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arXiv:quant-ph/0302131 · Physical Review A

Collective sideband cooling in an optical ring cavity

Th. Elsässer, Boris Nagorny, Andreas Hemmerich

Published May 13, 2003• 30 citations
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Abstract

We propose a cavity-based laser-cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave that acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate traveling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high-frequency component, which is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering.

DOI
10.1103/physreva.67.051401

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We propose a cavity-based laser-cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave that acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate traveling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high-frequency component, which is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering.
Cavity cooling of an atom works best on a cyclic optical transition in the strong coupling regime near resonance, where small-cavity photon numbers suffice for trapping and cooling. A straightforward application to the cooling of the translational motion of other polarizable particles without sharply defined two-level transitions (such as molecules) fails as optical pumping transfers the particle into uncoupled states. An alternative operation in the far-off-resonant regime generates only very slow cooling due to the reduced field-particle coupling. We suggest one can overcome this by using a strongly driven ring cavity operated in the sideband cooling regime. The dynamics can be mapped onto the optomechanics setup with a movable mirror and allows one to take advantage of a collectively enhanced field-particle coupling by large photon numbers. A linearized analytical treatment confirmed by full numerical quantum simulations predicts fast cooling despite the off-resonant small single-particle--single-photon coupling. Even ground-state translational cooling (in the external potential) can be obtained by tuning the cavity field close to the Anti-stokes sideband for sufficiently high trapping frequency. Numerical simulations show quantum jumps of the particle between the lowest two trapping levels, which can be directly and continuously monitored via scattered light intensity detection.
We present a simple and general optical cooling method based on 3D degenerate Raman sideband cooling with adiabatic release that goes significantly beyond the density and temperature limitations of optical molasses. In 10 ms we cool a sample of 3×108 cesium atoms to a temperature of 330 nK at a density of 1.1×1011 cm−3, which corresponds to a phase-space density nλdB3=1/500.We further propose to cool atoms or molecules inside an optical cavity that enhances the scattering of blue-detuned photons and show that the dissipative mechanism can be viewed as a cavity-induced generalized Doppler cooling. Since the cooling depends on the atom’s internal level structure only through the photon scattering rate, cavity Doppler cooling is applicable to particles that do not possess a closed optical transition, which may allow one to extend laser cooling to a greater class of atoms or molecules. Large samples are cooled at the same rate as single atoms if the effect of one atom on the cavity resonance frequency is small. We also show how to achieve 3D cooling with a single optical cavity.
We discuss a scheme to cool, trap and manipulate an ensemble of polarizable particles moving in the field of a multimode optical cavity via the correlated dynamics of the field and the particle motion. Using a large detuning between the atoms and the field, spontaneous emission plays a negligible role in the dynamics and the cooling scheme only requires a sufficiently large optical dipole moment. Increasing the particle number slows down the cooling process but it can be accelerated using an increasing number of field modes with higher pump amplitudes. For the special case of a two mode ring cavity and assuming small deviations of the particle positions from the potential minima, the frequencies and damping rates of the vibrational excitation modes can be explicitly calculated. We find a rapid damping of the centre-of-mass motion and relatively slow damping rates for the relative particle oscillations. These predictions agree quite well with a quantum treatment of the atomic motion as used for the excitations of a non-interacting Bose gas (at T = 0) inside the cavity field. Due to the position-dependent mode coupling, the cooling process in a multimode configuration in general happens much faster than for a standing wave geometry. These analytical results are confirmed by N-particle simulations of the semiclassical equations and show even enhanced damping due to the anharmonicity of the full potential.
We propose a ground-state cavity-mediated cooling scheme for a trapped atom, which is in the $\ensuremath{\Lambda}$ configuration and confined inside a high-finesse optical cavity, using a standing-wave cooling laser. The carrier transition can be prohibited by placing the atom at the node of the cavity field, and the blue-sideband transition can be simultaneously eliminated by exploiting quantum interference via tuning the frequency of the cooling laser. As a consequence, the ground-state cooling for the trapped atom can be achieved. Moreover, we numerically demonstrate the superiority by placing the atom at the antinode of the standing-wave cooling laser as compared with the running-wave cooling laser, and the robustness of the scheme using the standing-wave laser. Meanwhile, the cooling rate can reach the same order of magnitude as that obtained in the cavity--electromagnetically-induced-transparency cooling scheme, and the explicit expression for the final phonon number in higher order is also presented.
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.
Based on a classical point particle description, we study light induced transverse collimation and phase space compression of a fast molecular beam traversing the crossover region of a high- Q optical cavity and a standing-wave laser beam. The molecules scatter pump laser light, far detuned from any molecular transition, into the resonant cavity mode. We show that despite a very small probability for this process for a single particle, collective enhancement can lead to significant transverse cooling and collimation above the self-organization threshold. The analytical formulae for this threshold derived from homogeneous one-dimensional (1D) models give surprisingly good estimates for the pulsed 3D case. We compare ring and standing wave cavity geometries and show that phase space compression can be achieved even for extremely small particle field coupling if compensated by a large density and pump power. In the vicinity of the critical point the compression time can be reduced by tailored seeding of the cavity mode or using a second buildup cavity for the pump field.