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arXiv:0809.5229 · Physical Review A

Lifshitz theory of atom-wall interaction with applications to quantum reflection

V. B. Bezerra, G. L. Klimchitskaya, V. M. Mostepanenko, C. Romero

Published Oct 22, 2008• 72 citations
arXivHTMLPDF

Abstract

The Casimir-Polder interaction of an atom with a metallic wall is investigated in the framework of the Lifshitz theory. It is demonstrated that in some temperature (separation) region the Casimir-Polder entropy takes negative values and goes to zero when the temperature vanishes. This result is obtained both for an ideal metal wall and for real metal walls. Simple analytical representations for the Casimir-Polder free energy and force are also obtained. These results are used to make a comparison between the phenomenological potential used in the theoretical description of quantum reflection and exact atom-wall interaction energy, as given by the Lifshitz theory. Computations are performed for the atom of metastable ${\mathrm{He}}^{*}$ interacting with metal (Au) and dielectric (Si) walls. It is shown that the relative differences between the exact and phenomenological interaction energies are smaller in the case of a metallic wall. This is explained by the effect of negative entropy which occurs only for a metal wall. More accurate atom-wall interaction energies computed here can be used for the interpretation of measurement data in the experiments on quantum reflection.

DOI
10.1103/physreva.78.042901

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The Casimir-Polder interaction of an atom with a metallic wall is investigated in the framework of the Lifshitz theory. It is demonstrated that in some temperature (separation) region the Casimir-Polder entropy takes negative values and goes to zero when the temperature vanishes. This result is obtained both for an ideal metal wall and for real metal walls. Simple analytical representations for the Casimir-Polder free energy and force are also obtained. These results are used to make a comparison between the phenomenological potential used in the theoretical description of quantum reflection and exact atom-wall interaction energy, as given by the Lifshitz theory. Computations are performed for the atom of metastable He∗{\mathrm{He}}^{*}He∗ interacting with metal (Au) and dielectric (Si) walls. It is shown that the relative differences between the exact and phenomenological interaction energies are smaller in the case of a metallic wall. This is explained by the effect of negative entropy which occurs only for a metal wall. More accurate atom-wall interaction energies computed here can be used for the interpretation of measurement data in the experiments on quantum reflection.
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.
We consider the out-of-thermal-equilibrium Casimir-Polder interaction between atoms of He*, Na, Cs, and Rb and a cavity wall made of sapphire coated with a vanadium dioxide film which undergoes the dielectric-to-metal phase transition with increasing wall temperature. Numerical computations of the Casimir-Polder force and its gradient as the functions of atom-wall separation and wall temperature are made when the latter exceeds the temperature of the environment. The obtained results are compared with those in experiment on measuring the gradient of the Casimir-Polder force between 87Rb atoms and a silica glass wall out of thermal equilibrium. It is shown that the use of phase-change wall material significantly increases the force magnitude and especially the force gradient, as opposed to the case of a dielectric wall.
Collisions between ultracold atoms and material surfaces are characterized by the reflection of the atomic matter wave from the attractive Casimir-Polder potential. This quantum reflection is particularly relevant to experiments such as GBAR, which will determine the gravitational acceleration of a cold antihydrogen atom by timing its fall onto a detection plate. In this thesis, the Casimir-Polder potential is computed from the electromagnetic scattering properties of the atom and surface and it is found to depend notably on the dielectric response, thickness and density of the medium. We show that reflection on this potential is associated with a breakdown of the semiclassical approximation and that it is enhanced for slow atoms and weak potentials. Liouville transformations relate Schrödinger equations with different potential landscapes but identical scattering properties. We gain new insights on the problem of quantum reflection on a potential well by mapping it onto an equivalent problem of tunneling through a wall. We also discuss the effect of gravity on the atomic wavepacket and its implications for free fall experiments with atoms. When combined with quantum reflection from a horizontal mirror, gravity can be used to trap particles in long lived states with promising applications for metrology. In particular, we suggest a scheme to improve the precision of the GBAR experiment by reducing the velocity dispersion of the falling atoms.
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.
We investigate the quantum reflection governed by the Casimir?Polder potential which scales as ?1/r3 at short separation and as ?1/r4 at long separation. Using the available analytical solutions for the ?1/r4 potential and quantum defect theory, we develop a three-parameter model for quantum reflection. The three parameters characterizing the potential are essentially constant near the threshold. The application scope of the model is examined. For a potential dominated by the ?1/r4 behaviour, which is the case in many realistic atom?surface systems, our model gives accurate results over the energy range in which the quantum reflection is significant. Moreover, this parameterized model allows one to fit the experimental data efficiently.
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.