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arXiv:0709.2095 · Physical Review Letters

Probing Quantum-Vacuum Geometrical Effects with Cold Atoms

Diego A. R. Dalvit, Paulo A. Maia Neto, Astrid Lambrecht, Serge Reynaud

Published Feb 1, 2008• 72 citations
arXivHTMLPDF

Abstract

The lateral Casimir-Polder force between an atom and a corrugated surface should allow one to study experimentally nontrivial geometrical effects in the electromagnetic quantum vacuum. Here, we derive the theoretical expression of this force in the scattering approach. We show that large corrections to the "proximity force approximation" could be measured using present-day technology with a Bose-Einstein condensate used as a vacuum field sensor.

DOI
10.1103/physrevlett.100.040405

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The lateral Casimir-Polder force between an atom and a corrugated surface should allow one to study experimentally nontrivial geometrical effects in the electromagnetic quantum vacuum. Here, we derive the theoretical expression of this force in the scattering approach. We show that large corrections to the "proximity force approximation" could be measured using present-day technology with a Bose-Einstein condensate used as a vacuum field sensor.
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.
We propose to use a rotating corrugated material plate in order to stir, through the Casimir-Polder interaction, quantized vortices in an harmonically trapped Bose-Einstein condensate. The emergence of such vortices within the condensate cannot be explained with a computation of the Casimir-Polder potential based on the pairwise summation approach or on the proximity force approximation. It thus appears as a genuine signature of non-trivial geometry effects on the electromagnetic vacuum fluctuations, which fully exploits the superfluid nature of the sample. In order to discuss quantitatively the generation of Casimir-driven vortices, we derive an exact non-perturbative theory of the Casimir-Polder potential felt by the atoms in front of the grating. Our numerical results for a Rb condensate close to a Si grating show that the resulting quantum vacuum torque is strong enough to provide a contactless transfer of angular momentum to the condensate and generate quantized vortices under realistic experimental conditions at separation distances around 3 μm.
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.