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Physical Review A

Three-dimensional cavity Doppler cooling and cavity sideband cooling by coherent scattering

Vladan Vuletić, Hilton W. Chan, Adam T. Black

Published Aug 2, 2001• 116 citations
Publisher

Abstract

Laser cooling by coherent scattering inside an optical cavity, a method proposed for cooling the motion of arbitrary particles that scatter light, is analyzed in terms of the modified emission spectrum. In contrast to conventional Doppler cooling, this method invokes the two-photon Doppler effect along the direction of the momentum transferred in the scattering process. Three-dimensional cooling can therefore be achieved with a single optical cavity. Both in the free-particle regime (cavity Doppler cooling) and in the strong-confiment regime (cavity sideband cooling) the minimum temperature is determined by the resonator linewidth and independent of the atomic level structure. The cooling efficiency and volume are significantly enhanced in resonators with transverse-mode degeneracy, such as the confocal resonator.

DOI
10.1103/physreva.64.033405

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Laser cooling by coherent scattering inside an optical cavity, a method proposed for cooling the motion of arbitrary particles that scatter light, is analyzed in terms of the modified emission spectrum. In contrast to conventional Doppler cooling, this method invokes the two-photon Doppler effect along the direction of the momentum transferred in the scattering process. Three-dimensional cooling can therefore be achieved with a single optical cavity. Both in the free-particle regime (cavity Doppler cooling) and in the strong-confiment regime (cavity sideband cooling) the minimum temperature is determined by the resonator linewidth and independent of the atomic level structure. The cooling efficiency and volume are significantly enhanced in resonators with transverse-mode degeneracy, such as the confocal resonator.
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We point out a laser cooling method for atoms, molecules, or ions at low saturation and large detuning from the particles' resonances. The moving particle modifies the field inside a cavity with a time delay characteristic of the cavity linewidth, while the field acts on the particle via the light shift. The dissipative mechanism can be interpreted as Doppler cooling based on preferential scattering rather than preferential absorption. It depends on particle properties only through the coherent scattering rate, opening new possibilities for optically cooling molecules or interacting atoms.
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.
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Conventional laser cooling relies on repeated electronic excitations by near-resonant light, which constrains its area of application to a selected number of atomic species prepared at moderate particle densities. Optical cavities with sufficiently large Purcell factors allow for laser cooling schemes, avoiding these limitations. Here, we report on an atom-cavity system, combining a Purcell factor above 40 with a cavity bandwidth below the recoil frequency associated with the kinetic energy transfer in a single photon scattering event. This lets us access a yet-unexplored regime of atom-cavity interactions, in which the atomic motion can be manipulated by targeted dissipation with sub-recoil resolution. We demonstrate cavity-induced heating of a Bose-Einstein condensate and subsequent cooling at particle densities and temperatures incompatible with conventional laser cooling.
The semiclassical dynamics of atoms, when the atoms are confined inside a standing-wave high-finesse resonator, is theoretically studied. The atoms are cooled by scattering processes in which the photons of a transverse laser are coherently scattered into the cavity mode. We derive a Fokker-Planck equation for the atomic center-of-mass variables which allows us to determine the equations of motion in the semiclassical limit for any value of the intensity of the laser field. We extract its prediction for the dynamics when the resonator is essentially in the vacuum state and the atoms are cooled by scattering photons into the cavity mode, which then decays. Its predictions for the stationary atomic distribution are compared with the ones of the Fokker-Planck equation by Domokos et al. [J. Phys. B 34, 187 (2001)], which has been derived under different assumptions. We find full agreement in the considered parameter regime.