RU2312457C1 - Method for forming support resonance on ultra-thin transitions of main state of alkali metal atom - Google Patents

Abstract

FIELD: electric engineering, possible use, for example, in metrology for determining frequency and time, in particular during creation of atomic standards of frequency or in atomic clock.

SUBSTANCE: principally new method is claimed for generation of high contrast resonance on ultra-thin transitions of main state of atom of alkali metal in bichromatic field, where frequency components are identically linearly polarized. Full angular momentums of ultra-thin components in main state have values F=1 and 2, and excitation is performed through ultra-thin component with full angular momentum F'=1. Condition of spectral resolution of ultra-thin structure of excited state is required. Among alkali metals, aforementioned states in common conditions are only fulfilled for D₁ - line of ⁸⁷Rb. As opposed to standard 0-0 resonance, here passing resonance or coherent population capture resonance is formed at frequencies of atom transitions of ⁸⁷Rb: F=2, m=1↔F=1, m=-1 and F=2, m=-1↔F=1,m=1, where F - quantum number of full angular momentum of atom, m - quantum number of projection of full angular atom onto direction of magnetic field.

EFFECT: increased support resonance contrast with simultaneous simplification of method and reduction of dimensions of device for realization of aforementioned method.

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Description

The invention relates to metrology of frequency and time and may find application in atomic frequency standards and clocks.

There is a traditional method of forming a reference resonance for stabilizing the microwave electromagnetic oscillation generator in the frequency standard for rubidium atoms (and other alkali metals) using resonant optical pumping, which changes the populations of the hyperfine sublevels of the ground state - empties one of them and populates the other [1] . Exposure to a microwave field with a frequency corresponding to the energy difference of the hyperfine sublevels returns some of the atoms to the emptied level and increases the absorption of the optical field. The dependence of the transmission of the optical field by a cell with an ensemble of atoms on the frequency of the microwave field forms the reference resonance.

The source of the optical field is either the light of a resonant lamp [2] or a diode laser [3]. To increase the efficiency of the interaction of the microwave field with rubidium atoms, the cell is placed in the microwave cavity.

4,4 см), что делает его трудноприменимым, например, в мобильных системах.The disadvantage of this method is the large dimensions of the device implementing it, determined by the fact that the characteristic size of the microwave cavity is close to the wavelength of the microwave field in order of magnitude (

4.4 cm), which makes it difficult to apply, for example, in mobile systems.

Another method is known [4], in which the direct sounding of atoms by a microwave field is replaced by their interaction with a two-frequency (bichromagic) field of a diode laser. Two codirectional laser fields with frequencies ω ₁ and ω ₂ acting in the Λ configuration on the allowed electric dipole transitions F = 1↔F '= 1, 2 and F = 2↔F' = 1, 2 (Fig. 1) create a long-lived non-absorbing superposition of states of hyperfine sublevels of ⁸⁷ Rb atoms. Here F and F 'are the quantum numbers of the total angular momentum of the atom of the ground and excited states, respectively. When the frequency difference of the two components of the bichromatic field Δω = ω ₁ -ω ₂ changes near the atomic transition frequency Ω ₀ , a transmission resonance is observed (resonance of coherent population trapping (CPT) or Λ resonance). The width of the resonance in the limit of low intensities of the optical fields is determined by the lifetime of coherence in the ground state. In this method, information about the frequency of the stabilized generator of electromagnetic waves is enclosed in the frequency interval between the two components of the bichromatic field. In this case, both components of the bichromatic field have the same circular polarizations, and to stabilize the frequency, the resonance generated at the frequency of the 0-0 transition is used: F = 1, m = 0↔F = 2, m = 0, where m is the quantum number of the projection of the total angular atomic moment in the direction of the magnetic field. In all known versions of the frequency standards for alkali metal atoms, a 0-0 transition is used.

The main disadvantage of this method is the low contrast of the reference resonance due to parasitic non-absorbing states.

