Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate

TL;DR

This paper investigates how the Casimir-Polder force influences the collective oscillations of a trapped Bose-Einstein condensate near a surface, providing explicit formulas and numerical estimates for frequency shifts in various regimes.

Contribution

It offers a detailed theoretical analysis of the substrate-induced frequency shifts in BEC oscillations, including explicit expressions and numerical results for realistic experimental conditions.

Findings

Frequency shifts of order 10^{-4} at 4-8 μm distances

Thermal effects become significant at these distances

Predictions for radial breathing mode frequency shifts

Abstract

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 details 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 $^{87}$Rb atoms. We find that at distances of $4-8 \mu m$, where thermal effects become visible, the relative frequency shifts produced by the substrate are of the order $10^{-4}$ and hence accessible experimentally. The effects of non linearities due to the finite amplitude of the oscillation are explicitly discussed. Predictions are also given for the radial breathing mode.