CN107806820B - Method for regulating and controlling reflection coefficient and phase of atomic grating - Google Patents
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Abstract
the invention relates to a method for regulating and controlling the reflection coefficient and phase of an atomic grating, which is characterized in that the reflection coefficient and phase of the atomic grating are regulated and controlled by controlling the laser parameters in the forming process of the atomic grating, wherein, the reflection coefficient of the atomic grating is realized by controlling the time length of the action of the laser and the atoms, the phase of the atomic grating is realized by controlling the phase shift caused by the frequency change of the laser, the invention can realize the continuous and accurate adjustment of the reflection coefficient of the atomic grating and the phase of the atomic grating, in addition, the invention does not relate to the movement of a mechanical structure, avoids the vibration, the hysteresis error and the return error caused by the movement, has the advantages of simple and convenient regulation and control method, continuous regulation and control, high regulation and control precision, high regulation and control repeatability and the like, and can be used for regulating and controlling the atomic grating in the precision measurement.
Description
Technical Field
The invention relates to the technical field of atomic optical instruments, in particular to a method for regulating and controlling the reflection coefficient and the phase of an atomic grating, which can be used for regulating and controlling the atomic grating in precise measurement.
Background
Photonic crystals are periodic nanostructures that can manipulate photons like semiconductor-manipulated electrons, and have been vigorously developed over the last 30 years. Photonic crystals can be classified into one-dimensional, two-dimensional and three-dimensional according to structural characteristics. One-dimensional photonic crystals, commonly referred to as bragg gratings, are typically fabricated using nanofabrication processes, including etching and self-assembly, or a combination of both. Among the one-dimensional bragg gratings, gratings having a grating period close to the range of visible light to near infrared have wide and important applications in the fields of optics, communication, biomedicine and precision measurement. In these applications, the reflection coefficient, period and phase of the grating need to be optimized and adjusted. The adjustment of the reflection coefficient and the period is realized by controlling relevant parameters of a grating manufacturing process, and the adjustment of the phase is realized by adopting a high-precision mechanical translation stage. However, the steps required to rework the grating are complex and time consuming, resulting in increased costs for adjusting the grating period and reflection coefficient; meanwhile, the high-precision mechanical translation stage is not free from vibration and hysteresis phenomena in the moving process, so that the repeatability of phase regulation is poor. In the last 10 years, with the gradual and deep research on quantum optics and atomic physics, an atomic-based Bragg grating can be constructed by adopting an atomic interferometer. The atomic grating is realized by adopting a Talbot-Lau atomic interferometer: firstly, atoms, generally alkali metal atoms or alkaline earth metal atoms, are cooled to form a coherent cold atom source, and the temperature of the coherent cold atom source is reduced to the Doppler cooling limit or even lower to form a glassy einstein condensed state; and then two beams of oppositely emitted laser are utilized to form standing wave pulses to diffract the cooled atom source, after two times of diffraction of the standing wave pulses with the interval of T, the atom grating is formed at the time of 2T, the duration is in the order of mu s, the grating period is the period lambda/2 of the standing wave of the laser, and lambda is the laser wavelength forming the standing wave. Although such atomic gratings have a short duration, they are easy and time-consuming to fabricate (about 1s), and can be repeatedly fabricated to achieve long-term measurement applications. Moreover, by controlling the wavelength lambda of the standing wave laser, the period lambda/2 of the atomic grating can be changed; and the high-order atomic grating with the period of lambda/4, lambda/8 and the like can be formed by controlling the coherence time and other methods, so that the adjustment requirement on the grating period in practical application is met. In the aspect of adjusting and controlling the reflection coefficient of the grating, the reflection coefficient of the grating can be adjusted and controlled by changing the time interval T of the first standing wave pulse and the second standing wave pulse, but at the same time, the evolution of atoms between the two pulse intervals also changes, so that the phase of the atomic grating changes, which is not in accordance with the requirement that the reflection coefficient and the phase of the grating can be respectively adjusted in practical application.
