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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

First observation of the temperature dependence of the van der Waals Casimir-Polder interaction in the condition of thermal equilibrium

Athanasios Laliotis, Thierry Passerat de Silans, M.–P. Gorza, Isabelle Maurin, Philippe Ballin, M. Ducloy, Daniel Bloch

Published May 1, 2011• 1 citation
Publisher

Abstract

The Casimir-Polder (C-P) interaction between an atom and a surface, described as early as 1948, but observed much later on, is now a topic of broad interest, as connected to fundamental problems of quantum fluctuations, with the atomic energy levels renormalized by the wall-dependent vacuum fluctuations. Dependence of the C-P interaction with the equilibrium temperature is predicted, but had not been observed until now. However, more pronounced effects were predicted in an out-of-equilibrium situation, and were remarkably observed on a Rb BEC, at 6-10 μm from the wall, with the vacuum temperature (~ 300K) strongly differing from the surface temperature (~ 1000 K).

DOI
10.1109/cleoe.2011.5943461

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The Casimir-Polder (C-P) interaction between an atom and a surface, described as early as 1948, but observed much later on, is now a topic of broad interest, as connected to fundamental problems of quantum fluctuations, with the atomic energy levels renormalized by the wall-dependent vacuum fluctuations. Dependence of the C-P interaction with the equilibrium temperature is predicted, but had not been observed until now. However, more pronounced effects were predicted in an out-of-equilibrium situation, and were remarkably observed on a Rb BEC, at 6-10 μm from the wall, with the vacuum temperature (~ 300K) strongly differing from the surface temperature (~ 1000 K).
Summary form only given. Experimental studies of the atom-surface or surface-surface interactions provide a physical insight on the interaction of quantum bodies with the fluctuating vacuum. They can be of great practical interest in the ever expanding field of nanotechnologies. In particular the dependence of the Casimir and Casimir-Polder interaction on the thermal fluctuations is a fundamental effect that could in the future provide a useful knob for tuning these interactions. Temperature effects are usually very small and have so far been observed on a BEC placed 6-10 μm away from a fused-silica substrate due to an out of thermal equilibrium enhancement. Here we report on spectroscopic selective reflection measurements of the interaction between a Cs (7D3/2) atom and a sapphire surface. A virtual coupling between a surface resonance of sapphire at 12.1 μm and the Cs 7D3/2Æ5F5/2 transition at 10.8 μm almost eliminates the resonant contribution for this dipole transition. Reaching the temperatures required to observe an effect is extremely challenging. For this reason our experiment is performed in an all-sapphire vapour cell with super polished windows with an annealing post-treatment. The interaction is probed up to unusually high temperatures reaching more than 1000 K. Experimental measurements show C3coefficient as a function of temperature compared to a full QED calculation. Each point is deduced by fitting reflection spectra to a theoretical model and is averaged for different vapour densities and different spots on the window. Statistical and systematic uncertainties have been reduced compared to our previous experiments performed on a different all-sapphire cell with windows of uncertain surface quality. The chemical stability of sapphire under these extreme conditions seems to be a key factor for this experimental achievement. Previous measurements between Cs (8P3/2) and a CaF2surface in a specially designed cell were unsuccessful due to chemical deterioration of the surface. This experiment is the first to provide a sensitive measurement of temperature effects on the atom-surface interaction in thermal equilibrium and highlights the QED nature of van der Waals regime.
The modification of quantum fluctuations by a surface of finite reflectivity shifts the energy levels of atoms and changes their radiative properties (Casimir-Polder effect). At nanometric distances away from a surface (near field), the Casimir-Polder energy shift is given by −C3/z3 (where C3 is the van der Waals coefficient and z is the atom-surface distance) corresponding to the interaction of the fluctuating atomic dipole with its surface induced image. Near field Rydberg-surface interactions are of fundamental interest because the atomic size, scaling as n∗2 (where n∗ is the principle quantum number corrected by the quantum defect), is no longer negligible compared to the atom-surface separation, z. In this case, the dipole approximation, (−C3/z3 law of interaction), is no longer valid and higher-order terms, corresponding to the interaction of the fluctuation quadrupole with its own image, need to be taken into account. Quadrupole interaction terms in the atom-surface interaction manifest themselves with a novel distance dependence of z5 that has not been experimentally investigated yet1. Casimir-Polder experiments were first performed with low-lying Rydberg states (n= 10-14), demonstrating the −C3/z3 law of interaction2. Nevertheless, more recent experiments with high-lying rubidium Rydbergs (n=32-43)3 were not in agreement with Casimir-Polder theory thus highlighting the need for further experimental studies.
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 distance dependence of the anisotropic atom-wall interaction is studied. The central result is the 1/z61/{z}^{6}1/z6 quadrupolar anisotropy decay in the retarded Casimir-Polder regime. Analysis of the transition region between nonretarded van der Waals regime (in 1/z31/{z}^{3}1/z3) and Casimir-Polder regime shows that the anisotropy crossover occurs at very short distances from the surface, on the order of $0.03\ensuremath{\lambda}$, where $\ensuremath{\lambda}$ is the atom characteristic wavelength. Possible experimental verifications of this distance dependence using surface-induced inelastic transitions are discussed.
The 1%-accurate calculations of the van der Waals interaction between an atom and a cavity wall are performed in the separation region from 3nmto150nm3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}150\phantom{\rule{0.3em}{0ex}}\mathrm{nm}3nmto150nm. The cases of metastable He∗{\mathrm{He}}^{*}He∗ and Na atoms near metal, semiconductor, and dielectric walls are considered. Different approximations to the description of wall material and atomic dynamic polarizability are carefully compared. The smooth transition to the Casimir-Polder interaction is verified. It is shown that to obtain accurate results for the atom-wall van der Waals interaction at short separations with an error less than 1% one should use the complete optical-tabulated data for the complex refractive index of the wall material and the accurate dynamic polarizability of an atom. The obtained results may be useful for the theoretical interpretation of recent experiments on quantum reflection and Bose-Einstein condensation of ultracold atoms on or near surfaces of different kinds.