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arXiv:cond-mat/0511341 · Journal of Physics A Mathematical and General

Surface–atom force out of thermal equilibrium and its effect on ultra-cold atoms

Mauro Antezza

Published May 10, 2006• 63 citations
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Abstract

The surface–atom Casimir–Polder–Lifshitz force out of thermal equilibrium is investigated in the framework of macroscopic electrodynamics. Particular attention is devoted to its large distance limit that shows a new, stronger behaviour with respect to the equilibrium case. The frequency shift produced by the surface–atom force on the centre-of-mass oscillations of a harmonically trapped Bose–Einstein condensate and on the Bloch oscillations of an ultra-cold fermionic gas in an optical lattice are discussed for configurations out of thermal equilibrium.

DOI
10.1088/0305-4470/39/21/s02

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Bulletin of the American Physical Society•May 17, 2006•1 citation
The surface–atom Casimir–Polder–Lifshitz force out of thermal equilibrium is investigated in the framework of macroscopic electrodynamics. Particular attention is devoted to its large distance limit that shows a new, stronger behaviour with respect to the equilibrium case. The frequency shift produced by the surface–atom force on the centre-of-mass oscillations of a harmonically trapped Bose–Einstein condensate and on the Bloch oscillations of an ultra-cold fermionic gas in an optical lattice are discussed for configurations out of thermal equilibrium.
We calculate the effect of the interaction between an optically active material and a Bose-Einstein condensate on the collective oscillations of the condensate. We provide explicit expressions for the frequency shift of the center-of-mass oscillation in terms of the potential generated by the substrate and of the density profile of the gas. The form of the potential is discussed in detail and various regimes (van der Waals--London, Casimir-Polder, and thermal regimes) are identified as a function of the distance of atoms from the surface. Numerical results for the frequency shifts are given for the case of a sapphire dielectric substrate interacting with a harmonically trapped condensate of 87Rb^{87}\mathrm{R}\mathrm{b}87Rb atoms. We find that at distances of $4--8\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, where thermal effects become visible, the relative frequency shifts produced by the substrate are of the order ${10}^{\ensuremath{-}4}$ and hence accessible experimentally. The effects of nonlinearities due to the finite amplitude of the oscillation are explicitly discussed. Predictions are also given for the radial breathing mode.
We study the influence of thermal Casimir-Polder forces on the near-surface trapping of cold polar molecules, with emphasis on LiH and YbF near a Au surface at room temperature. We show that even for a molecule initially prepared in its electronic and rovibrational ground state, the Casimir-Polder force oscillates with the molecule-wall separation. The nonresonant force and the evanescent part of the resonant force almost exactly cancel at high temperature which results in a saturation of the (attractive) force in this limit. This implies that the Casimir-Polder force on a fully thermalized molecule can differ dramatically from that obtained using a naive perturbative expansion of the Lifshitz formula based on the molecular ground-state polarizability. A dynamical calculation reveals how the spatial oscillations die out on a typical time scale of several seconds as thermalization of the molecule with its environment sets in.
We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure 87Rb Bose-Einstein condensate a few microns from a dielectric substrate and exciting its dipole oscillation. Changes in the collective oscillation frequency of the magnetically trapped atoms result from spatial variations in the surface-atom force. In our experiment, the dielectric substrate is heated up to 605 K, while the surrounding environment is kept near room temperature (310 K). The effect of the Casimir-Polder force is measured to be nearly 3 times larger for a 605 K substrate than for a room-temperature substrate, showing a clear temperature dependence in agreement with theory.
We have performed a measurement of the Casimir-Polder force using a magnetically trapped 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate. By detecting perturbations of the frequency of center-of-mass oscillations of the condensate perpendicular to the surface, we are able to detect this force at a distance $\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$, significantly farther than has been previously achieved, and at a precision approaching that needed to detect the modification due to thermal radiation. Additionally, this technique provides a limit for the presence of non-Newtonian gravity forces in the $\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ range.
We derive an expression for the collective Casimir-Polder interaction of a trapped gas of condensed bosons with a plane surface through coupling of the condensate atoms with the electromagnetic field. A systematic perturbation theory is developed based on a diagrammatic expansion of the electromagnetic self-energy. In the leading order, the result for the interaction energy is proportional to the number of atoms and involves the one-body density matrix of the trapped gas. At this order, atom-atom interactions and recoil effects lead to corrections compared to the single-atom theory, through shifts of the atomic transition energies. We also discuss the impact of spatial delocalization of the condensate mode.
. In particular, when the tem-perature of the surface is different from the temperature of free space, the forceis predicted to decay more slowly at large distances and to exhibit a strongerdependence on the temperature. By positioning a Rb-87 Bose-Einstein con-densate a few microns from a dielectric surface and resonantly exciting it intoa mechanical dipole oscillation, the JILA team has recently observed changesin the collective oscillation frequency that result from the spatial variations inthe force