Disclosure of Invention
The invention solves the problem of providing a method for independently regulating and controlling the reflection coefficient and the phase of an atomic grating.
the solution of the invention is as follows:
Firstly, forming an atomic grating by using a two-pulse Talbot-Lau atomic interferometer, wherein the two pulses are a first standing wave pulse and a second standing wave pulse respectively; the method is characterized in that:
Regulating and controlling the reflection coefficient of the atomic grating by controlling the action time of the second standing wave pulse; the reflection coefficient R of the atomic grating is proportional to the amplitude ρ (x, Δ t) of the atomic grating, and the relationship is:
Where Δ T-2T is the time window in which the atomic grating exists, T is the atomic grating evolution time, T is the time interval between the first standing wave pulse and the second standing wave pulse, u is the most probable rate of the atomic sample along the x-axis, Q is the equivalent wave vector of the diffracted standing wave pulses forming the interferometer, J2(x) Is a second order Bessel function, Θ2Ω τ is the area of action of the second pulse, τ is the action time of the second standing wave pulse, Ω is the two-photon-to-one ratio oscillation frequency, ω isQIs the atom two-photon recoil oscillation frequency, phi is the phase of the atom grating; changing the action area theta of the second standing wave pulse by changing the action time tau of the second standing wave pulse2Thereby changing the reflection coefficient R of the atomic grating;
regulating and controlling the phase of the atomic grating by controlling the phase change of the second standing wave pulse relative to the first standing wave pulse; the phase formula of the atomic grating is:
Wherein a is the acceleration along the pulse direction of the first and second standing waves,Is the phase of the ith standing wave pulse (i ═ 1 or 2).
In the method for regulating and controlling the reflection coefficient and the phase of the atomic grating, the atomic interferometer adopts alkali metal atoms as an atomic source, and the atomic source needs to be in a state after laser cooling or a state of a Bose Einstein condensate; the atomic interferometer has a timing sequence of { T }1＝0,T2t, wherein the first standing wave pulse is a standing wave pulse formed by two beams of laser light, and the pulse action area Θ is12 to 10; the second standing wave pulse is a standing wave pulse formed by two beams of laser, and the pulse action area theta2About 2; the atomic grating is formed at time T-2T and has a duration of about 4 mus.
In the method for regulating and controlling the reflection coefficient and the phase of the atomic grating, the action time of the second standing wave pulse is controlled by respectively adopting two Acousto-optic modulators (AOMs) to control two beams of laser forming the second standing wave pulse, and the on-off of the radio frequency drive of the two AOMs is simultaneously controlled by using a high-speed radio frequency switch, so that the control of the on-off time of the two beams of laser, namely the standing wave pulse is realized, wherein the on-off time (10% -90%) of the high-speed radio frequency switch is less than 20 ns.
In the method for regulating and controlling the reflection coefficient and the phase of the atomic grating, the phase difference control method of the second standing wave pulse relative to the first standing wave pulse is to respectively adopt two AOMs to control two beams of laser forming the second standing wave pulse, adjust the frequency difference delta f of the driving sources corresponding to the two AOMs and control the accumulation time T of the frequency differencedObtaining the phase difference of the second pulse relative to the first pulse
after the cooled atomic substance wave is subjected to the action of two standing wave pulses on a time domain, an atomic grating is formed at a specific time point, and the phenomenon is called a Talbot-Lau phenomenon of atoms and is also called a grating echo effect. The basic principle of the method is similar to the Talbot-Lau effect on optics, and belongs to a near-field diffraction phenomenon. Considering an atomic monochromatic wave, with momentum p, it can be expressed as:
The atoms are acted by standing wave pulses formed by laser, and the action time meets the Raman-Nath approximate condition, namely the displacement of the atoms relative to the standing wave pulses during the interaction is not considered. The wave function of the available atoms after being subjected to the standing wave pulse becomes (t is 0 time being subjected to the standing wave pulse):
Then, atoms freely evolve in space until receiving the action of the second standing wave pulse, the evolution time is T, and the wave function is as follows:
In the formula, after the second standing wave pulse action, the atomic wave function becomes:
Then, atoms freely evolve in space, and near the 2T moment, atomic waves form atomic interference fringes, namely an atomic grating. Considering that the momentum distribution of atoms conforms to the boltzmann distribution, the density distribution of atoms in space can be written as:
wherein the echo time techo＝(1-N2/N1) T is the time of occurrence of the atomic grating, when N2When T is equal to 2T, forming an atomic grating with the period of 2 pi/Q being equal to lambda/2;it can be seen that the atoms form a periodic structure in space, i.e. an atomic grating. The reflection coefficient R of an atomic grating is proportional to the amplitude of the atomic grating:
By changing the action area theta of the second standing wave pulse2And then to the reflection of the atomic gratingthe coefficients are controlled. The principle is as follows: the atom grating is formed by the interference of two groups of atoms diffracted by the second standing wave pulse, the total number of the two groups of atoms is constant, and at the position where the tau takes the optimal value, the diffraction of the second standing wave pulse enables the number of the two groups of atoms participating in the formation of the atom grating to be equal, so that the reflection coefficient of the formed atom grating obtains the maximum value; when tau deviates from the optimum value, the numbers of atoms of the two groups are unequal, and the reflection coefficient of the atomic grating is determined by the number of the atomic groups with the smallest number.
