We study the Brownian motion of a charged test particle driven by quantum electromagnetic fluctuations in the vacuum region near a non-dispersive and non-absorbing dielectric half-space and calculate the mean squared fluctuations in the velocity of the test particle. Our results show that a nonzero susceptibility of the dielectrics has its imprints on the velocity dispersions of the test particles. The most noteworthy feature in sharp contrast to the case of an idealized perfectly conducting interface is that the velocity dispersions in the parallel directions are no longer negative and does not die off in time, suggesting that the potentially problematic negativeness of the dispersions in those directions in the case of perfect conductors is just a result of our idealization and does not occur for real material boundaries.
We introduce the concept of Casimir friction, i.e. friction due to quantum fluctuations. In this first article we describe the calculation of a constant torque, arising from the scattering of quantum fluctuations, on a dielectric rotating in an electromagnetic vacuum.
Electro-optical sampling has been recently used to perform spectrally-resolved measurements of electromagnetic vacuum fluctuations. In order to understand which information on the ground state of an interacting system can be acquired thanks to this technique, in this paper we will develop the quantum theory of electro-optical sampling in arbitrary dispersive dielectrics. Our theory shows that a measure of the time correlations of the vacuum fluctuations effectively implements an ellipsometry measurement on the quantum vacuum, allowing to access the frequency-dependent dielectric function. We d…
More recently, Feigel has considered the quantum vacuum contribution to the momentum of electromagnetic media. However, in Feigel's treatment he did not take into account the relativistic transformation of the optical constants (electric permittivity and magnetic permeability) of moving media. Here it is shown that the effect arising from such a transformation will also provide a quantum vacuum contribution to the velocity of media, in addition to the one derived by Feigel himself.
We study the fluctuation-induced dissipative dynamics of the quantized center of mass motion of a polarizable dielectric particle trapped near a surface. The particle's center of mass is treated as an open quantum system coupled to the electromagnetic field acting as its environment, with the resulting system dynamics described by a quantum Brownian motion master equation. The dissipation and decoherence of the particle's center of mass are characterized by the modified spectral density of the electromagnetic field that depends on surface losses and the strength of the classical trap field. Ou…
We derive the quantum-mechanical master equation (generalized optical Bloch equation) for an atom in the vicinity of a flat dielectric surface. This equation gives access to the semiclassical radiation pressure force and the atomic momentum diffusion tensor, that are expressed in terms of the vacuum field correlation function (electromagnetic field susceptibility). It is demonstrated that the atomic center-of-mass motion provides a nonlocal probe of the electromagnetic vacuum fluctuations. We show in particular that in a circularly polarized evanescent wave, the radiation pressure force experi…
A new mathematical and computational technique for calculating quantum vacuum expectation values of energy and momentum densities associated with electromagnetic fields in bounded domains containing inhomogeneous media is discussed. This technique is illustrated by calculating the mode contributions to the difference in the vacuum force expectation between opposite ends of an inhomogeneous dielectric non-dispersive medium confined to a perfectly conducting rigid box.
