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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Laser pumping magnetic resonance of theory research based on coherent population trapping

Zhang Yang, Kang Chong, Qingtao Wang, Lei Cheng, Caiping Zheng, Weimin Sun

Published May 13, 2010• 0 citations
Publisher

Abstract

In the Λ three-level system, we will make use of semi-classical density matrix method to analyze cesium (Cs) hyperfine structure of coherent population trapping (CPT) phenomenon. Coherent population trapping has been widely used in electromagnetically induced transparency, non-inversion laser, optical storage and ultra-slow speed of light fields, then strong-coupling light and weak detecting light form coherent laser light to change the hyperfine structure energy levels of particles number distribution, which impacts on laser pumping magnetic resonance. In this paper, we will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the Zeeman sublevels to produce the results of magneto-optical double resonance and on this basis we analyze the influence of laser pumping magnetic resonance based on coherent population trapping.

DOI
10.1117/12.864914

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In the Λ three-level system, we will make use of semi-classical density matrix method to analyze cesium (Cs) hyperfine structure of coherent population trapping (CPT) phenomenon. Coherent population trapping has been widely used in electromagnetically induced transparency, non-inversion laser, optical storage and ultra-slow speed of light fields, then strong-coupling light and weak detecting light form coherent laser light to change the hyperfine structure energy levels of particles number distribution, which impacts on laser pumping magnetic resonance. In this paper, we will discuss the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling, the hyperfine structure has been further split into Zeeman sublevels for the effects of magnetic field. To use laser pump and RF magnetic field make electrons transition in the Zeeman sublevels to produce the results of magneto-optical double resonance and on this basis we analyze the influence of laser pumping magnetic resonance based on coherent population trapping.
Laser pumping magnetometers using alkali vapors as sensing medium can reach very high sensitivities in magnetic fields covering the range from the earth magnetic field to biological magnetic fields. In this paper, the theoretical analysis and system design of laser pumping cesium magnetometer, cesium atomic energy level formed hyperfine structure with the I-J coupling are discussed. The hyperfine structure is further split into Zeeman sublevels for the effects of magnetic field. The electrons transition is made by using laser pumping and RF magnetic field in the hyperfine structure. The results of magne-to-optical double resonance is obtained. The accurate value of the external magnetic field could be measured by the resonant frequency.
The evolution of the hyperfine structure magnetic sublevel populations of 87 Rb and 133 Cs atoms in resonant linearly polarized laser fields is theoretically analyzed. Analytical expressions are obtained for stationary populations of the magnetic sublevels of the ground state 5 2 S 1/2 F g = 1, F f = 2 in 87 Rb and 6 2 S 1/2 F g = 3, F f = 4 in 133 Cs under optical pumping at the F g ↔ F e = F g and F f ↔ F e = F f transitions of the D 2 lines ( n 2 S 1/2 n 2 P 3/2 ) versus the initial populations. The characteristic population stabilization time are obtained by numerical solution for the density matrix equations, depending on the intensity of the laser fields and the detuning of the optical resonance. It is shown that the alternation of the polarization direction of the laser field at the transition F f ↔ F e = F f almost completely transfers atoms to the lower sublevel of the "clock" M1 transition F g M = 0 ↔ F f M = 0 in rubidium and cesium frequency standards, which proportionally increases the signal of the recording system.
Coherent population beating (CPB) phenomenon occurs in a typical three-level system. When the frequency difference between two coherent pumping laser fields has a certain detuning from the ground-state hyperfine splitting, the excited state population will experience a transient oscillation before reaching equilibrium, and the oscillation frequency is equal to the detuning. The CPB phenomenon enables us to directly obtain the beat frequency between the measured radio frequency (RF) signal and the atomic transition frequency. Then we can get the standard frequency by compensating the beat frequency to the RF. We propose a scheme to implement atomic clock based on the CPB phenomenon in 2009, and the scheme has been implemented. When this effect is used to achieve an atomic clock, the frequency stability is directly related to the amplitude and SNR (signal to noise ratio) of the CPB signal. Influence of the ground-state hyperfine sublevels' coherence on CPB signal is theoretically simulated and experimentally