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Acta Physica Sinica

Velocity-selective coherent population trapping of a nondegenerate Λ three-level atom

Xie Min, Ling Lin, Guojian Yang, 北京师范大学物理系，北京 100875

Published Jan 1, 2005• 1 citation
Publisher

Abstract

We present in this paper a detailed discussion of the velocity_selective coherent population trapping of an atomic system in a nondegenerate Λ three_level configuration.Compared with the case of degenerate ground states and laser_atom resonance,the most probable value of the atomic_momentum distribution greatly decreases and much longer trapping time is needed in order to generate the same trapping effect.

DOI
10.7498/aps.54.3616

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Journal of the Optical Society of America B•Mar 1, 1992•41 citations
We present in this paper a detailed discussion of the velocity_selective coherent population trapping of an atomic system in a nondegenerate Λ three_level configuration.Compared with the case of degenerate ground states and laser_atom resonance,the most probable value of the atomic_momentum distribution greatly decreases and much longer trapping time is needed in order to generate the same trapping effect.
An analytical theory of optical pumping of velocity-selective coherent population trapping states in three-level Λ-atoms is presented. The theory is based on an atomic density matrix in the superpositional state representation. The representation introduced for the atomic density matrix directly describes coherent population trapping (CPT) states in a three-level Λ-atom and yields an approximate analytical description for the shape of the two-peak momentum (velocity) distribution of atoms. Optical pumping of velocity-selective CPT states is described in the superpositional state representation as a process of redistribution of atoms in the region of small velocities due to the photon recoil. Typical times of formation of velocity-selective CPT states are found to be inversely proportional to the square of the recoil energy.
In Section 8.3.9, we mentioned that the recoil temperature was not the ultimate barrier to cooling. Several mechanisms have been conceived and implemented to concentrate the atomic velocity distribution in a range of values of width less than V R . In contrast to Doppler or Sisyphus cooling, these mechanisms do not appeal to a friction force, but rather to an optical pumping process (see Complement 2B), able to accumulate the atoms in this narrow range of velocities. We now present one such mechanism called ‘velocity-selective coherent population trapping’, considering only the case where the motion occurs in one space direction (the O z -axis). Note, however, that the method generalizes to two or three dimensions. Coherent population trapping Coherent population trapping is a phenomenon that occurs when an atom has a system of three energy levels in the ∧ configuration shown in Figure 8A.1, where each leg of the ∧ interacts with a laser L − or L + . This was discussed in detail in Section 2D.2 of Complement 2D. Here we consider the case where the two ground states g + and L − , have exactly the same energy, and the two lasers have frequencies ω + and ω − , very close to the resonance frequency ω 0 . In this situation, the selectivity of the interactions is obtained via the polarization selection rules (see Complement 2B): if g − , g + and e have magnetic quantum numbers m = −1, +1 and 0, respectively, the laser wave L − is right-circularly polarized (σ + polarization), while the laser wave L + is left-circularly polarized (σ − polarization).
A theoretical analysis of one-dimensional cooling of atoms is presented. The method of cooling is based on velocity-selective coherent population trapping. Both internal and translational degrees of freedom of the atoms are treated quantum mechanically. The analytic expression for atomic density matrix is obtained in the limit of large interaction time and small kinetic momentum of atom. It is demonstrated that: (i) there is a limit on the lowest temperature that can be achieved by such a method and it is determined by the small but finite rate of decay of the coherence between two low-lying states in the three-level Lambda -configuration; (ii) the fraction of atoms involved in the cooling process decreases to zero as the atom-field interaction time increases, because of the presence of such a relaxation which always takes place in real experimental systems.
We have demonstrated velocity-selective coherent population trapping (VSCPT) in a two-level system created by circularly polarized light driving the $2{}^{3}{S}_{1}\ensuremath{\rightarrow}3{}^{3}{P}_{2}$ transition in metastable helium. It is quite different from the usual VSCPT because there need be no consideration of selection rules, polarization, or internal atomic states. This most primitive case elicits the simple nature of VSCPT as a special kind of quantum interference, and demonstrates the presence of VSCPT in a system that has only two internal levels. It is readily observed for this transition because the ratio of the recoil frequency to the natural linewidth is 0.22, two orders of magnitude larger than for most laser cooling experiments. Our trapped state is fed by Doppler cooling, which is unusually effective here because of the large recoil, and is totally absent in previously described VSCPT experiments.
We show theoretically that velocity-selective coherent population trapping in one dimension may be realized in atomic transitions other than Jg = 1 ↔ Je = 1. The atomic momentum distribution resulting from irradiation by counterpropagating σ+–σ− waves on the Jg = 3/2 ↔ Je = 1/2 and the Jg = 2 ↔ Je = 1 atomic transitions is investigated through solution of the optical Bloch equations and determination of the effective loss rates for atomic eigenstates. An inverted-W atomic level configuration is also used to investigate the features of velocity-selective coherent population trapping. The momentum distribution exhibits peaks at the ±ħk or the ±ħ2k and the 0 momenta, depending on the atomic transitions and the laser intensity. These structures, generated by atomic states that do not interact with the laser radiation, are stable when associated with eigenstates of the kinetic energy, or metastables; i.e., the structures last several hundred spontaneous lifetimes when generated by nonexact kinetic-energy eigenstates.