Momentum diffusion for coupled atom-cavity oscillators

Abstract

It is shown that the momentum diffusion of free-space laser cooling has a natural correspondence in optical cavities when the internal state of the atom is treated as a harmonic oscillator. We derive a general expression for the momentum diffusion which is valid for most configurations of interest: The atom or the cavity or both can be probed by lasers, with or without the presence of traps inducing local atomic frequency shifts. It is shown that, albeit the (possibly strong) coupling between atom and cavity, it is sufficient for deriving the momentum diffusion to consider that the atom couples to a mean cavity field, which gives a first contribution, and that the cavity mode couples to a mean atomic dipole, giving a second contribution. Both contributions have an intuitive form and present a clear symmetry. The total diffusion is the sum of these two contributions plus the diffusion originating from the fluctuations of the forces due to the coupling to the vacuum modes other than the cavity mode (the so called spontaneous emission term). Examples are given that help to evaluate the heating rates induced by an optical cavity for experiments operating at low atomic saturation. We also point out intriguing situations where the atom is heated although it cannot scatter light.Comment: More information adde

Trapping and Observing Single Atoms in a Blue-Detuned Intracavity Dipole Trap

“…While trapped, the atom heats up due to spontaneous emission and dipole-force fluctuations [8,9]. The latter heating process is largely compensated by cavity cooling [5].…”

“…Because the energy gain due to guiding and switching is kept small, the requirement to cool the atom after the capture process is relaxed. (5) Since during the whole loading sequence the atomic detuning is preserved, parameter regimes of large cavity-enhanced heating [8,9] can be avoided. The experimental setup presented in Fig.…”

Rate-equation approach to cavity-mediated laser cooling

“…1 and 2 which has already been studied by many authors [27,28,35,36,[39][40][41][42][43][44][45][46][47]. Analogously to ordinary laser cooling [48][49][50], the effective cooling rate of cavity-mediated laser cooling scales as the Lamb-Dicke parameter η squared.…”

“…[25,26]. Later, Ritsch and collaborators [27][28][29][30][31], Vuletić et al [32,33], and others [34][35][36][37] developed semiclassical theories to model cavity-mediated cooling processes very efficiently. The analysis of cavity-mediated laser cooling based on a master equation approach was pioneered by Cirac et al [38] in 1993.…”

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“…Because of the tight confinement, it is expected that stimulated Raman sideband cooling can be employed [25]. Heating in the trap is expected to be small due to the low-excitation probability of the atom and because the atom is strongly in the Lamb-Dicke regime [26], which means momentum diffusion [27] is strongly suppressed. Experimentally, multiple coupled cavities can also be readily fabricated on the same device [28].…”