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Journal of Physics B Atomic Molecular and Optical Physics

Quantum jump calculations of velocity-selective coherent population trapping in one and two dimensions

Haocheng Wu, Murray Holland, Christopher J. Foot

Published Dec 14, 1995• 6 citations
Publisher

Abstract

Velocity-selective coherent population trapping is a technique for laser-cooling atoms to below the recoil limit where the momenta of the atoms and photons in the light field are equal. We have studied this mechanism using an efficient simulation model, which both simplifies the calculations and gives a physical insight into the dynamics of the anomalous diffusion process. Our calculations have been carried out for transitions in which the total atomic angular momentum is F=1 to 1 in both one and two dimensions and F=2 to 2 in one dimension. In the latter case, no exact dark state exists, and the momentum distribution tends towards a Lorentzian in the steady state.

DOI
10.1088/0953-4075/28/23/012

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Velocity-selective coherent population trapping is a technique for laser-cooling atoms to below the recoil limit where the momenta of the atoms and photons in the light field are equal. We have studied this mechanism using an efficient simulation model, which both simplifies the calculations and gives a physical insight into the dynamics of the anomalous diffusion process. Our calculations have been carried out for transitions in which the total atomic angular momentum is F=1 to 1 in both one and two dimensions and F=2 to 2 in one dimension. In the latter case, no exact dark state exists, and the momentum distribution tends towards a Lorentzian in the steady state.
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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).
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
We give a systematic analysis of the extension of the one-dimensional velocity-selective coherent population trapping cooling mechanism to atoms with integer angular momenta F>1F>1F>1 using additional light shifts to compensate for the kinetic energy mismatch between the various Zeeman sublevels contributing to the internally decoupled (i.e., dark) state of the atom. Different configurations to achieve the proper light shifts to obtain a very long lifetime of the velocity-selective dark states are discussed and compared. In addition we show that the maximum occupation probability of the resulting quasidark state and its filling time scale strongly depend on the proper choice of detunings to exploit extra precooling mechanisms involving the Zeeman sublevels not contributing to the dark state. We show that additional cooling can also be implemented on the hyperfine repumping transition. This result should prove important for other schemes involving gray states such as, e.g., dark optical lattices and superlattices as well. As a concrete example we consider cesium including all relevant hyperfine levels.
In this paper we propose a new and simple velocity selective method, which combines the velocity selective coherent population trapping of atoms in a light field and the kinetic energy coupling between the dark state and coupled state(s) during free flight, in order to reach a very narrow momentum distribution in a short period of time. This technique combined with force-assisted velocity selective coherent population trapping can produce very efficient cooling and trapping. It can also be used to overcome the cooling limit caused by the leakage of the dark state.