The Brownian motion of a charged test particle caused by quantum electromagnetic vacuum fluctuations between two perfectly conducting plates is examined and the mean squared fluctuations in the velocity and position of the test particle are calculated. Our results show that the Brownian motion in the direction normal to the plates is reinforced in comparison to that in the single-plate case. The effective temperature associated with this normal Brownian motion could be three times as large as that in the single-plate case. However, the negative dispersions for the velocity and position in the …
We consider the electric and magnetic field fluctuations in the vacuum state in the region external to a half-space filled with a homogeneous non-dissipative dielectric. We discuss an appropriate limit to an ideal metal and concentrate our interest on the renormalized field fluctuations, or equivalently to renormalized electric and magnetic energy densities, in the proximity of the dielectric-vacuum interface. We show that surface divergences of field fluctuations arise at the interface in an appropriate ideal conductor limit, and that our limiting procedure allows to discuss in detail their s…
We develop a general numerical method aimed at studying particle production from vacuum states in a variety of settings. As a first example we look at particle production in a simple cosmological model. We apply the same approach to the dynamical Casimir effect, with special focus on the case of an oscillating mirror. We confirm previous estimates and obtain long-time production rates and particle spectra for both resonant and off-resonant frequencies. Finally, we simulate a system with space and time-dependent optical properties, analogous to a one-dimensional expanding dielectric bubble. We …
We consider classical particles coupled to the quantized electromagnetic field in the background of a spatially flat Robertson-Walker universe. We find that these particles typically undergo Brownian motion and acquire a non-zero mean squared velocity which depends upon the scale factor of the universe. This Brownian motion can be interpreted as due to non-cancellation of anti-correlated vacuum fluctuations in the time dependent background space-time. We consider several types of coupling to the electromagnetic field, including particles with net electric charge, a magnetic dipole moment, and …
We have observed a distance-dependent absorption linewidth of cold $^{87}$Rb atoms close to a dielectric-vacuum interface. This is the first observation of modified radiative properties in vacuum near a dielectric surface. A cloud of cold atoms was created using a magneto-optical trap (MOT) and optical molasses cooling. Evanescent waves (EW) were used to observe the behavior of the atoms near the surface. We observed an increase of the absorption linewidth with up to 25% with respect to the free-space value. Approximately half the broadening can be explained by cavity-quantum electrodynamics (…
We extend Schwinger's ideas regarding sonoluminescence by explicitly calculating the Bogolubov coefficients relating the QED vacuum states associated with changes in a dielectric bubble. Sudden (non-adiabatic) changes in the refractive index lead to an efficient production of real photons with a broadband spectrum, and a high-frequency cutoff that arises from the asymptotic behaviour of the dielectric constant.
We study quantum Darwinism -- the redundant recording of information about a decohering system by its environment -- in zero-temperature quantum Brownian motion. An initially nonlocal quantum state leaves a record whose redundancy increases rapidly with its spatial extent. Significant delocalization (e.g., a Schroedinger's Cat state) causes high redundancy: many observers can measure the system's position without perturbing it. This explains the objective (i.e. classical) existence of einselected, decoherence-resistant pointer states of macroscopic objects.
We study the Brownian motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary. The presence of the boundary modifies the quantum fluctuations of the electric field, which in turn modifies the motion of the test particle. We calculate the resulting mean squared fluctuations in the velocity and position of the test particle. In the case of directions transverse to the boundary, the results are negative. This can be interpreted as reducing the quantum uncertainty which would otherwise be present.
The Brownian motion of small particles interacting with a field at a finite temperature is a well-known and well-understood phenomenon. At zero temperature, even though the thermal fluctuations are absent, quantum fields still possess vacuum fluctuations. It is then interesting to ask whether a small particle that is interacting with a quantum field will exhibit Brownian motion when the quantum field is assumed to be in the vacuum state. In this paper, we study the cases of a small charge and an imperfect mirror interacting with a quantum scalar field in (1+1) dimensions. Treating the quantum …
We study from a critical perspective several quantum-electrodynamic phenomena commonly related to vacuum electromagnetic (EM) fluctuations in complex media. We compute the resonance-shift, the spontaneous emission rate, the local density of states and the van-der-Waals-Casimir pressure in a dielectric medium using a microscopic diagrammatic approach. We find, in agreement with some recent works, that these effects cannot be attributed to variations on the energy of the EM vacuum but to variations of the dielectric self-energy. This energy is the result of the interaction of the bare polarizabi…