According to the principle of the fisherman path integration, the phase of an atomic grating can be written as:
After the first standing wave pulse action is finished and before the second pulse action, if the two lasers forming the grating have frequency deviation delta f, the duration time of the frequency deviation is TdThe phase difference of the second standing wave pulse compared with the first standing wave pulse
The phase difference is finally reflected in the phase of the atomic grating, and the specific expression of the modified phase phi' is as follows:
Therefore, the frequency difference Δ f and the accumulation time T of the two laser beams forming the standing wave pulse are controlleddThe phase deviation of the second standing wave pulse relative to the first standing wave pulse can be controlled, and then the control of the atomic grating phase is realized. The principle is as follows: the second standing wave pulse diffracts the atomic substance wave as a phase grating, and transmits its own phase to the atomic substance wave while changing the amount of fluctuation of the atomic substance. The elements carrying the phase of the second pulseThe sub-species waves interfere to form an atomic grating, and the phase is finally represented on the atomic grating.
Compared with the prior art, the invention has the advantages that:
(1) The invention can realize the independent adjustment of the reflection coefficient and the phase of the atomic grating.
According to the analysis of the principle, the number of atoms participating in forming the atomic grating can be adjusted by adjusting the action time of the second standing wave pulse, so that the purpose of adjusting the reflection coefficient of the atomic grating is achieved; whereas the adjustment of the phase of the atomic grating is only related to the phase of the pulse, independent of the pulse action time. Compared with the existing method for adjusting the reflection coefficient of the atomic grating by changing the interval T between two pulses and causing the phase deviation of the atomic grating, the method has the advantage of realizing the independent adjustment of the reflection coefficient and the phase.
(2) The invention has high phase regulation precision and good repeatability, and does not relate to mechanical movement.
From the above principle analysis, it is found that the atomic grating phase can be shifted by adjusting the frequency difference between the two laser beams constituting the second standing wave pulse. Compared with a method of moving the grating in space by adopting a mechanical translation stage, the method avoids vibration, hysteresis error and return error caused by control, mechanical structure and the like in the moving process of the mechanical translation stage, and has the characteristic of good repeatability; meanwhile, the laser frequency is very high in adjustment precision, so that the phase adjustment of milliradian can be realized, the spatial movement corresponding to the atomic grating is in nanometer level or even sub-nanometer level, the limit of the existing high-precision translation stage is broken through, and the high-precision translation stage has very high adjustment precision.
Drawings
FIG. 1 is a flow chart of a method of modulating the reflection coefficient and phase of an atomic grating according to the present invention;
FIG. 2 is a graph comparing experimental results and theoretical calculations for adjusting the reflection coefficient of an atomic grating in accordance with the present invention;
FIG. 3 is a graph comparing the phase adjustment results of the atomic grating in the present invention with theoretical calculations.
Detailed Description
Fig. 1 is an auxiliary flowchart illustrating the method for adjusting and controlling the reflection coefficient and phase of the atomic grating according to the present invention. Firstly, preparing a cold atom source to form a cold atom group or a bose einstein condensed state; applying a first standing wave pulse action to the prepared atomic source, wherein the standing wave pulse is a standing wave laser grating formed by two beams of laser, and the pulse action area theta is12 to 10; after the interval T, a second standing wave pulse is applied, the standing wave is also a standing wave laser grating formed by two beams of laser, and the pulse action area theta2is about 2. After a further interval T, an atomic grating is formed in space. The detection of the atomic grating adopts a Bragg backscattering method, and the backscattering light carries information of the phase phi and the reflection coefficient R of the atomic grating; and then, carrying out information calculation on the obtained back detection light by using an optical heterodyne method, specifically, carrying out beat frequency on a beam of local oscillation light with stable phase and back scattering light, and obtaining the information of the yard grating and the reflection coefficient by analyzing the phase and the amplitude of a beat frequency signal. The pulse action area theta is adjusted by regulating and controlling the action time of the second standing wave pulse2The reflection coefficient R of the atomic grating can be regulated and controlled; regulating the frequency difference delta f of the two laser beams of the second standing wave pulse and controlling the accumulation time T of the frequency differencedObtaining the phase difference of the second pulse relative to the first pulsethereby changing the phase of the atomic gratingwhere φ is the atomic grating phase before being changed.