The main advantage of this method is the exclusion of the microwave resonator from the circuit of the device, which can significantly reduce the size of the atomic clock.

The closest method of resonance formation to the proposed one is the method described in [5]. The method is based on the use of atomic cells of small size (less than the wavelength of the microwave transition) and the configuration of the field formed by oncoming traveling bichromatic waves with orthogonal circular polarizations (σ ⁺ -σ ^- configuration). In [5], a method is described for forming a reference resonance in cesium atoms, however, the method is also suitable for other alkali metals.

Ω₀. Во втором варианте рабочими компонентами лазерного поля являются несущая ω₁ и одна из боковых полос ω₂=ω₁+ Ω.This method also uses the CPT effect and the resonant bichromatic field of a diode laser, the transmission of which, as a function of the frequency difference of the two components, of the field forms a reference resonance. Components bichromatic fields are directly modulated pump current (and frequency) of the laser diode at a frequency Ω, close to half of the reference microwave transition Ω _0/2 = 4.6 GHz, either directly at the frequency Ω _0. In the first embodiment, the side bands in the emission spectrum of a modulated laser have frequencies ω ₁ = ω _L - Ω / 2 and ω ₁ = ω _L + Ω / 2, where ω _L is the carrier frequency, so that ω ₂ -ω ₁ = Ω

Ω ₀ . In the second embodiment, the working components of the laser field are the carrier ω ₁ and one of the side bands ω ₂ = ω ₁ + Ω.

Each of the hyperfine sublevels with a quantum number F in a magnetic field is split into 2F + 1 Zeeman sublevels, as shown in FIG. The dependence of the transition frequency F = 1, m = 0↔F = 2, m = 0 (0-0 transition) is quadratic in the field and insignificant at small zeros, therefore this transition is used to form a reference resonance in frequency standards. To isolate it, the cell is placed in a constant magnetic field.

It is essential that the simplest way to create a bichromatic field — modulation of the pump current of a diode laser — leads to the fact that the polarizations of the working components of the spectrum are the same and, as a rule, linear. According to the selection rules, one of the hyperfine optical π transitions necessary for creating the Λ configuration is forbidden. In the configuration F = 3, 4↔F = 3 the transition F = 3 is forbidden, m = 0↔F '= 3, m' = 0, and in the configuration F = 3, 4↔F '= 4 the transition F = 4 is forbidden m = 0 ↔ F '= 4, m' = 0. The Λ configuration connecting the required Zeeman sublevels m = 0 and m '= 0 is realized using σ transitions, for which the linear polarizations of both components are transformed into circular polarities by one quarter-wave plate. Circularly polarized waves (σ-σ polarization configuration) in a constant magnetic field form seven Λ-schemes, each of which has its own resonant frequency. To stabilize the frequency, an average resonance corresponding to a 0–0 transition is used. Dictated by the selection rules, the need to use circular polarization leads to a significant drawback of this method - the presence of an additional "trap" non-absorbing state (it is marked with an asterisk in figure 2). The absorption of the laser field transfers the atoms to the sublevels m '= 3, 4 of the excited state, from where they spontaneously pass into the trap state (F = 4, m = 4). Some atoms accumulate in this state regardless of the fulfillment of the CPT resonance condition, i.e. they do not participate in the formation of resonance, which significantly limits its contrast.

This obstacle can be overcome by using small cells and σ ⁺ -σ ^, a two-frequency field configuration formed by oncoming traveling (along the z axis) bichromatic waves with opposite circular polarizations. In this case, there is no trap state.

