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arXiv:physics/0608074 · Physical Review Letters

Measurement of the Temperature Dependence of the Casimir-Polder Force

John Obrecht, Robert J. Wild, Mauro Antezza, Лев П. Питаевский, S. Stringari, Eric Cornell

Published Feb 8, 2007• 452 citations
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Abstract

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.

DOI
10.1103/physrevlett.98.063201

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arXiv:0812.1914•Physical Review A•May 7, 2009•29 citations
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.
. 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
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.
The experiment reported by J. M. Obrecht et al. in 2007 provided the first direct measurement of the temperature dependence of the Casimir–Polder interaction between ultracold atoms and a dielectric surface. A nearly pure Bose–Einstein condensate of 87Rb atoms was positioned a few micrometers from a fused-silica substrate, whose temperature was varied while the surrounding environment remained near room temperature. The experiment detected changes in the collective dipole oscillation frequency of the trapped atomic cloud and showed that the Casimir–Polder effect became nearly three times larger when the substrate was heated to approximately 605 K. The results were consistent with the nonequilibrium theory developed by Antezza, Pitaevskii, and Stringari (Obrecht et al. 2007; Antezza, Pitaevskii, and Stringari 2005). This article develops a critical–propositional examination of that experiment in dialogue with the Theory of Objectivity (TO), especially its modal axioms, its conception of boundaries, triangular observation, phenomenic elements, Inducing Effects, cosmogenic theorem, cosmological eras, and its concept of transcendent substance as information or knowledge generated through atomic relations and associated with atomic radiation. Particular attention is given to Absolute Truth I, according to which a logical, mathematical, and eternal Nothingness precedes the universe without being an absolute metaphysical non-being; Absolute Truth II, according to which each existing element possesses its own individualizing magnetic field; and Absolute Truth V, according to which an element possesses logical existence only when it is observed by, or situated within the frequencies of, at least two other elements, observation being understood as physical relation rather than human cognition (Cabannas and Silva 2016, 2018, 2025, 2026f). The central thesis developed here is deliberately restricted. Obrecht et al. do not experimentally verify the modal ontology of the Theory of Objectivity. Their experiment nevertheless provides an unusually productive operational environment for examining some of its proposed bridge principles. Particularly significant are the constitutive role of a material boundary, the measurable influence of electromagnetic fields in the absence of mechanical contact, the relational dependence of the atom–surface interaction on an external thermal environment, and the conversion of thermal and electromagnetic states into experimentally recoverable information. At the same time, major points of tension remain. The quantum vacuum of Casimir–Polder physics cannot be identified with the logical Nothingness of Absolute Truth I. The experiment does not demonstrate that every physical element possesses a unique individualizing magnetic field in the strong sense proposed by Absolute Truth II. Nor does the triadic configuration of atom, substrate, and environment establish that triangular observation constitutes a necessary ontological condition of existence. The equation of radiation, information, and transcendent knowledge also requires an explicit bridge theory not supplied by standard quantum electrodynamics. Accordingly, the article argues that the strongest scientific role of the Obrecht ex- periment for the TO is not retrospective confirmation but prospective operationalization. It provides a model for transforming modal claims into measurable bridge hypotheses. A scientifically discriminating version of the TO must ultimately identify quantitative observables for which its predictions differ from those of quantum electrodynamics and nonequilibrium Lifshitz theory. Keywords: Theory of Objectivity; Casimir–Polder force; quantum vacuum; thermal radiation; nonequilibrium physics; Bose–Einstein condensate; modal ontology; boundary; information; triangular observation; quantum electrodynamics; phenomenic elements.
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 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 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.