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arXiv:0906.2272 · Physical Review A

Enhancement of thermal Casimir-Polder potentials of ground-state polar molecules in a planar cavity

Simen Å. Ellingsen, Stefan Yoshi Buhmann, Stefan Scheel

Published Aug 13, 2009• 10 citations
arXivHTMLPDF

Abstract

We analyze the thermal Casimir-Polder potential experienced by a ground-state molecule in a planar cavity and investigate the prospects for using such a setup for molecular guiding. The resonant atom-field interaction associated with this nonequilibrium situation manifests itself in oscillating standing-wave components of the potential. While the respective potential wells are normally too shallow to be useful, they may be amplified by a highly reflecting cavity whose width equals a half-integer multiple of a particular molecular transition frequency. We find that with an ideal choice of molecule and the use of a cavity bounded by Bragg mirrors of ultrahigh reflectivity, it may be possible to boost the potential by up to two orders of magnitude. We analytically derive the scaling of the potential depth as a function of reflectivity and analyze how it varies with temperature and molecular properties. It is also shown how the potential depth decreases for standing waves with a larger number of nodes. Finally, we investigate the lifetime of the molecular ground state in a thermal environment and find that it is not greatly influenced by the cavity and remains in the order of several seconds.

DOI
10.1103/physreva.80.022901

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We analyze the thermal Casimir-Polder potential experienced by a ground-state molecule in a planar cavity and investigate the prospects for using such a setup for molecular guiding. The resonant atom-field interaction associated with this nonequilibrium situation manifests itself in oscillating standing-wave components of the potential. While the respective potential wells are normally too shallow to be useful, they may be amplified by a highly reflecting cavity whose width equals a half-integer multiple of a particular molecular transition frequency. We find that with an ideal choice of molecule and the use of a cavity bounded by Bragg mirrors of ultrahigh reflectivity, it may be possible to boost the potential by up to two orders of magnitude. We analytically derive the scaling of the potential depth as a function of reflectivity and analyze how it varies with temperature and molecular properties. It is also shown how the potential depth decreases for standing waves with a larger number of nodes. Finally, we investigate the lifetime of the molecular ground state in a thermal environment and find that it is not greatly influenced by the cavity and remains in the order of several seconds.
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.
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Cold atoms can be trapped and guided using nanofabricated wires on microengineered surfaces, achieving the scales required by quantum information proposals on the consequences of Casimir-Polder (CP) force to its stability and lifetime. The atoms are found to be less attractive to the thin films compared to dielectric half plate, where the attractive potential drops even further when the thickness of the surface is lower than both thermal wavelength and the spacing length. Amiably, for the spherical surface, the CP potential decays even further as radial thickness decreases. We approximate the CP potential using the analytical expression obtained from the pairwise summation (PWS) calculated by taking a sum of single atom with the jumbled atoms inside the surface, treating them as two-bodies system as a whole. The means of PWS are to calculate the possibilities of geometrical effect: planar and curved surface on the CP potential.