The stress tensor for the quantized electromagnetic field is calculated in the region between a pair of dispersive, dielectric half-spaces. This generalizes the stress tensor for the Casimir energy to the case where the boundaries have finite reflectivity. We also include the effects of finite temperature. This allows us to discuss the circumstances under which the weak energy condition and the null energy condition can be violated in the presence of finite reflectivity and finite temperature.
Based on calculations involving an idealized boundary condition, it has long been assumed that the stress on a spherical conducting shell is repulsive. We use the more realistic case of a Drude dielectric to show that the stress is attractive, matching the generic behavior of Casimir forces in electromagnetism. We trace the discrepancy between these two cases to interactions between the electromagnetic quantum fluctuations and the dielectric material.
It has always been conventionally understood that, in the dilute limit, the Casimir energy of interaction between bodies or the Casimir self-energy of a dielectric body could be identified with the sum of the van der Waals or Casimir-Polder energies of the constituents of the bodies. Recently, this proposition for self-energies has been challenged by Avni and Leonhardt [Ann.\ Phys.\ {\bf 395}, 326 (2018)], who find that the energy or self-stress of a homogeneous dielectric ball with permittivity $\varepsilon$ begins with a term of order $\varepsilon-1$. Here we demonstrate that this cannot be …
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…
In this paper we consider possible analogue Hawking radiation from a normal dielectric and metamaterial composite, having an analogue horizon where the dielectric parameters vanish and change sign upon crossing this transition zone. We follow a complex path analysis to show the presence of an analogue Hawking temperature at the horizon and subsequent photon production from the ambient electromagnetic field. Possibility of experimental observation is also commented upon.
A general, exact formula is derived for the expectation value of the electromagnetic energy density of an inhomogeneous absorbing and dispersive dielectric medium in thermal equilibrium, assuming that the medium is well approximated as a continuum. From this formula we obtain the formal expression for the Casimir force density. Unlike most previous approaches to Casimir effects in which absorption is either ignored or admitted implicitly through the required analytic properties of the permittivity, we include dissipation explicitly via the coupling of each dipole oscillator of the medium to a …
We present a Gupta-Bleuler quantization scheme for the electromagnetic field in time-dependent dielectric media. Starting from the Maxwell equations, a generalization of the Lorentz gauge condition adapted to time varying dielectrics is derived. Using this gauge, a Gupta-Bleuler approach to quantize all polarizations of the radiation field and the corresponding constraint condition are introduced. This new approach is different from the quantized electromagnetic field in vacuum in the sense that here the contributions of unphysical photons cannot be thoroughly eliminated, which further lead to…
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 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 microscopic theory of the Casimir effect in the dielectric is studied in the framework when absorption is realized via a reservoir modeled by a set of oscillators with continuously distributed frquencies with the aim to see if the effects depend on the form of interaction with the reservoir. A simple case of the one-dimensional dielectric between two metallic plates is considered. Two possible models are investigated, the direct interaction of the electromagnetic field with the reservoir and indirect interaction via an intermediate oscillator imitating the atom. It is found that with the s…
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 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…
The electromagnetic field is canonically quantized in the presence of a linear, dispersive and dissipative medium that is in uniform motion. Specifically we calculate the change in the normal modes of the coupled matter-field system and find a Hamiltonian that contains negative energy normal modes. We interpret these modes as the origin of phenomena such as quantum friction, and find that a detector initially in its ground state and coupled to the electromagnetic field in the vicinity of, or within a uniformly moving medium has a non-zero probability of excitation at T=0K.
Mathematical Foundation for Quantum Computing of Electromagnetic Wave Propagation in Dielectric Media
Plasma Science and Fusion Center Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）；School of Electrical and Computer Engineering National Technical University of Athens（雅典国立技术大学电气与计算机工程学院）；Department of Physics College of William & Mary（威廉玛丽学院物理系）
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…
A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of four vectors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler- Lagrange equations using the Lagrangian of the total system. A tensor of the third rank which couples the electromagnetic field with the medium is introduced and the susceptibility tensor of the medium is obtained in terms of the coupli…
It has very recently been suggested that asymmetric coupling of electromagnetic fields to thermal reservoirs under nonequilibrium conditions can produce unexpected oscillatory behavior in the local photon statistics in layered structures. Better understanding of the predicted phenomena could enable useful applications related to thermometry, noise filtering, and enhancing optical interactions. In this work we briefly review the field quantization and study the local steady state temperature distributions in optical cavities formed of lossless and lossy media to show that also local field tempe…
Starting from a Lagrangian, the electromagnetic field is quantized in the presence of a body rotating along its axis of symmetry. Response functions and fluctuation-dissipation relations are obtained. A general formula for rotational friction and power radiated by a rotating dielectric body is obtained in terms of the dyadic Green's tensor. Hamiltonian is determined and possible generalizations are discussed. As an example, the rotational friction and power radiated by a spherical dielectric in the vicinity of a semi-infinite dielectric plane is obtained and discussed in some limiting cases.
Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general no…
We derive expressions for the quantum electromagnetic field in a dispersive and dissipative dielectric medium, treating the medium as a continuum. We compare the Langevin approach with the Fano diagonalization procedure for the coupled system composed of the electromagnetic field, the dielectric medium, and the reservoir. In particular, we show that the quantized electric and magnetic fields obtained in both methods have exactly the same form. More generally, in thermal equilibrium, correlation functions computed in both methods are identical.
The derivation of Casimir forces between dielectrics can be simplified by ignoring absorption, calculating energy changes due to displacements of the dielectrics, and only then admitting absorption by allowing permittivities to be complex. As a first step towards a better understanding of this situation we consider in this paper the model of a dielectric as a collection of oscillators, each of which is coupled to a reservoir giving rise to damping and Langevin forces on the oscillators and a noise polarization acting as a source of a fluctuating electromagnetic (EM) field in the dielectric. Th…
In this paper we deal with the macroscopic electromagnetic response of a finite size dispersive dielectric object, in unbounded space, in the framework of quantum electrodynamics using the Heisenberg picture. We apply a Hopfield type scheme to account for the dispersion and dissipation of the matter. We provide a general expression of the polarization density field operator as functions of the initial conditions of the matter field operators and of the electromagnetic field operators. It is a linear functional whose kernel is a linear expression of the impulse response of the dielectric object…
