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Physical Review A

Cold atoms in a high-Qring cavity

Markus Gangl, Helmut Ritsch

Published Mar 6, 2000• 69 citations
Publisher

Abstract

We investigate the coupled dynamics of N two-level atoms in the field of a weakly pumped multimode high-Q cavity. While the field mode amplitudes are coupled by the atoms depending on their positions, the motion of the atoms is influenced by the radiation pressure and dipole force induced by the total intracavity field. In the strong coupling regime, where the atom field coupling g dominates the atomic and cavity decay rates (\ensuremath{\Gamma}, \ensuremath{\kappa}) strong correlations between the atoms themselves and between the atoms and the light field build up. For suitable operating conditions an efficient motional cooling of the atoms occurs. At the example of two atoms coupled to two counterpropagating modes in a ring cavity, we show that this can lead to a strong binding force between atoms trapped at a large distance at different antinodes of the cavity field.

DOI
10.1103/physreva.61.043405

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We investigate the coupled dynamics of N two-level atoms in the field of a weakly pumped multimode high-Q cavity. While the field mode amplitudes are coupled by the atoms depending on their positions, the motion of the atoms is influenced by the radiation pressure and dipole force induced by the total intracavity field. In the strong coupling regime, where the atom field coupling g dominates the atomic and cavity decay rates (\ensuremath{\Gamma}, \ensuremath{\kappa}) strong correlations between the atoms themselves and between the atoms and the light field build up. For suitable operating conditions an efficient motional cooling of the atoms occurs. At the example of two atoms coupled to two counterpropagating modes in a ring cavity, we show that this can lead to a strong binding force between atoms trapped at a large distance at different antinodes of the cavity field.
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.
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.
We study the motion of two atoms trapped at distant positions in the field of a driven standing-wave high-QQQ optical resonator. Even without any direct atom-atom interaction the atoms are coupled through their position dependent influence on the intracavity field. For sufficiently good trapping and low cavity losses the atomic motion becomes significantly correlated and the two particles oscillate in their wells preferentially with a $90\ifmmode^\circ\else\textdegree\fi{}$ relative phase shift. The onset of correlations seriously limits cavity cooling efficiency, raising the achievable temperature to the Doppler limit. The physical origin of the correlation can be traced back to a cavity mediated crossfriction, i.e., a friction force on one particle depending on the velocity of the second particle. Choosing appropriate operating conditions allows for engineering these long range correlations. In addition this cross-friction effect can provide a basis for sympathetic cooling of distant trapped clouds.
Cavity-mediated cooling of the center--of--mass motion of a transversally, coherently pumped atom along the axis of a high--Q cavity is studied. The internal dynamics of the atomic dipole strongly coupled to the cavity field is treated by a non-perturbative quantum mechanical model, while the effect of the cavity on the external motion is described classically in terms of the analytically obtained linear friction and diffusion coefficients. Efficient cavity-induced damping is found which leads to steady-state temperatures well-below the Doppler limit. We reveal a mathematical symmetry between the results here and for a similar system where, instead of the atom, the cavity field is pumped. The cooling process is strongly enhanced in a degenerate multimode cavity. Both the temperature and the number of scattered photons during the characteristic cooling time exhibits a significant reduction with increasing number of modes involved in the dynamics. The residual number of spontaneous emissions in a cooling time for large mode degeneracy can reach and even drop below the limit of a single photon.
We show that an ensemble of two-level atoms commonly coupled to a single, driven, damped high-QQQ cavity mode could be cooled and trapped via the correlated dynamics of cavity field and the atomic motion. For sufficiently large detuning between the atoms and the field, spontaneous emission plays no role in the dynamics, and the cooling scheme can be applied to all particles with a sufficient optical dipole moment. The time scale of this collective cooling process increases with the particle number and can be optimized by suitably tailoring the pump field amplitude and frequency. The key properties of the underlying mechanism are discussed using a linearized model, where one can derive a closed set of equations for certain ensemble averages and the field. The results are then compared with N-particle dynamical simulations of the full equations.
We describe the apparatus of an optical cavity loaded with cold 85Rb atoms of high optical depth (OD) in the weak coupling regime. The relevant cavity-atom parameters are the single-photon Rabi frequency g0 = 2π × 0.25 MHz, the cavity power decay rate κ = 2π × 9.0 MHz, and the atomic excited state decay rate Γ = 2π × 5.75 MHz. In this bad-cavity configuration where the atomic natural linewidth (Γ/2π) is less than the cavity linewidth (κ/2π), the cavity enhancement factor for the longitudinal OD is about 188. We obtain a cavity enhanced OD up to 7600, corresponding to an atomic ensemble with a bare single-pass OD of 40, coupled to the cavity mode. Our intracavity cold atomic ensemble with high OD may have many applications in studying collective atom-light interaction inside an optical cavity.