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Physical Review A

Dynamics of high-angular-momentum velocity-selective coherent population trapping

Chiara Menotti, Péter Horák, Helmut Ritsch, Jörg Helge Müller, E. Arimondo

Published Sep 1, 1997• 7 citations
Publisher

Abstract

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 $F>1$ 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.

DOI
10.1103/physreva.56.2123

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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.
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.
We propose a scheme to achieve one-dimensional velocity-selective coherent population trapping in a five-level system under two-frequency laser excitation. It may be applied to either D line of alkali-metal atoms. The trapped state is a time-dependent superposition of three sublevels from two different hyperfine ground states. Stable trapping may be produced by correctly detuning the laser beams to compensate for different hyperfine and kinetic energies of these ground states. We present numerical results for a five-level model, as well as for the complete level systems appropriate for alkali-metal atoms.
We have observed long-lived dark states in velocity-selective coherent population trapping (VSCPT) in a one-dimensional lin-angle-lin configuration with metastable He atoms using the $J=1\ensuremath{\Rightarrow}1$ transition at $\ensuremath{\lambda}=1.083$ \ensuremath{\mu}m. These states are characterized by two peaks in the atomic momentum distribution at $\ifmmode\pm\else\textpm\fi{}Q\ensuremath{\hbar}k(Q=\mathrm{positive}\mathrm{integer})$, where kkk is the magnitude of the optical wave vector. VSCPT states previously observed are characterized by Q=1Q=1Q=1, but we have observed long-lived states with Q=2Q=2Q=2. Optical Bloch equation calculations show that these high-velocity dark states appear at higher QQQ for greater light intensity.
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.
We propose a scheme that combines velocity-selective coherent population trapping (CPT) and Raman sideband cooling (RSC) for subrecoil cooling of optically trapped atoms outside the Lamb-Dicke regime. This scheme is based on an inverted Y\mathsf{Y}Y configuration in an alkali-metal atom. It consists of a $\mathrm{\ensuremath{\Lambda}}$ formed by two Raman transitions between the ground hyperfine levels and the DDD transition, allowing RSC along two paths and formation of a CPT dark state. Using the state-dependent difference in vibration frequency of the atom in a circularly polarized trap, we can tune the $\mathrm{\ensuremath{\Lambda}}$ to make only the motional ground state a CPT dark state. We call this scheme motion-selective coherent population trapping (MSCPT). We write the master equations for RSC and MSCPT and solve them numerically for a 87Rb^{87}\mathrm{Rb}87Rb atom in a one-dimensional optical lattice when the Lamb-Dicke parameter is 1. Although MSCPT reaches the steady state slowly compared with RSC, the former consistently produces colder atoms than the latter. The numerical results also show that subrecoil cooling by MSCPT outside the Lamb-Dicke regime is possible under a favorable, yet experimentally feasible, condition. We explain this performance quantitatively by calculating the relative darkness of each motional state. Finally, we discuss the application of the MSCPT scheme to an optically trapped diatomic polar molecule whose Stark shift and vibration frequency exhibit large variations depending on the rotational quantum number.