When using counterpropagating waves, the efficiency of the interaction of an atom with a field undergoes spatially periodic modulation. This variation is due to the spatial incursion of the phase difference of the frequency components for counterpropagating waves 2 (k ₁ -k ₂ ) z, where k _i = 2π / λ _i , are the wave field vectors with frequencies ω _i , az is the coordinate of the observation point. The effect of spatial modulation with a period of π / (k ₁ -k ₂ ) is due to the difference in wavelengths λ ₁ and λ _{2 of} different frequency components. So, for example, for ¹³³ Cs atoms, the period π / (k ₁ -k ₂ ) = 1.6 cm. In the case of a "large" cell size L≥π / (k ₁ -k ₂ ), a significant increase in the amplitude of the total absorption resonance in σ ⁺ -σ ^{- the} field will not be observed due to spatial averaging. However, for small cells with a characteristic longitudinal size L≤π / (k ₁ -k ₂ ), the phase relations between the field components are approximately constant throughout the volume. Therefore, when placing such a cell in a region in which z differs little from the optimal value, a significant increase in the resonance amplitude is observed (for the D _{1 line} ). In this case, the nonabsorbing state for the total field exists only in resonance, and the parasitic trap state insensitive to the difference frequency is absent, which leads to an increase in contrast. Note that the σ ⁺ -σ ^- configuration of counterpropagating waves is implemented in the standard manner shown in Fig.3. If the incident wave is σ ⁺ - polarization, the wave is reflected from the mirror after a second pass the quarter-wave plate (λ / 4) takes the opposite σ ^{- -} polarization. The minimum distance from the mirror to the cell is π / 2 (k ₁ -k ₂ ). For example, for ¹³³ Cs atoms, this distance is about 0.8 cm.

The advantages of the method are the absence of trap states, relative compactness and the possibility of obtaining high contrast resonance. The disadvantages are: the presence of additional elements (mirrors and quarter-wave plates), the restriction on the minimum dimensions L≥0.8 cm, the need for special measures to eliminate feedback. In practice, a resonance was observed with a low contrast value (<10%) [5].

The problem solved by the invention is to increase the contrast of the reference resonance while simplifying the method and reducing the size of the device that implements it, which is very important, for example, when creating a mobile atomic clock.

To solve the problem, a new method is proposed for the formation of a high-contrast reference resonance at ultrathin transitions of the ground state of an alkali metal atom in a bichromatic field in which the frequency components are equally linearly polarized (lin || lin). In this case, the total angular momenta of the hyperfine components in the ground state are F = 1 and 2, and the excitation is carried out through the hyperfine component with the total angular momentum F '= 1. An obligatory condition is the spectral resolution of the hyperfine structure of the excited state. For alkali metals, under the usual conditions, the above requirements are satisfied only for the D _{1 line} ⁸⁷ Rb, in which the hyperfine splitting in the excited state (812 MHz) noticeably exceeds the Doppler half-width of ~ 260 MHz. Unlike the standard 0-0 resonance, here the CPT resonance is formed immediately by two transitions between the Zeeman sublevels, namely the transitions: (-1) - (+ 1) and (+1) - (- 1) resonances. Moreover, in exact resonance, nonabsorbing superpositional states exist, while a parasitic trap state is absent.

Figure 4 shows a diagram of light-induced transitions when two components of the laser field are tuned to spectrally resolved hyperfine transitions F = 1↔F '= 1 and F = 2↔F' = 1 (the level F '= 2 is not excited in this case). It can be seen that in this scheme two Λ configurations are shown, depicted by solid lines: one of them has at its base sublevels F = 1, m = -1 and F = 2, m = + 1, the other - F = 1, m = + 1 and F = 2, m = -1. Both Λ-schemes have a magnetic sublevel at the vertex of the excited state F '= 1, m = 0. The advantage of this method is that in the case of exact resonance there are two superpositional non-absorbing states, and when detuning from resonance there are no non-absorbing states, that is, there are no parasitic trap states in both cases, which leads to a large amount of contrast.

