _modl ), which is substantially equal to the frequency (v _HFS ) of the splitting of the ground state of the atoms of the measuring medium is generated, with the basic electromagnetic radiation to generate a sideband structure is modulated, and which in turn is modulated with a relatively low-frequency second modulation signal (v _mod2 ).

4. The method according to claim 3, characterized in that the first modulation frequency (v _modl ) is fixed and the second modulation frequency (v _mod2 ) is tuned to the resonance state.

5. The method according to claim 3 or 4, characterized that the low frequency second modulation signal in turn is also modulated to facilitate its tuning to the resonant condition.

6. Apparatus for measuring magnetic fields based on the Zeeman effect, using dark resonance, with a measuring cell

(14) exposed to the magnetic field (B) to be measured and containing the atoms of a measuring medium in a buffer gas whose excitation by irradiation is provided with a radiation source (11) connected to a modulation frequency generator and an electromagnetic radiation having different Frequencies outputs, and with a measuring cell (14) downstream frequency detector (17) with a control loop (18) for frequency tuning to a dark resonance frequency, characterized in that the modulation frequency generator (24) at least one modulator (22) for modulating a comparatively high first modulation frequency with a lower second modulation frequency is followed by generating a double sideband structure to provide with the thus modulated electromagnetic radiation (12) a coupling of several dark states, wherein substantially only one frequency corresponding to the magnetic field-dependent Frequenzverschie is detected.

7. Apparatus according to claim 6, characterized in that the modulation frequency generator (24) to a fixed frequency substantially equal to the frequency the splitting of the ground state of the atoms of the medium is set.

8. Apparatus according to claim 6 or 7, characterized in that in a further control loop (43) a lock-in amplifier (20) is provided which receives a mixing frequency from a frequency converter (41) supplied, and its output signal to the modulation frequency generator ( 24) is supplied via a servo circuit (42).

9. Apparatus according to claim 7 or 8, characterized in that the modulation frequency generator (24) is associated with a high frequency oscillator (23) as a time base.

10. The device according to claim 9, characterized in that the high-frequency oscillator (23) is a quartz oscillator.

11. Device according to one of claims 6 to 10, characterized in that the modulator (22) which modulates the first modulation frequency with the lower, second modulation frequency is a Ringrαischer.

12. Device according to one of claims 6 to 11, characterized in that for generating the lower, second modulation frequency, a tunable frequency generator or voltage / frequency converter (25) is provided, the one of the measurement signal 'of the frequency detector (17) dependent voltage supplied receives.

13. The apparatus according to claim 12, characterized in that the frequency detector (17) has a lock-in amplifier (18), from whose output the frequency generator or voltage / frequency converter (25), the input voltage via a servo circuit (32). is supplied.

14. The device according to claim 13, characterized in that the input of the frequency generator or voltage / frequency converter (25) is selectively connectable to the output of a ramp generator (37).

15. Device according to one of claims 6 to 14, characterized in that the radiation source (11) is formed by a VCSEL laser.

16. The apparatus according to claim 15, characterized in that the VCSEL laser is associated with a temperature stabilizing circuit (31).

17. Device according to one of claims 6 to 16, characterized in that the radiation source (11), the modulation signal via an attenuator (26) is supplied.

18. Device according to one of claims 6 to 17, characterized indicates that the modulation frequency generator (24) generates a frequency in the range of up to several GHz, in particular 3.4 GHz, and the lower modulation frequency is up to a few MHz.