We have investigated the role of the quantum size effects in the evaluation of the force caused by electromagnetic vacuum fluctuations between ultra-thin films, using the dielectric tensor derived from the particle in a box model. Comparison with the results obtained by adopting a continuum dielectric model shows that, for film thicknesses of 1-10 nm, the electron confinement causes changes in the force intensity with respect to the isotropic plasma model which range from 40% to few percent depending upon the film electron density and the film separation. The calculated force shows quantum siz…
The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz's theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the hom…
On this work, we consider a particle moving in front of a dielectric plate, and study two of the most relevant effects of the vacuum field fluctuations: the dissipation, and the decoherence of the particle's internal degrees of freedom. We consider the particle to follow a classical, macroscopically-fixed trajectory. To study the dissipative effects, we calculate the in-out effective action by functionally integrating over the vacuum field and the microscopic degrees of freedom of both the plate and the particle. This in-out effective action develops an imaginary part, hence a non-vanishing pr…
A model for observable effects of electromagnetic vacuum fluctuations is presented. The model involves a probe pulse which traverses a slab of nonlinear optical material with a nonzero second order polarizability. We argue that the pulse interacts with the ambient vacuum fluctuations of other modes of the quantized electric field, and these vacuum fluctuations cause variations in the flight time of the pulse through the material. The geometry of the slab of material defines a sampling function for the quantized electric field, which in turn determines that vacuum modes whose wavelengths are of…
We review recent works on optomechanics of optically trapped microspheres and nanoparticles in vacuum, which provide an ideal system for studying macroscopic quantum mechanics and ultrasensitive force detection. An optically trapped particle in vacuum has an ultrahigh mechanical quality factor as it is well-isolated from the thermal environment. Its oscillation frequency can be tuned in real time by changing the power of the trapping laser. Furthermore, an optically trapped particle in vacuum may rotate freely, a unique property that does not exist in clamped mechanical oscillators. In this re…
Topology optimization of low-temperature type-II superconductors with superconductor-dielectric/vacuum interfaces based on Ginzburg-Landau theory under Weyl gauge
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
Experimentalists have come to temperatures very close to absolute zero at which physics that was once ordinary becomes extraordinary. In such a regime quantum effects and fluctuations start to play a dominant role. In this context we study the simplest open quantum system, namely, a free quantum Brownian particle coupled to thermal vacuum, i.e. thermostat in the limiting case of absolute zero temperature. We analyze the average energy $E=E(c)$ of the particle from a weak to strong interaction strength $c$ between the particle and thermal vacuum. The impact of various dissipation mechanisms is …
The quantum Brownian motion of a charged particle in the electromagnetic vacuum fluctuations is investigated near a perfectly reflecting flat boundary, taking into account the smooth switching process in the measurement. Constructing a smooth switching function by gluing together a plateau and the Lorentzian switching tails, it is shown that the switching tails have a great influence on the measurement of the Brownian motion in the quantum vacuum. Indeed, it turns out that the result with a smooth switching function and the one with a sudden switching function are qualitatively quite different…
We consider an atom (represented by a two-level system) moving in front of a dielectric plate, and study how traces of dissipation and decoherence (both effects induced by vacuum field fluctuations) can be found in the corrections to the unitary geometric phase accumulated by the atom. We consider the particle to follow a classical, macroscopically-fixed trajectory and integrate over the vacuum field and the microscopic degrees of freedom of both the plate and the particle in order to calculate friction effects. We compute analytically and numerically the non-unitary geometric phase for the mo…
We have calculated the intensity of electromagnetic radiation from particles rotating in close vicinity to a transparent dielectric plate. The radiation is a result of quantum and thermal friction occurring during particle rotation, while the driving factor of radiation is a decrease in the kinetic energy of particle. The characteristic frequency of radiation is determined by the angular velocity and the temperature of the plate and surrounding vacuum background. These results are challenging for experimental verification in future.
