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Physical Review A

Dynamical cooling of trapped gases. II: Many-atom problem

Luis Santos, Maciej Lewenstein

Published Nov 1, 1999• 15 citations
Publisher

Abstract

We analyze the laser cooling of trapped bosonic gases beyond the Lamb-Dicke limit. We use a quantum master equation formalism to study the cooling dynamics, and show that dark-state cooling methods similar to those previously proposed for a single trapped atom allow for the condensation of a collection of bosons into a single state of the trap, either the ground state or an excited state. Using Monte Carlo simulations we analyze the condensation dynamics for different dimensions, and two different cooling schemes; we also demonstrate the appearance of multistability and hysteresis phenomena.

DOI
10.1103/physreva.60.3851

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We analyse the effects of atom-atom collisions on collective laser cooling scheme. We derive a quantum Master equation which describes the laser cooling in presence of atom-atom collisions in the weak-condensation regime. Using such equation, we perform Monte Carlo simulations of the population dynamics in one and three dimensions. We observe that the ground-state laser-induced condensation is maintained in the presence of collisions. Laser cooling causes a transition from a Bose-Einstein distribution describing collisionally induced equilibrium,to a distribution with an effective zero temperature. We analyse also the effects of atom-atom collisions on the cooling into an excited state of the trap.
We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state ∣0>|0>∣0>. The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.
We analyze theoretically a one-dimensional model of laser cooling of an atom or ion trapped in a cavity. We assume that the cavity loss rate is much larger than the atom-cavity coupling (bad-cavity limit) and that the atomic excited state is weakly occupied (low saturation limit). After elimination of the cavity mode and the atomic excited state, we derive rate equations for the populations of the trap states. We find that in the Lamb-Dicke limit the atom can be cooled to the ground state of the trap even in the strong confinement limit. This result is interpreted in terms of quantum interferences between different cooling and heating processes involving spontaneous emission in the cavity.
The collective Raman cooling of trapped one- and two-component Fermi gases is considered. We obtain the quantum master equation that describes laser cooling in the festina lente regime, for which the heating due to photon reabsorption can be neglected. For the two-component case the collisional processes are described within the formalism of the quantum Boltzmann master equation. The inhibition of the spontaneous emission can be overcome by properly adjusting the spontaneous Raman rate during the cooling. Our numerical results, based on Monte Carlo simulations of the corresponding rate equations, show that three-dimensional temperatures of the order of 0.08 T F (single component) and 0.03 T F (two components) can be achieved. We investigate the statistical properties of the equilibrium distribution of the laser-cooled gas, showing that the number fluctuations are enhanced compared with the thermal distribution close to the Fermi surface. Finally, we analyse the heating related to the background losses, concluding that our laser-cooling scheme should maintain the temperature of the gas without significant additional losses.