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arXiv:0810.4281 · Physical Review A

Thermal disequilibrium effects in quantum reflection

В. В. Дружиніна, Marcel Carto Constantin Mudrich, Florian Arnecke, Javier Madroñero, Andreas Buchleitner

Published Sep 28, 2010• 8 citations
arXivHTMLPDF

Abstract

We show that the quantum reflection coefficient of ultracold heavy atoms scattering off a dielectric surface can be tuned in a wide range by suitable choice of surface and environment temperatures. This effect results from a temperature-dependent repulsive part of the van der Waals-Casimir-Polder-Lifshitz atom-surface interaction potential.

DOI
10.1103/physreva.82.032714

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When cold atoms approach a surface, they can be quantum reflected by quantal regions in the tail of the atom-surface potential. We study the phase of the reflection amplitude for Casimir--van der Waals potential tails, depending on the critical parameter $\ensuremath{\rho}=\ensuremath{\rho}({C}_{3},{C}_{4})$, which describes the relative importance of the $\ensuremath{-}{C}_{3}∕{r}^{3}$ and $\ensuremath{-}{C}_{4}∕{r}^{4}$ parts of the potential. The phase is related to observable kinematic quantities, the space and time shifts, the reflected atom experiences. We study three different models for the shape of the potential between the asymptotic limits and observe that the phases are more sensitive to the potential shape than the quantum reflection probabilities. At threshold, there are always time delays in comparison to the free movement. This is in contrast to the classical movement, which shows time gains. Further above threshold, the quantum reflected atom experiences a time gain relative to free motion, but this time gain is generally smaller than that of the classical particle.

Physical Review A•Sep 23, 2004•53 citations
We show that the quantum reflection coefficient of ultracold heavy atoms scattering off a dielectric surface can be tuned in a wide range by suitable choice of surface and environment temperatures. This effect results from a temperature-dependent repulsive part of the van der Waals-Casimir-Polder-Lifshitz atom-surface interaction potential.
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.
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.
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.
When cold atoms approach a surface, they can be quantum reflected by quantal regions in the tail of the atom-surface potential. We study the phase of the reflection amplitude for Casimir--van der Waals potential tails, depending on the critical parameter $\ensuremath{\rho}=\ensuremath{\rho}({C}_{3},{C}_{4})$, which describes the relative importance of the $\ensuremath{-}{C}_{3}∕{r}^{3}$ and $\ensuremath{-}{C}_{4}∕{r}^{4}$ parts of the potential. The phase is related to observable kinematic quantities, the space and time shifts, the reflected atom experiences. We study three different models for the shape of the potential between the asymptotic limits and observe that the phases are more sensitive to the potential shape than the quantum reflection probabilities. At threshold, there are always time delays in comparison to the free movement. This is in contrast to the classical movement, which shows time gains. Further above threshold, the quantum reflected atom experiences a time gain relative to free motion, but this time gain is generally smaller than that of the classical particle.