The interaction between a polarizable particle and a reflecting wall is examined. A macroscopic approach is adopted in which the averaged force is computed from the Maxwell stress tensor. The particular case of a perfectly reflecting wall and a sphere with a dielectric function given by the Drude model is examined in detail. It is found that the force can be expressed as the sum of a monotonically decaying function of position and of an oscillatory piece. At large separations, the oscillatory piece is the dominant contribution, and is much larger than the Casimir-Polder interaction that arises…
Electromagnetic field fluctuations are responsible for the destruction of electron coherence (dephasing) in solids and in vacuum electron beam interference. The vacuum fluctuations are modified by conductors and dielectrics, as in the Casimir effect, and hence, bodies in the vicinity of the beams can influence the beam coherence. We calculate the quenching of interference of two beams moving in vacuum parallel to a thick plate with permittivity $ε(ω)=ε_{0}+i 4πσ/ω$. In case of an ideal conductor or dielectric $(|ε|=\infty)$ the dephasing is suppressed when the beams are close to the surface of…
Within the framework of exact quantum electrodynamics in dielectric, we study the topological Berry phase of a classically pumped $Λ$-type three-level atom, prepared initially in a superposition of its two pumped levels and located near a planar dielectric half-space with model permittivity of Lorentz type, interacts with a vacuum field. The effects of material losses, expressed in terms of the Green tensor of the dielectric-matter formation including dispersion and absorption, on the topological Berry phase of the photon transition between the pumped levels have been studied. The outcomes are…
Quantum vacuum forces dictate the interaction between individual atoms and dielectric surfaces at nanoscale distances. For example, their large strengths typically overwhelm externally applied forces, which makes it challenging to controllably interface cold atoms with nearby nanophotonic systems. Here, we show that it is possible to tailor the vacuum forces themselves to provide strong trapping potentials. The trapping scheme takes advantage of the attractive ground state potential and adiabatic dressing with an excited state whose potential is engineered to be resonantly enhanced and repulsi…
The definition of the photon in the vacuum of general relativity provided by Kermack et al. and by Synge is extended to nondispersive, nonhomogeneous, isotropic dielectrics in arbitrary motion by Hamiltonian methods that rely on Gordon's effective metric. By these methods the old dilemma, whether the momentum-energy vector of the photon in dielectrics is timelike or spacelike in character, is shown to reappear under a novel guise.
Quantum fluctuations of electromagnetic vacuum are investigated in a half-space bounded by a perfectly reflecting plate by introducing a probe described by a charged wave-packet distribution in time-direction. The wave-packet distribution of the probe enables one to investigate the smearing effect upon the measured vacuum fluctuations caused by the quantum nature of the probe particle. It is shown that the wave-packet spread of the probe particle significantly influences the measured velocity dispersion of the probe. In particular, the asymptotic late-time behavior of its $z$-component, $ < \D…
Based on a microscopic approach, we propose a Lagrangian for the combined system of a rotating dielectric nanoparticle above a plane surface in the presence of electromagnetic vacuum fluctuations. In the framework of canonical quantization, the electromagnetic vacuum field is quantized in the presence of dielectric fields describing the nanoparticle and a semi-infinite dielectric with planar interface. The radiative heat power absorbed by the rotating nanoparticle is obtained and the result is in agreement with previous results when the the rotational frequency of the nanoparticle is zero or m…
The dielectric sphere has been an important test case for understanding and calculating the vacuum force of a dielectric body onto itself. Here we develop a method for computing this force in homogeneous spheres of arbitrary dielectric properties embedded in arbitrary homogeneous backgrounds, assuming only that both materials are isotropic and dispersionless. Our results agree with known special cases; most notably we reproduce the prediction of Boyer and Schwinger et al. of a repulsive Casimir force of a perfectly reflecting shell. Our results disagree with the literature in the dilute limit.…
A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the AbrahamLorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is also found that for the case of a charged particle, moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, …
