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arXiv:2101.06995 · Atoms

Casimir-Polder Interaction of an Atom with a Cavity Wall Made of Phase-Change Material out of Thermal Equilibrium

Galina L. Klimchitskaya, Vladimir M. Mostepanenko

Published Jan 14, 2021• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.3390/atoms9010004

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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.
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.
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 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).
Abstract We investigate the dynamical Casimir-Polder force between an atom and a conducting wall during the time evolution of the system from a partially dressed state. This state is obtained by a sudden change of the atomic position with respect to the plate. To evaluate the time-dependent atom-plate Casimir-Polder force we solve the Heisenberg equations for the field and atomic operators by an iterative technique. We find that the dynamical atom-plate Casimir-Polder interaction exhibits oscillation in time, and can be attractive or repulsive depending on time and the atom-wall distance. We also investigate the time dependence of global observables, such as the field and atomic Hamiltonians, and discuss some interesting features of the dynamical process bringing the interaction energy to the equilibrium configuration.
We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure 87Rb Bose-Einstein condensate a few microns from a dielectric substrate and exciting its dipole oscillation. Changes in the collective oscillation frequency of the magnetically trapped atoms result from spatial variations in the surface-atom force. In our experiment, the dielectric substrate is heated up to 605 K, while the surrounding environment is kept near room temperature (310 K). The effect of the Casimir-Polder force is measured to be nearly 3 times larger for a 605 K substrate than for a room-temperature substrate, showing a clear temperature dependence in agreement with theory.
We study the modification by the presence of a plane wall of energy-level shifts of two-level atoms which are in multipolar coupling with quantized electromagnetic fields in a thermal bath in a formalism which separates the contributions of thermal fluctuations and radiation reaction and allows a distinct treatment to atoms in the ground and excited states. The position-dependent energy shifts give rise to an induced force acting on the atoms. We are able to identify three different regimes where the force shows distinct features and examine, in all regimes, the behaviors of this force in both the low-temperature limit and the high-temperature limit for both the ground-state and excited-state atoms, thus providing some physical insights into the atom-wall interaction at finite temperature. In particular, we show that both the magnitude and the direction of the force acting on an atom may have a clear dependence on the atomic polarization directions. In certain cases, a change in relative ratio of polarizations in different directions may result in a change in direction of the force.