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Annual Meeting Optical Society of America

Cooling and trapping of atoms in the presence of a colored vacuum

THOMAS W. MOSSBERG, Maciej Lewenstein, Daniel J. Gauthier

Published Jan 1, 1991• 0 citations
Publisher

Abstract

The characteristics of dissipative mechanical forces acting on strongly driven atoms depend on the spontaneous decay rate of the driven transition. In previous studies,1 it has been assumed that the spontaneous decay rates arise from the coupling of the atoms to the free-space electromagnetic vacuum reservoir. Recently, it has been shown2 that new and novel physics can arise when the reservoir that mediates atomic relaxation is colored (frequency dependent) as can be accomplished by a suitably designed cavity or waveguide. We show that a two-level atom moving in an intense rest-frame-resonant standing-wave and decaying via coupling to a colored vacuum reservoir experiences a damping force (which is substantially larger than that predicted in other studies) useful in slowing the atom. This force, unlike traditional cooling forces, is effective over a dramatically wide range of atomic velocities. In fact, the force can be effective even for thermal velocity atoms if the vacuum is strongly colored.

DOI
10.1364/oam.1991.tuvv4

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The characteristics of dissipative mechanical forces acting on strongly driven atoms depend on the spontaneous decay rate of the driven transition. In previous studies,1 it has been assumed that the spontaneous decay rates arise from the coupling of the atoms to the free-space electromagnetic vacuum reservoir. Recently, it has been shown2 that new and novel physics can arise when the reservoir that mediates atomic relaxation is colored (frequency dependent) as can be accomplished by a suitably designed cavity or waveguide. We show that a two-level atom moving in an intense rest-frame-resonant standing-wave and decaying via coupling to a colored vacuum reservoir experiences a damping force (which is substantially larger than that predicted in other studies) useful in slowing the atom. This force, unlike traditional cooling forces, is effective over a dramatically wide range of atomic velocities. In fact, the force can be effective even for thermal velocity atoms if the vacuum is strongly colored.
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 semiclassical model of the force and momentum diffusion on a point particle is used to describe the motion of a two-level atom strongly coupled to a single Gaussian cavity mode. The effects of the momentum diffusion on the motion of an atom in a cavity are investigated in a regime similar to that of the experiment performed by Mabuchi et al. [Opt. Lett. 21, 1393 (1996)]. It is found that a slow atom quickly develops significant velocities along the cavity axis. The limited bandwidth in the experiment of Mabuchi et al. means that the full intensity signal due to atomic motion in the standing wave is filtered leading to the apparently smaller velocities observed. It is shown that a negative detuning of the laser and cavity from the atomic resonance would lead to nonzero dipole forces and significantly reduced velocities along the standing wave. An analysis of the intensity signal with a larger bandwidth is proposed, which would track the velocity of the atom along the cavity axis. These results are compared with a Monte Carlo wave-function simulation similar to that used to treat Doppler cooling.
The boundary conditions imposed on the vacuum field by the superconfocal cavity (SCC) create a region of space, the active volume, at the cavity center in which the spectral structure of the vacuum field is perturbed. These perturbations transform the normally white spectrum of the free-space vacuum field into a colored vacuum whose spectrum is a comb of peaks coincident with the cavity resonance frequencies. Operating as designed, atoms resonant with the cavity and in the active region will experience a vacuum field mode density 1.5 times that in free-space. Perturbations in the vacuum field mode density of this magnitude and operative over so large an active volume (1.4 × 107µm3) have not, to our knowledge, been previously achieved in an open optical cavity. We expect to observe a plethora of new and novel phenomena associated with laser–atom interactions in the presence of a colored vacuum. The first experiment will focus on the dynamic suppression of spontaneous emission1 which predicts a dramatic narrowing of the central Mollow peak as the Rabi frequency becomes larger than the FWHM of the SCC-induced peaks in the vacuum field mode density.
We show that a three-level atom in the cascade configuration can be stably trapped and cooled in one dimension by an intense bichromatic standing wave. At the two-photon resonance, rectified dipole forces result in a deep potential well which can be used to localize the atoms in space. In the vicinity of the rectified potential minimum, the spatial dependence of the dressed state energies can lead to a velocity dependence of the force which produces damping of the atomic motion. Consideration of the heating effects of momentum diffusion indicates that cooling and stable trapping at low temperatures is possible in such a bichromatic field.
Interesting new aspects of atomic behavior in the presence of strong driving fields appear when the driven atom resides not in free space, but in a region (such as an optical cavity) that displays a frequency-dependent photon-mode density. Under such conditions, it is found that a strong driving field can modify the spontaneous decay properties of an atom, and thereby give rise to interesting new features in the spectrum of strong-field resonance fluorescence. It is also found that a high level of dressed-state polarization can be maintained in a sample of resonantly or nonresonantly driven atoms by appropriate tuning of an enclosing cavity. Furthermore, for appropriate laser and cavity tunings, it is found that the atomic states become highly squeezed. In the course of analyzing these effects, a set of modified Bloch equations is derived that explicitly accounts for the finite response time associated with a frequency-dependent photon-mode density.