In a nonzero magnetic field, the frequencies of the two Λ resonances corresponding to the transitions F = 1, m = -1↔F = 2, m = + 1 and F = 1, m = + 1↔F = 2, m = -1 do not coincide. In this case, in contrast to the frequency of the 0–0 transition (independent of the magnetic field in the linear approximation), the dependences of the resonance frequencies of the two transitions contain not only quadratic, but also terms linear in the magnetic field. The linear shift coefficients for the two resonances have different signs, but coincide in absolute value equal to 2.8 kHz / G. It is significant that these shifts are 250 times smaller than the shifts of the magnetic sublevels themselves, between which the transitions occur. This is due to the fact that in each resonance the Zeeman sublevels involved in the transition are shifted in one direction. Incomplete compensation of the sublevel shifts is due to the contribution of the nuclear magneton to the Zeeman splitting. In weak magnetic fields, the smallness of the shifts of two resonant frequencies and their different signs only lead to a slight broadening (but not a shift) of the line, which is especially important for metrological applications. The Zeeman shift of this resonance quadratic in magnetic zero is 1.33 times smaller than for the 0–0 resonance.

(5/700)δν (Гс), где

700 кГц/Гс - коэффициент линейного сдвига зеемановских уровней с магнитным полем. При этом уширение опорного резонанса не превысит величины 5,6 кГц/Гс (5δν/700)Гс, то есть составит менее 5% от его ширины в нулевом магнитном поле.If the total width of the resonance in the proposed method is δν, then to exclude the influence of neighboring resonances it is sufficient to apply a magnetic field that ensures their splitting by ≤5δν, that is, a magnetic field equal to

(5/700) δν (G), where

700 kHz / Gs is the linear shift coefficient of Zeeman levels with a magnetic field. In this case, the broadening of the reference resonance will not exceed 5.6 kHz / G (5δν / 700) G, that is, it will be less than 5% of its width in a zero magnetic field.

An example of the method can serve as an experiment. The experimental setup is shown in FIG. 5. It consists of a laser system (1, 2, 3, 4, 5), a cell with ⁸⁷ Rb pairs (6, 7, 8), and a detection system (9). The experiment was carried out with a pyrex cylindrical cell (40 mm long, 25 mm in diameter) containing 4 Ne tori and ⁸⁷ Rb isotopically pure (6). The cell was placed inside the solenoid (8), which allowed changing the longitudinal magnetic field. To isolate it from an external laboratory field, the cell was placed inside three cylindrical magnetic screens (9). The cell was heated to 50 ° C by a bifilar nichrome thread wound around an internal magnetic screen. A bichromatic resonance field was created by modulating the current of a diode laser (3), whose frequency was optically captured by the frequency of a single-mode injection laser with an external resonator (1). For this, the radiation of the latter was directed through isolation (2) into the active region of the driven laser (3). In this case, the modulation does not violate the mode of the master laser (1). Slave laser injection current (3) modulated at the frequency Ω ₀ /2=3.417 GHz microwave generator via signals Agilent E8257D-502 which was consistent with the laser via tee Minicircuits ZFBT-6G. This technique ensured the generation of resonant optical fields with a high degree of phase noise correlation. Resonance fields contained approximately 50% of the total radiation power (2 mW). When the ratio of the intensities of the resonance fields equal to 1.4, the amplitude of the CPT resonance was maximum. The remaining power was attributed to the carrier and higher order side frequencies. The diameter of the laser beam in the cell was 4 mm. The CPT resonance was excited using linearly polarized modulation components of the first order, which were tuned to F = 1↔F '= 1 and F = 2↔F' = 1 transitions. A high degree of linearity of polarization was provided by a quartz polarizer (5). The quarter-wave plate λ / 4 (4) made it possible to change the polarization of the laser field from linear to circular. The power of the field transmitted through the cell was recorded by a photodiode (9).

