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arXiv:1002.4036 · Journal of the Physical Society of Japan

Enhanced Cooling of a Λ-Type Three-Level Atom in a High-Finesse Optical Cavity

Lei Tan, Li-Wei Liu, Yu-Qing Zhang

Published Apr 26, 2010• 2 citations
arXivHTMLPDF

Abstract

A theoretical study is carried out for the cavity cooling of a $Λ$-type three level atom in a high-finesse optical cavity with a weakly driven field. Analytical expressions for the friction, diffusion coefficients and the equilibrium temperatures are obtained by using the Heisenberg equations, then they are calculated numerically and shown graphically as a function of controlling parameters. For a suitable choice of these parameters, the dynamics of the cavity field interaction with the $Λ$-type three-level atom introduces a sisyphus cooling mechanism yielding lower temperatures below the Doppler limit and allowing larger cooling rate, avoiding the problems induced by spontaneous emission.

DOI
10.1143/jpsj.79.054401

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A theoretical study is carried out for the cavity cooling of a ΛΛΛ-type three level atom in a high-finesse optical cavity with a weakly driven field. Analytical expressions for the friction, diffusion coefficients and the equilibrium temperatures are obtained by using the Heisenberg equations, then they are calculated numerically and shown graphically as a function of controlling parameters. For a suitable choice of these parameters, the dynamics of the cavity field interaction with the ΛΛΛ-type three-level atom introduces a sisyphus cooling mechanism yielding lower temperatures below the Doppler limit and allowing larger cooling rate, avoiding the problems induced by spontaneous emission.
A theoretical study is carried out for the modification and implication of the effect on the Ξ-type three level atom in a high-finesse optical cavity driven by light field including spontaneous emission and the cavity decay. Analytic expressions for the dipole force, the friction force, the optical potentials and the friction coefficient are obtained. Then the numerical and graphical methods are used to investigate the friction coefficient with the controlling parameters. It is shown that the friction coefficient is strongly dependent on the controlling parameters. The cooling rate can increase by one order of magnitude more than that of a two-level atomic system. The reason can be given using the dressed states and the Sisyphus cooling mechanism, which would stimulate further experimental investigations.
We investigate the external and internal dynamics of a two-level atom in a standing wave cavity. In the strong coupling regime, where the atom field coupling ggg dominates the atomic and cavity decay rates (\ensuremath{\Gamma},\ensuremath{\kappa}), a cooling mechanism entirely different from free-space Doppler cooling appears. Under suitable operating conditions, the cavity dynamics induces a Sisyphus type cooling, which is the dominant contribution to the total friction force acting on a moving atom. Simple equations describing the key properties of this effect are derived from a completely classical picture and confirmed by a semiclassical approach. The model is investigated in the bad and good cavity limits, and analytic expressions for the friction coefficient and the momentum diffusion for slow atoms are derived. Using a continued fractions expansion the cooling force for arbitrary velocities is evaluated numerically. The result is used to calculate the equilibrium temperatures of the atom of the order of $\mathrm{kT}\ensuremath{\approx}\ensuremath{\Elzxh}\ensuremath{\kappa},$ which can be much lower than the free-space Doppler limit and agree well to those obtained by quantum wave-function simulations.
A theoretical study is carried out for the cavity cooling of a V-type three-level atom in a high-finesse optical cavity driven by a light field. The dynamical equations are obtained by a semiclassical approach, which is based on the joint atom-field Wigner function of both the motional atomic degrees of freedom and cavity field, including the spontaneous emission and cavity decay. The numerical results show that the highest cooling rate of the V-type three-level atom can be increased 10 times that of a two-level atom. In addition, the cooling rate can be significantly improved by modulating parameters.
We investigate the possibility of all optical trapping and cooling a single atom at the antinodes of a high QQQ optical cavity mode to which the atom is strongly coupled. For properly chosen parameters the dynamics of the cavity field introduces a novel Sisyphus type cooling mechanism yielding final temperatures much below the Doppler limit and allowing for long trapping times, avoiding the problems induced by spontaneous emission.
We extend an earlier semiclassical model to describe the dissipative motion of N atoms coupled to M modes inside a coherently driven high-finesse cavity. The description includes momentum diffusion via spontaneous emission and cavity decay. Simple analytical formulas for the steady-state temperature and the cooling-time for a single atom are derived and show surprisingly good agreement with direct stochastic simulations of the semiclassical equations for N atoms with properly scaled parameters. A thorough comparison with standard free-space Doppler cooling is performed and yields a lower temperature and a cooling-time enhancement by a factor of M times the square of the ratio of the atom-field coupling constant to the cavity decay rate. Finally, it is shown that laser cooling with negligible spontaneous emission should indeed be possible, especially for relatively light particles in a strongly coupled field configuration.