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Semi-classical theory of coherent atom cooling with a single mirror

André Xuereb, Péter Horák, Tim Freegarde

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We investigate theoretically a novel optical technique to cool atomic or molecular species without a closed transition: a particle in front of a mirror illuminated by an off-resonant light beam. The interaction between the particle, the pump and the time-delayed reflected pump results in a net loss of energy from the particle to the field and therefore cooling. Cooling rates depending on particle position and coupling parameters are obtained by an analytical perturbative approach. Finally, we present a semiclassical computational model incorporating momentum diffusion, which will eventually allow us to predict steady-state temperatures.

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We investigate theoretically a novel optical technique to cool atomic or molecular species without a closed transition: a particle in front of a mirror illuminated by an off-resonant light beam. The interaction between the particle, the pump and the time-delayed reflected pump results in a net loss of energy from the particle to the field and therefore cooling. Cooling rates depending on particle position and coupling parameters are obtained by an analytical perturbative approach. Finally, we present a semiclassical computational model incorporating momentum diffusion, which will eventually allow us to predict steady-state temperatures.
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.
We study a single incoherently pumped atom moving within an optical high-QQQ resonator in the strong-coupling regime. Using a semiclassical description for the atom and field dynamics, we derive a closed system of differential equations to describe this coupled atom-field dynamics. For sufficiently strong pumping, the system starts lasing when the atom gets close to a field antinode, and the associated light forces provide for self-trapping of the atom. For a cavity mode blue detuned with respect to the atomic transition frequency, this is combined with cavity-induced motional cooling, allowing for long-term steady-state operation of such a laser. The analytical results for temperature and field statistics agree well with our earlier predictions based on quantum Monte Carlo simulations. We find sub-Doppler temperatures that decrease with gain and coupling strength, and can even go beyond the limit of passive cavity cooling. Besides demonstrating the importance of light forces in single-atom lasers, this result also gives strong evidence to enhance laser cooling through stimulated emission in resonators.
The dipole force, which avoids the closed cycle of pumping and spontaneous emission that renders laser cooling unsuitable for molecules, is conservative: without dissipation, particles entering a trap retain the energy to escape. Fortunately, dissipation need not involve spontaneous emission if it instead results from the decoherence or decay of the optical trapping field that is coupled to the particle. To enhance the weak attraction of an atom to its reflection, cavity-mediated cooling recycles light through multiple reflections, amplifying the force and the retardation - a process related to the mechanical amplification in a near confocal cavity [5]. Resonant cavities and structures can increase the retardation, but not the intensity, even when the atoms or particles lie outside them - e.g. when the cavity is the narrow-band coating of a single mirror. Plasmon resonances of a structured metal can enhance both the delay and the optical intensity. Such processes, possible with arrays of micromirrors, resemble speckle field cooling [6], except that spontaneous emission is again replaced by decay of the optical field, and offer a new class of cooling mechanisms in which weak cooling is extended over a broad array, rather than concentrated at the centre of a single external cavity.
We study laser cooling of atoms with narrow-line optical transition, i.e. in regimes when quantum nature of laser-light interactions results significant effect on atom kinetics. We demonstrate the minimum of laser cooing temperature is reached for the light field detuning close to -3 recoil frequency, i.e. is much differ from standard Doppler cooling theory is used for semiclassical description of laser cooling. We define a set of dimensionless parameters that describe the steady state solution of cold atom distribution in laser light and cooling time. The results can be used for analysis an optimal conditions of laser cooling of atoms with narrow lines Ca, Sr and Mg are of interest for optical time standards.