The following description will be made of a specific embodiment of the present invention by taking a cesium atom Talbot-Lau interferometer as an example. Firstly, capturing and cooling cesium atoms from background thermal atoms by adopting a magneto-optical trap method; when the number of magneto-optical traps reaches about 109And then, cutting off the current of the magneto-optical trap coil, and turning off the cooling light and the anti-pumping light to obtain cold atomic groups. Wherein the frequency of the cooling light is | F ═ 4>→|F'＝5>Detuned-2 Γ (natural line width, Γ ═ 2 π × 5.234 MHz); frequency of anti-pumping light is | F ═ 3>→|F'＝4>Detuning 0. ColdThe cooling light is turned off 4ms later than the back pumping light, so that the atoms in the cold radical are in | F ═ 3>. Two laser beams E are oppositely directed along the direction perpendicular to the gravityaAnd Ebthe two laser beams have the same frequency and are all | F ═ 3>→|F'＝4>detuned +200 MHz; the width of the cross section is 2mm (Gaussian radius), the two beams of laser are overlapped in space to form a standing wave pulse, and meanwhile, the atomic group is ensured to be positioned at the center of the cross section of the laser. Applying a first beam of standing wave pulse to the prepared cesium cold atom source, wherein the pulse action area theta is14; after the interval T is 137 mu s, a second beam standing wave pulse is applied, and the action area theta of the second beam pulse is controlled2After an interval T of 137 μ s, the atomic grating is formed in space. The detection of the atomic grating adopts a Bragg backscattering method, and E is opened in a time window of 2 mus backward from 2T to 274 musaAt this time EaIs 1/2 before, E due to the presence of the atomic gratingawill be back-scattered by the atomic grating, the scattered light is along EbDirection; at the same time, EbOpening, Ebfrequency shift E ofaThe frequency of (4 MHz) is attenuated to 1 μ W. Ebcoincident with the back-scattered light, and converge on an Avalanche Photodiode (APD) to form interference, and due to the limitation of the APD bandwidth, only E can be detectedbAnd the difference frequency information of the signal light, namely, the oscillation signal of 4 MHz. The light intensity of the scattered light is in direct proportion to the amplitude of the atomic grating and further in direct proportion to the reflection coefficient of the atomic grating, and the phase of the scattered light carries the phase information of the atomic grating, so that the amplitude of the oscillation signal received by the APD is in direct proportion to the amplitude of the atomic grating, and the phase is the phase of the atomic grating.
Two beams of laser forming standing wave pulses are controlled by two AOMs respectively. The on-off of the radio frequency drive of the two AOMs is controlled by one high-speed radio frequency switch, so that the control of the on-off time of two beams of laser, namely standing wave pulses, is realized. FIG. 2 is a comparison of experimental results of atomic grating reflection coefficient controlled by second pulse action time with theoretical calculations, where scatter is normalized grating reflection coefficient and solid line is theoretical calculations. The on-off time of the AOM is controlled from 50ns to 650ns, and the backscattering signal of the atomic grating is observed. It can be seen that when the action time of the second standing wave pulse is 400ns, the backscattering signal of the atomic grating, i.e. the reflection coefficient of the atomic grating, reaches a maximum value; the adjustment of the reflection coefficient of the atomic grating from 0 to the maximum value in the full range can be realized by adjusting the action time, and the experimental result is consistent with the calculation result of a theoretical formula. The experimental results verify the feasibility of the method.
