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Journal of Experimental and Theoretical Physics

Optical pumping of velocity-selective coherent population trapping states in three-level atoms

Vladimir G. Minogin, Gerard Nienhuis

Published Aug 1, 1998• 0 citations
Publisher

Abstract

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.

DOI
10.1134/1.558657

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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.
We present a new scheme of sub-Doppler laser cooling for atoms used in atomic frequency standards, particularly for 40Ca. We perform calculations concerning optical pumping via a velocity- selective state based upon velocity-selective coherent population trapping. Optical pumping on the Raman transition 41S0- 41P1-31D2 leads to population of the metastable singlet state followed by a decay into the metastable triplet state 4P1. The momentum distribution of atoms in that state (with a half-maximum width of about one corresponding photon recoil momentum) is a direct replica of the distribution of atoms in the 3D2 state.
ABSTRACT In this work we present an investigation of velocity-selective coherent population trapping (VSCPT) in asym- metric three-level schemes. The light force in such schemes is of an intrinsically transient character and shouldnot be described in a quasiclassical approach. Instead, results of the full quantum-mechanical calculations are presented with emphasis on their meaning to the efficiency of subrecoil laser cooling. 1 INTRODUCTION Laser cooling of neutral atoms has received significant advances by the introduction of velocity-selectivecoherent population trapping ((VSCPT) some years ago.1 Since it leads to atomic temperatures well below therecoil limit, studies of ultracold atoms and atomic interactions may be improved by magnitudes.The effect of VSCPT relies on optical pumping of atoms into a state WNC) which is a trap state for a certaincenter-of-mass velocity vO. This trap state is created by a destructive superposition of atomic states within amultilevel quantum system. Once being in such a state LWNC) the laser light does not interact anymore with theatom which leads to a decoupling with the rest of the system at vo. Atoms located outside this small velocityregion get a chance to be trapped by the momentum diffusion due to spontaneous emission of photons. Aftera sufficient long interaction time nearly all atoms are trapped inside a narrow momentum distribution whichcan be interpreted as cooling. The theoretical and experimental investigation of VSCPT is usually consideredby use of a three-level A-system as shown in Fig.1. Such a system can be found for example in a symmetrical
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.
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).