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arXiv:1103.0410 · Physical Review A

Laser cooling of a trapped particle with increased Rabi frequencies

Tony Blake, Andreas Kurcz, Norah S. Saleem, Almut Beige

Published Nov 15, 2011• 9 citations
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Abstract

This paper analyzes the cooling of a single particle in a harmonic trap with red-detuned laser light with fewer approximations than previously done in the literature. We avoid the adiabatic elimination of the excited atomic state but are still interested in Lamb-Dicke parameters $\ensuremath{\eta}\ensuremath{\ll}1$. Our results show that the Rabi frequency of the cooling laser can be chosen higher than previously assumed, thereby increasing the effective cooling rate but not affecting the final outcome of the cooling process. Since laser cooling is already a well-established experimental technique, the main aim of this paper is to present a model which can be extended to more complex scenarios, like cavity-mediated laser cooling.

DOI
10.1103/physreva.84.053416

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This paper analyzes the cooling of a single particle in a harmonic trap with red-detuned laser light with fewer approximations than previously done in the literature. We avoid the adiabatic elimination of the excited atomic state but are still interested in Lamb-Dicke parameters \ensuremathη\ensuremath≪1\ensuremath{\eta}\ensuremath{\ll}1\ensuremathη\ensuremath≪1. Our results show that the Rabi frequency of the cooling laser can be chosen higher than previously assumed, thereby increasing the effective cooling rate but not affecting the final outcome of the cooling process. Since laser cooling is already a well-established experimental technique, the main aim of this paper is to present a model which can be extended to more complex scenarios, like cavity-mediated laser cooling.
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 cooling rate for cavity-mediated laser cooling scales as the Lamb-Dicke parameter $\ensuremath{\eta}$ squared. A proper analysis of the cooling process hence needs to take terms up to ${\ensuremath{\eta}}^{2}$ in the system dynamics into account. In this paper, we present such an analysis for a standard scenario of cavity-mediated laser cooling with $\ensuremath{\eta}\ensuremath{\ll}1$. Our results confirm that there are many similarities between ordinary and cavity-mediated laser cooling. However, for a weakly confined particle inside a strongly coupled cavity, which is the most interesting case for the cooling of molecules, numerical results indicate that more detailed calculations are needed to model the cooling process accurately.
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.
Laser cooling of a single trapped ion in a Paul trap is discussed theoretically in the Lamb-Dicke limit, with full consideration of the time dependence of the trapping potential. Resulting mean kinetic energies are defined as time averages over one period of the micromotion and are compared with final temperatures expected from the laser-cooling treatment with harmonic traps. For laser-atom detunings close to the micromotion frequency the results differ significantly from those expected for a harmonic trap potential. A physical interpretation is given and simple formulas are derived for the strong confinement case.
Here we analyze cavity-mediated laser cooling for an experimental setup with an external trap which strongly confines the motion of a particle in the direction of the cavity axis. It is shown that the stationary-state phonon number exhibits three sharp minima as a function of the atom-cavity detuning due to a direct atom-phonon-photon coupling term in the system Hamiltonian. These resonances have the same origin as the Mollow triplet in the resonance fluorescence of a laser-driven atomic system. It is shown that a laser-Rabi-frequency-dependent atom-cavity detuning yields the lowest stationary-state phonon number for a wide range of experimental parameters.
The authors consider the laser cooling of a trapped two-level system during its final approach to equilibrium. Then it moves only within one optical wavelength and an expansion in the Lamb-Dicke parameter is possible. This allows an adiabatic elimination of the internal degrees of freedom. There remains a slow time evolution on a new time scale related to the Lamb-Dicke parameter. This scale is determined by an effective time evolution operator, which the authors derive using the method of degenerate perturbation theory. The ensuing master equation can be completely solved both for its time evolution and the ultimate steady state. In addition to providing a complete description of the final stages of the laser cooling, the calculation can be seen to add one more soluble case to the discussion of non-equilibrium statistical mechanics.