We study the Casimir pressure between two similar plates of finite thickness kept at different temperatures in the case when the dielectric permittivity of the plates depends on temperature. It is suggested to consider the dielectric permittivity at two different temperatures as the permittivities of two dissimilar bodies, thus allowing to apply the theory of Casimir forces out of thermal equilibrium developed earlier in the literature. Following this approach, we show that, in addition to the equilibrium contribution to the nonequilibrium Casimir pressure, a proper nonequilibrium contribution arises for temperature-dependent dielectric permittivities. Furthermore, the equilibrium contribution in this case does not equal the mean of the equilibrium Casimir pressures at the temperatures of the plates. As an application, the total nonequilibrium Casimir pressure between two gold plates and between two titanium plates is calculated as a function of the plate thickness and their separation, using the Drude and the plasma model. For plate separations ranging from 0.5 to 2 micrometers, the relative difference between the theoretical predictions for these two models reaches 39%. The proper nonequilibrium term may be as large as 4% of the magnitude of the total nonequilibrium pressure.
We study the nonequilibrium Casimir-Polder force on an atom prepared in an incoherent superposition of internal energy-eigenstates, which is placed in a magnetoelectric environment of nonuniform temperature. After solving the coupled atom--field dynamics within the framework of macroscopic quantum electrodynamics, we derive a general expression for the thermal Casimir-Polder force.
We investigate how the combination of nonequilibrium effects and material properties impacts on the Casimir-Polder interaction between an atom and a surface. By addressing systems with temperature inhomogeneities and laser interactions, we show that nonmonotonous energetic landscapes can be produced where barriers and minima appear. Our treatment provides a self-consistent quantum theoretical framework for investigating the properties of a class of nonequilibrium atom-surface interactions.
We show that an isotropic dipolar particle in the vicinity of a substrate made of nonreciprocal plasmonic materials can experience a lateral Casimir force and torque when the particle's temperature differs from that of the slab and the environment. We connect the existence of the lateral force to the asymmetric dispersion of nonreciprocal surface polaritons and the existence of the lateral torque to the spin-momentum locking of such surface waves. Using the formalism of fluctuational electrodynamics, we show that the features of lateral force and torque should be experimentally observable usin…
In this work, we consider a Casimir apparatus that is put into free fall (e.g., falling into a black hole). Working in 1+1D, we find that two main effects occur: First, the Casimir energy density experiences a tidal effect where negative energy is pushed toward the plates and the resulting force experienced by the plates is increased. Second, the process of falling is inherently nonequilibrium and we treat it as such, demonstrating that the Casimir energy density moves back and forth between the plates after being "dropped,'' with the force modulating in synchrony. In this way, the Casimir ene…
Recently the Casmir-Polder force felt by an atom near a substrate under nonequilibrium stationary conditions has been studied theoretically with macroscopic quantum electrodyanamics (MQED) and verified experimentally with cold atoms. We give a quantum field theory derivation of the Langevin equation describing the atom's motion based on the influence functional method valid for fully nonequilibrium (nonstationary) conditions. The noise associated with the quantum field derived from first principles is generally colored and nonlocal, which is at variance with the `local source hypothesis' of MQ…
A general theory of photon-mediated energy and momentum transfer in N-body planar systems out of thermal equilibrium is introduced. It is based on the combination of the scattering theory and the fluctuational-electrodynamics approach in many-body systems. By making a Landauer-like formulation of the heat transfer problem, explicit formulas for the energy transmission coefficients between two distinct slabs as well as the self-coupling coefficients are derived and expressed in terms of the reflection and transmission coefficients of the single bodies. We also show how to calculate local equili…
In this paper we review different aspects of the dynamical Casimir- Polder potential between a neutral atom and a perfectly conducting plate under nonequilibrium conditions. In order to calculate the time evolution of the atom-wall Casimir-Polder potential, we solve the Heisenberg equations describing the dynamics of the coupled system using an iterative technique. Different nonequilibrium initial states are considered, such as bare and partially dressed states. The partially dressed states considered are obtained by a sudden change of a physical parameter of the atom or of its position relati…
A general analysis of thermal noise in torsion pendulums is presented. The specific case where the torsion angle is kept fixed by electronic feedback is analyzed. This analysis is applied to a recent experiment that employed a torsion pendulum to measure the Casimir force. The ultimate limit to the distance at which the Casimir force can be measured to high accuracy is discussed, and in particular the prospects for measuring the thermal correction are elaborated upon.