A comparative analysis of the proposed scheme with the same linear polarizations of the two components of the bichromatic field and the scheme described in [4] was carried out at the experimental setup. The dependences of the amplitude and contrast of the resonance on the total power of the resonant optical fields were obtained. Figure 6 shows the CPT resonances in the case of the proposed lin || lin excitation circuit (the reference resonance is located in the middle). The dependences of the amplitude of the CPT resonance and contrast for the proposed excitation circuit and for the circuit described in [4] are shown in Fig. 7 and Fig. 8, respectively. It can be seen from these dependences that the parameters of the reference resonance in the case of the lin || lin of the resonance formation method significantly exceed the resonance parameters in the case of the σ-σ excitation scheme [4] (in the proposed scheme, the contrast is an order of magnitude higher, and the amplitude is ~ 50 times larger).

Thus, it is shown that the proposed scheme for the formation of the CPT resonance on the D _{1 line} of ⁸⁷ Rb atoms allows one to realize Λ resonance with improved metrological parameters, namely, a high value of contrast and resonance amplitude. In this case, both components of the laser field have the same linear polarizations, which allows the application of the simplest method of their formation - modulation of the injection current of the diode laser. This scheme is one of the most promising for use in atomic clocks at ⁸⁷ Rb.

The proposed method for the formation of high-contrast Λ resonance can be used to create atomic clocks with increased stability and small-sized atomic clocks that can replace quartz oscillators.

Commercial applications of atomic clocks [6] include navigation, synchronization of telecommunication networks, and scientific instrumentation. To protect communication channels and the ability to quickly determine the location, it is planned to install small-sized atomic clocks in mobile phones.

There are also important (and massive) applications in such areas of military technology as fast receivers for global positioning systems, communication systems with protection against channel overloads, noise-resistant tactical communication systems with fast carrier switching, and new recognition and tracking technologies [7]. An important advantage of atomic clocks in comparison with crystalline generators is a lower sensitivity to acceleration and, accordingly, higher reliability during operation on vibrating platforms. For military applications, low power consumption and compactness are especially important.

Information sources

[1] M.Arditi, "A gas cell atomic clock as a high-stability frequency standard", IRE Trans. Mil. Electron 4, 25-28, 1960.

[2] M.E. Packard, B.E. Swartz, "The opticaly pumped rubidium vapor frequency standard", IRE Trans. Instrum. 11, 215-223, 1962.

[3] LLLewis and M. Feldman, Proceedings of 35 ^th Annual Symposium on Frequency Control (Washington DC: Electronic Industires Assosiation), 1981, 612.

[4] S.Knappe, PDDSchwindt, V.Shah, L.Hollberg, and J.Kitching, "A chip-scale atomic clock based on ⁸⁷ Rb with improved frequency stability", OPTICS EXPRESS, Volume 13, Number 4, 2004.

[5] A.V. Taichenachev, V.I. Yudin, V.L. Velichansky, S.V. Kargapoltsev, R.Vinands, J.Kitsching, L.Hollberg, "High-contrast dark resonances on the D ₁ -line of alkali metals in the field of counterpropagating waves ", JETP Letters, Volume 80, Issue 4, 2004.

[6] J. A. Kusters, C. A. Adams, "Performance requirements of communication base station time standards", RF Design May, 1999, pp. 28-38.

[7] Vig J. "Military applications of high-accuracy frequency standards and clocks", IEEE Trans. Ultrason Ferrelectr. Freq. Control, 40, (1993), pp. 522-7.

Claims (1)

A method of forming a reference resonance at ultrathin transitions of the ground state of an alkali metal atom to stabilize the frequency of an electromagnetic oscillation generator, based on the effect of coherent population trapping in a bichromatic laser field, characterized in that the resonance is formed at the transition frequencies of ⁸⁷ Rb atoms: F = 2, m = 1 ↔F = 1, m = -1 and F = 2, m = -1↔F = 1, m = 1, where F is the quantum number of the total angular momentum of the atom, m is the quantum number of the projection of the total angular momentum of the atom on the direction of the magnetic field , and the components are bichromatic th laser field have the same linear polarization.

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