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arXiv:cond-mat/0506208 · Physical Review A

Measurement of the Casimir-Polder force through center-of-mass oscillations of a Bose-Einstein condensate

D. M. Harber, John Obrecht, J. M. McGuirk, Eric Cornell

Published Sep 13, 2005• 269 citations
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Abstract

We have performed a measurement of the Casimir-Polder force using a magnetically trapped $^{87}\mathrm{Rb}$ 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.

DOI
10.1103/physreva.72.033610

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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∼5\ensuremathμm\ensuremath{\sim}5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ensuremath∼5\ensuremathμm, 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∼1\ensuremathμm\ensuremath{\sim}1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ensuremath∼1\ensuremathμm range.
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 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.
Abstract Modern laboratory techniques make possible the investigation of the role of the Casimir–Polder force in experiments on Bose–Einstein condensation and quantum reflection. Thus, it has been demonstrated that the collective oscillations of a Bose–Einstein condensate of ultracold atoms provide a sensitive probe of Casimir–Polder forces. Later, the first measurement of the temperature dependence of the Casimir–Polder force was performed in this way. The Casimir–Polder interaction plays an important role in the scattering of atoms on various surfaces. Of special interest are situations where the wave nature of an atom dominates in comparison with its classical behavior as a particle (this is referred to as quantum reflection). This chapter considers both of the latter two types of experiments in connection with the properties of the Casimir–Polder force.
. 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
We investigate the stability of magnetically trapped atomic Bose-Einstein condensates and thermal clouds near the transition temperature at small distances $0.5\text{ }\ensuremath{\mu}\mathrm{m}\ensuremath{\le}d\ensuremath{\le}10\text{ }\ensuremath{\mu}\mathrm{m}$ from a microfabricated silicon chip. For a $2\text{ }\ensuremath{\mu}\mathrm{m}$ thick copper film, the trap lifetime is limited by Johnson noise induced currents and falls below 1 s at a distance of $4\text{ }\ensuremath{\mu}\mathrm{m}$. A dielectric surface does not adversely affect the sample until the attractive Casimir-Polder potential significantly reduces the trap depth.