In this paper we study the effects of quantum scalar field vacuum fluctuations on scalar test particles in an analog model for the Friedmann-Robertson-Walker spatially flat geometry. In this scenario, the cases with one and two perfectly reflecting plane boundaries are considered as well the case without boundary. We find that the particles can undergo Brownian motion with a nonzero mean squared velocity induced by the quantum vacuum fluctuations due to the time dependent background and the presence of the boundaries. Typical singularities which appears due to the presence of the boundaries in…
In a recent paper, it was shown that, under the action of the lateral van der Waals (vdW) force due to a perfectly conducting corrugated surface, a neutral anisotropic polarizable particle in vacuum can be attracted not only to the nearest corrugation peak, but also to a valley, or an intermediate point between a peak and a valley, with such behaviors called peak, valley and intermediate regimes, respectively. In the present paper, we investigate how these regimes are affected by the consideration of two non-dispersive semi-infinite dielectrics $ε_{1}$ and $ε_{2}$, separated by a corrugated in…
Spatially separated bodies in relative motion through vacuum experience a tiny friction force known as quantum friction. This force has so far eluded experimental detection due to its small magnitude and short range. Quantitative details revealing traces of the quantum friction in the degradation of the quantum coherence of a particle are presented. Environmentally induced decoherence for a particle sliding over a dielectric sheet can be decomposed into contributions of different signatures: one solely induced by the electromagnetic vacuum in presence of the dielectric and another induced by m…
In a companion paper [quant-ph/9904013] we have investigated several variations of Schwinger's proposed mechanism for sonoluminescence. We demonstrated that any realistic version of Schwinger's mechanism must depend on extremely rapid (femtosecond) changes in refractive index, and discussed ways in which this might be physically plausible. To keep that discussion tractable, the technical computations in that paper were limited to the case of a homogeneous dielectric medium. In this paper we investigate the additional complications introduced by finite-volume effects. The basic physical scenari…
Let us abandon for a moment the strict epistemological standpoint of quantum field theory, that eventually comes to declare nonsensical any question about the photon posed outside the quantum theoretical framework. We can then avail of the works by Whittaker et al. and by Synge about the particle and the wave model of the photon in the vacuum of general relativity. We can also rely on important results found by Gordon and by Pham Mau Quan: thanks to Gordon's discovery of an effective metric these authors have been able to reduce to the vacuum case several problems of the electromagnetic theory…
A diffraction problem for a flat Chern-Simons layer at plane boundary of a dielectric half space is solved. The Casimir energy of two dielectric half spaces with Chern-Simons layers at plane-parallel boundaries separated by a vacuum slit is derived. Crossing from the repulsive to the attractive Casimir force is analyzed for two Au and two Si half spaces with boundary Chern-Simons layers. Boundary quantum Hall layers in external magnetic field lead to Casimir repulsion at nanoscales. We discuss features that make systems with boundary quantum Hall layers unique for force measurements and search…
There are two types of fluctuations in the quantum vacuum: type 1 vacuum fluctuations are on shell and can interact with matter in specific, limited ways that have observable consequences; type 2 vacuum fluctuations are off shell and cannot interact with matter. A photon will polarize a type 1, bound, charged lepton-antilepton vacuum fluctuation in much the same manner that it would polarize a dielectric, suggesting the method used here for calculating the permittivity $ε_0$ of the vacuum. In a model that retains only leading terms, $ε_0 \cong (6μ_0/π)(8e^2/\hbar)^2= 9.10\times 10^{-12}$ C/(Vm…
Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as MEMS embedded in dielectric media, Casimir induced friction in nano-machinery, micro-fluidics and molecular electronics. Computation of such stresses based on cavity QED generally require numerical analysis based on a regularization process. A new scheme is described that has the potential for wide applicability to systems involving realistic inhomogeneous media. From a knowledge of the spectrum of the stationary modes of the electromagnetic field the scheme is illustrated by estimating n…
We consider the vacuum energy of the electromagnetic field in the background of spherically symmetric dielectrics, subject to a cut-off frequency in the dispersion relations. The effect of this frequency dependent boundary condition between media is described in terms of the {\it incomplete} $ζ$-functions of the problem. The use of the Debye asymptotic expansion for Bessel functions allows to determine the dominant (volume, area, ...) terms in the Casimir energy. The application of these expressions to the case of a gas bubble immersed in water is discussed, and results consistent with Schwing…