The driving sources for controlling the two AOMs are locked on an atomic clock, the frequency difference of any one of the AOM driving sources can be respectively controlled, and the phase of the second pulse is changed relative to the first pulse. Fig. 3 reflects the phase of the atomic grating versus the frequency adjustment voltage of the AOM drive source. Wherein (a) and (b) are used for respectively regulating two laser beams Ea、Ebthe round dots represent atomic grating phase experimental data, the solid lines represent phase experimental data fitting, and the squares represent corresponding signal amplitudes of the atomic gratings; the inner graph represents the fit residuals. Let Δ fa，ΔfbAre respectively EaAnd EbWhen the two laser beams deviate from the original frequency value, delta f is equal to delta fa-Δfb. In the experiment, T is 3.775ms, the frequency adjusting voltage is applied from 0.5ms after the first pulse is ended, and E is respectively adjusteda(Eb) While maintaining Eb(Ea) The frequency is not changed. The calibration calculation shows that the deviation of the applied voltage and the frequency is 0.0759 Rad/mV. Fitting the data of FIG. 3(a) yields EaThe deviation of the applied voltage from the frequency of (2) is 0.076(1) Rad/mV, and E can be obtained by fitting the data of FIG. 3(b)bThe applied voltage versus frequency deviation of-0.0761 (6) Rad/mV, consistent with theoretical predictions. Meanwhile, it can be seen that, in the process of adjusting the frequency of the atomic grating, the backscattering signal of the atomic grating remains stable, that is, the reflection coefficient of the atomic grating is unchanged. The experimental result verifies the correctness of the method.
Claims (4)
1. A method for regulating and controlling the reflection coefficient and the phase of an atomic grating comprises the steps of firstly, forming the atomic grating by utilizing a two-pulse Talbot-Lau atomic interferometer, wherein the two pulses are a first standing wave pulse and a second standing wave pulse respectively; the method is characterized in that:
(1) Regulating and controlling the reflection coefficient of the atomic grating by controlling the action time of the second standing wave pulse; the reflection coefficient R of an atomic grating is proportional to the amplitude ρ (x, Δ t) of the atomic grating, and the relationship is:
Where Δ T-2T is the time window in which the atomic grating exists, T is the atomic grating evolution time, T is the time interval between the first standing wave pulse and the second standing wave pulse, u is the most probable rate of the atomic sample along the x-axis, Q is the equivalent wave vector of the diffracted standing wave pulses forming the interferometer, J2(x) Is a second order Bessel function, Θ2Ω τ is the area of action of the second standing wave pulse, τ is the action time of the second standing wave pulse, Ω is the two-photon-to-one ratio oscillation frequency, ωQIs the atom two-photon recoil oscillation frequency, phi is the phase of the atom grating; changing the action area theta of the second standing wave pulse by changing the action time tau of the second standing wave pulse2Thereby changing the reflection coefficient R of the atomic grating;
(2) regulating and controlling the phase of the atomic grating by controlling the phase change of the second standing wave pulse relative to the first standing wave pulse; the phase formula of the atomic grating is:
Wherein a is the acceleration along the pulse direction of the first and second standing waves,Is the phase of the first standing wave pulse,is the phase of the second standing wave pulse; the second standing wave pulse is opposite to the first standing waveThe phase difference control method of the pulse comprises the steps of respectively adopting two acousto-optic modulators to control two beams of laser forming a second standing wave pulse, adjusting the frequency difference delta f of the driving sources corresponding to the two acousto-optic modulators and controlling the accumulated time T of the frequency differencedObtaining the phase difference of the second standing wave pulse relative to the first standing wave pulse
2. The method of modulating the reflection coefficient and phase of an atomic grating as recited in claim 1, wherein: the atomic interferometer adopts alkali metal atoms as an atom source, and the atom source needs to be in a state after laser cooling or a state of a Bose Einstein condensate; the atomic interferometer has a timing sequence of { T }1＝0,T2T, wherein the first standing wave pulse is a standing wave laser grating formed by two beams of laser light, and the pulse action area Θ is12 to 10; the second standing wave pulse is a standing wave laser grating formed by two beams of laser, and the pulse action area theta2Is 2; the atomic grating is formed at time T-2T and has a duration of 4 mus.
3. the method of modulating the reflection coefficient and phase of an atomic grating as recited in claim 1, wherein: the action time of the second standing wave pulse is controlled by two acousto-optic modulators to form two beams of laser of the second standing wave pulse, and the on-off of the radio frequency drive of the two acousto-optic modulators is controlled by a high-speed radio frequency switch simultaneously, so that the control of the on-off time of the two beams of laser, namely the standing wave pulse is realized, wherein the on-off time of the high-speed radio frequency switch is less than 20 ns.
4. The method of claim 1, wherein the reflection coefficient and phase of the atomic grating are adjusted according to the phase differenceObtaining the final phase phi' of the calculated atomic grating:
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