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arXiv:0904.0238 · New Journal of Physics

Bragg spectroscopy for measuring Casimir–Polder interactions with Bose–Einstein condensates above corrugated surfaces

Gustavo A Moreno, Diego A R Dalvit, Esteban Calzetta

Published Mar 9, 2010• 14 citations
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Abstract

We propose a method to probe dispersive atom–surface interactions by measuring via two-photon Bragg spectroscopy the dynamic structure factor of a Bose–Einstein condensate above corrugated surfaces. This method takes advantage of the condensate coherence to reveal the spatial Fourier components of the lateral Casimir–Polder interaction energy.

DOI
10.1088/1367-2630/12/3/033009

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We propose a method to probe dispersive atom–surface interactions by measuring via two-photon Bragg spectroscopy the dynamic structure factor of a Bose–Einstein condensate above corrugated surfaces. This method takes advantage of the condensate coherence to reveal the spatial Fourier components of the lateral Casimir–Polder interaction energy.
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.
Understanding the Casimir-Polder (CP) attraction between ultracold atoms and dielectric surfaces is of fundamental importance to the design and miniaturization of atom chips [1] and for understanding quantum reflection from, and sticking to, the surface [2 - 6]. So far, calculations have focussed on planar dielectrics, either semi-infinite or of finite width [7-9], and non-planar geometries including corrugated surfaces [10], spheres and carbon nanotubes [11-12]. Here, we present a simple scheme, based on the Pairwise-Summation (PWS) approximation, for estimating the CP interaction between a ground-state alkali atom and a dielectric volume of arbitrary shape. The PWS approximation integrates the van der Waals interaction between two ground-state atoms over the many atoms in the surface volume. We relate the microscopic polarizability of atoms in the surface to the bulk dielectric constant via the Clausius-Mossotti relation within the Lorentz local-field theory. We find that the CP potential depends strongly on both the geometry and density of the surface, which modify the fluctuation spectrum of the electromagnetic field that couples the alkali atoms to the dielectric. We compare our results with known analytical expressions for the CP potential near planar surfaces and use them to investigate how BECs interact with, and may quantum reflect from, curvilinear surface structures.
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.