investigated in this paper. A formula of the CPB signal is derived by using the semi-classical model of the interaction of atoms with light, and the theoretical simulation is done using the formula obtained. In the experiment two coherent pumping laser fields are used to interact with 87Rb atoms. A CPB process includes the coherence build-up and the CPB stimulation. The coherence of the ground-state hyperfine sublevels is achieved by controlling the pumping time of the coherent laser fields that are resonant to the ground-state hyperfine sublevels. With this method, the relationship between CPB signal and coherence of the ground-state hyperfine sublevels can be observed. Result shows that the amplitude of CPB signal is proportional to the ground-state hyperfine sublevels' coherence. The hign quality CPB signal can be achieved when the CPB stimulation is started with a pure coherent population trapping (CPT) state. In the CPB process, the coherence build-up rate is approximately equal to the coherence decay rate. So a 50% duty cycle square wave can be used to modulate the RF, and the period of the square wave had better be twice of the decay time of the ground-state hyperfine sublevels' coherence. To improve the SNR of CPB signal and the stability of atomic frequency standard, the ground-state hyperfine sublevels' coherence must be built up, improved, and maintained before the CPB stimulation. The feasibility of applying CPB phenomenon to the weak magnetic field measurement and other applications is also discussed in this paper.
The purpose of this communication is to summarize and compare the results obtained under the project "New all-optical systems and methods for magnetic and electromagnetic field measurement", financed by EC (contract G6RD-CT-2001-000642). The main aim of the project is investigation of the potential of different approaches based on the effect of Coherent Population Trapping (CPT) for magnetic field measurement. The investigated approaches are: (i) CPT prepared by coupling pairs of non-degenerate Zeeman sublevels belonging to the two ground-state hyperfine components of alkali atoms by means of polychromatic laser field; (ii) CPT prepared by coupling degenerate Zeeman sublevels belonging to a single ground-state hyperfine component of alkali atoms by means of single-frequency laser field of appropriate polarization at zero magnetic field (MF); and (iii) polychromatic laser field coupls pairs of non-degenerate Zeeman sublevels belonging to a single ground-state hyperfine level of alkali atoms.
The evolution of the populations of the magnetic sublevels of the cesium atom (133Cs isotope) in resonant laser fields with linear polarization is analyzed using the equations for the density matrix. Analytic expressions are derived for stationary populations resulting from laser-induced optical transitions on the hyperfine structure components F g = 3 ↔ F e = 2, 3 and F f = 4 ↔ F e = 3, 4 of lines D1 (62S1/2 → 62P1/2) and D2 (62S1/2 → 62P3/2) depending on the initial values of the populations. The numerical solution of the evolution equations gives the characteristic times of stabilization of the steady regime as functions of laser field intensities and detuning from optical resonance. We determine the sequences of optical transitions increasing (by more than an order of magnitude) the population of the lower sublevel 62S1/2F g = 3 M = 0 of the “clock” microwave transition F g = 3 M = 0 ↔ F f = 4 M = 0 in the cesium frequency standard, which increases the signal intensity in the recording system by the same proportion.
We study the peculiarities of the coherent population trapping (CPT) dark resonance in atomic vapor confined in a finite-size cell. Taking into account the scattering of atoms on anti-relaxation coating of the walls, we analyze the line shape of the CPT resonance in 133 C s depending on various parameters, such as the width of laser radiation spectrum, the type of pumping, and the magnitude of static magnetic field for both lin || lin and l i n ⊥ l i n polarization schemes. We show that for different parameters, the dependence of the line shape on the size of a cell is different, i.e., different factors affect the CPT resonance nonadditively. Thus, in the case when CPT resonance is excited by a narrowband laser, the shape of the resonance weakly depends on the size of a cell due to the laser-induced narrowing effect. We also show that the distortion of the line shape of the CPT resonance caused by nonresonant hyperfine sublevels of atomic excited states is modified with the size of a cell. Our calculation reveals the important role of accounting for the hyperfine and Zeeman structure of atomic levels. We have shown that the contrast of the CPT resonance differs about 5 times from the prediction of the simple three-level Λ model. The obtained results can be used for the optimization of the quantum frequency standards based on the CPT effect. In the final part of the paper, on the basis of the shot noise approximation we estimate the short-term stability of such standards.