We extend the quantum theory of dissipation in the context of system-reservoir model, where the reservoir in question is kept in a nonequilibrium condition. Based on a systematic separation of time scales involved in the dynamics, appropriate generalizations of the fluctuation-dissipation and Einstein's relations have been pointed out. We show that the Wigner-Weisskopf decay of the system mode results in a rate constant which depending on the relaxation of nonequilibrium bath is dynamically modified. We also calculate the time-dependent spectra of a cavity mode with a suitable gain when the ca…
We propose a test on the role of relaxation properties of conduction electrons in the Casimir pressure between two parallel metal-coated plates kept at different temperatures. It is shown that for sufficiently thick metallic coatings the Casimir pressure and pressure gradient are determined by the mean of the equilibrium contributions calculated at temperatures of the two plates and by the term independent on separation. Numerical computations of the nonequilibrium pressures are performed for two parallel Au plates of finite thickness as a function of separation and temperature of one of the p…
We study the joint probability distribution function of the work and the change of photon number of the nonequilibrium process of driving the electromagnetic (EM) field in a three-dimensional cavity with an oscillating boundary. The system is initially prepared in a grand canonical equilibrium state and we obtain the analytical expressions of the characteristic functions of work distributions in the single-resonance and multiple-resonance conditions. Our study demonstrates the validity of the fluctuation theorems of the grand canonical ensemble in nonequilibrium processes with particle creatio…
The nonlinear dynamics of a cylindrical pinion that is kept at a distance from a vibrating rack is studied, and it is shown that the lateral Casimir force between the two corrugated surfaces can be rectified. The effects of friction and external load are taken into account and it is shown that the pinion can do work against loads of up to a critical value, which is set by the amplitude of the lateral Casimir force. We present a phase diagram for the rectified motion that could help its experimental investigations, as the system exhibits a chaotic behavior in a large part of the parameter space…
We report on the first measurement of a temperature dependence of the Casimir-Polder force. This measurement was obtained by positioning a nearly pure 87-Rb 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 ne…
We demonstrate that the thermal Casimir-Polder forces on molecules near a conducting surface whose transition wavelengths are comparable to the molecule-surface separation are dependent on the ambient temperature and molecular polarization and they can even be changed from attractive to repulsive via varying the temperature across a threshold value for anisotropically polarizable molecules. Remarkably, this attractive-to-repulsive transition may be realized at room temperature. Let us note that the predicted repulsion is essentially a nonequilibrium effect since the force we calculated on a gr…
We study all known and as yet unknown forces between two neutral atoms, modeled as three dimensional harmonic oscillators, arising from mutual influences mediated by an electromagnetic field but not from their direct interactions. We allow as dynamical variables the center of mass motion of the atom, its internal degrees of freedom and the quantum field treated relativistically. We adopt the method of nonequilibrium quantum field theory which can provide a first principle, systematic and unified description including the intrinsic field fluctuations and induced dipole fluctuations. The inclusi…
The search for non-Newtonian forces has been pursued following many different paths. Recently it was suggested that hypothetical chameleon interactions, which might explain the mechanisms behind dark energy, could be detected in a high-precision force measurement. In such an experiment, interactions between parallel plates kept at constant separation could be measured as a function of the pressure of an ambient gas, thereby identifying chameleon interactions by their unique inverse dependence on the local mass density. During the past years we have been developing a new kind of setup complying…
Dynamical Casimir effect of the optomechanical cavity interacting with one-dimensional photonic crystal is theoretically investigated in terms of the complex spectral analysis of Floquet-Liouvillian in the symplectic-Floquet space. The quantum vacuum fluctuation of the intra-cavity mode is parametrically amplified by a periodic motion of the mirror boundary, and the amplified photons are spontaneously emitted to the photonic band. We have derived the non-Hermitian effective Floquet-Liouvillian from the total system Liouvillian with the use of the Brillouin-Wigner-Feshbach projection method in …
Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform for studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this pape…
We present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in plane optical anisotropy, separated by either vacuum or a liquid (ethanol). The torque is found to vary as $\sin(2θ)$, where $θ$ represents the angle between the two optical axes, and its magnitude rapidly increases with decreasing plate separation $d$. For a 40 $μ$m diameter disk, made out of either quartz or calcite, kept parallel to a Barium Titanate plate at $d\simeq 100$ nm, the maximum torque (at $θ={π\over 4}$) is of the order of $\simeq 10^{-19…
