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arXiv:quant-ph/0005133 · Physical Review A

Cooling of a single atom in an optical trap inside a resonator

S. J. van Enk, J. McKeever, Harry J. Kimble, J. Ye

Published Jun 6, 2001• 65 citations
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Abstract

We present detailed discussions of cooling and trapping mechanisms for an atom in an optical trap inside an optical cavity, as relevant to recent experiments. The interference pattern of cavity QED and trapping fields in space makes the trapping wells, in principle, distinguishable from one another. This adds considerable flexibility to creating effective trapping and cooling conditions and to detection possibilities. Friction and diffusion coefficients are calculated in and beyond the low excitation limit and full three-dimensional simulations of the quasiclassical motion of a Cs atom are performed.

DOI
10.1103/physreva.64.013407

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We present detailed discussions of cooling and trapping mechanisms for an atom in an optical trap inside an optical cavity, as relevant to recent experiments. The interference pattern of cavity QED and trapping fields in space makes the trapping wells, in principle, distinguishable from one another. This adds considerable flexibility to creating effective trapping and cooling conditions and to detection possibilities. Friction and diffusion coefficients are calculated in and beyond the low excitation limit and full three-dimensional simulations of the quasiclassical motion of a Cs atom are performed.
Two recent experiments have reported the trapping of individual atoms inside optical resonators by the mechanical forces associated with single photons [Hood et al., Science 287, 1447 (2000); Pinkse et al., Nature (London) 404, 365 (2000)]. Here we analyze the trapping dynamics in these settings, focusing on two points of interest. First, we investigate the extent to which light-induced forces in these experiments are distinct from their free-space counterparts, and whether or not there are qualitatively different effects of optical forces at the single-photon level within the setting of cavity QED. Second, we explore the quantitative features of the resulting atomic motion, and how these dynamics are mapped onto experimentally observable variations of the intracavity field. Toward these ends, we present results from extensive numerical simulations of the relevant forces and their fluctuations, as well as a detailed derivation of our numerical simulation method, based on the full quantum-mechanical master equation. Not surprisingly, qualitatively distinct atomic dynamics arise as the coupling and dissipative rates are varied. For the experiment of Hood et al., we show that atomic motion is largely conservative and is predominantly in radial orbits transverse to the cavity axis. A comparison with the free-space theory demonstrates that the fluctuations of the dipole force are suppressed by an order of magnitude. This effect is based upon the Jaynes-Cummings eigenstates of the atom-cavity system and represents distinct physics for optical forces at the single-photon level within the context of cavity QED. By contrast, even in a regime of strong coupling in the experiment of Pinkse et al., there are only small quantitative distinctions between the potentials and heating rates in the free-space theory and the quantum theory, so it is not clear that a description of this experiment as a novel single-quantum trapping effect is necessary. The atomic motion is strongly diffusive, leading to an average localization time comparable to the time for an atom to transit freely through the cavity, and to a reduction in the ability to infer aspects of the atomic motion from the intracavity photon number.
We investigate cooling and trapping of single atoms inside an optical cavity using a quasiresonant field and a far-off-resonant mode of the Laguerre-Gauss type. The far-off-resonant doughnut mode provides an efficient trapping in the case when it shifts the atomic internal ground and excited state in the same way, which is particularly useful for quantum information applications of cavity quantum electrodynamics systems. Long trapping times can be achieved, as shown by full three-dimensional simulations of the quasiclassical motion inside the resonator.
We theoretically analyze the cooling dynamics of an atom which is tightly trapped inside a high-finesse optical resonator. Cooling is achieved by suitably tailored scattering processes, in which the atomic dipole transition either scatters a cavity photon into the electromagnetic field external to the resonator, or performs a stimulated emission into the cavity mode, which then dissipates via the cavity mirrors. We identify the parameter regimes in which the atom center-of-mass motion can be cooled into the ground state of the external trap. We predict that, in particular, for high cooperativities, interference effects mediated by the atomic transition may lead to higher efficiencies. The dynamics is compared with the cooling dynamics of a trapped atom inside a resonator studied by Zippilli and Morigi [Phys. Rev. Lett. 95, 143001 (2005)] where the atom, instead of the cavity, is driven by a laser field.
We review the modifications and implications of the effect of light forces on atoms when the field is enclosed in an optical resonator of high finesse. The systems considered range from a single atom strongly coupled to a single mode of a high-Q microcavity to a large ensemble of atoms in a highly degenerate quasi-confocal resonator. We set up general models that allow us to obtain analytic expressions for the optical potential, friction, and diffusion. In the bad-cavity limit the modified cooling properties can be attributed to the spectral modifications of light absorption and spontaneous emission in a form of generalized and enhanced Doppler cooling. For the strong coupling regime in a good cavity, we identify the dynamical coupling between the light field intensity and the atomic motion as the central mechanism underlying the cavity-induced cooling. The dynamical cavity cooling, which does not rely on spontaneous emission, can be enhanced by multimode cavity geometries because of the effect of coherent photon redistribution between different modes. The model is then generalized to include several distinct frequencies to account for more general trap geometries. Finally we show that the field-induced buildup of correlations between the motion of different particles plays a central role in the scaling behavior of the system. Depending on the geometry and parameters, its effect ranges from strong destructive interference, slowing down the cooling process, to self-organized crystallization, implying atomic self-trapping and faster cooling to lower temperatures by cooperative coherent scattering.
We investigate the external and internal dynamics of a two-level atom strongly coupled to a weakly pumped nanophotonic cavity. We calculate the dipole force, friction force, and stochastic force due to the cavity pump field and show that a three-dimensional cooling region exists near the surface of a cavity. Using a two-color evanescent field trap as an example, we perform three-dimensional Monte Carlo simulations to demonstrate the efficient loading of single atoms into a trap by momentum diffusion, and the stability of cavity cooling near the trap center. Our analyses show that cavity cooling can be a promising method for directly loading cold atoms from free space into a surface microtrap. We further discuss the impact of pump intensity on atom trapping and loading efficiency.