In this paper we analyze the action of the gravitational field on the dynamical Casimir effect. We consider a massless scalar field confined in a cuboid cavity placed in a gravitational field described by a static and diagonal metric. With one of the plane mirrors of the cavity allowed to move, we compute the average number of particles created inside the cavity by means of the Bogoliubov coefficients computed through perturbative expansions. We apply our result to the case of an oscillatory motion of the mirror, assuming a weak gravitational field described by the Schwarzschild metric. The regime of parametric amplification is analyzed in detail, demonstrating that our computed result for the mean number of particles created agrees with specific associated cases in the literature. Our results, obtained in the framework of the perturbation theory, are restricted, under resonant conditions, to a short-time limit.
Motivated by recent experimental progress to manipulate the refractive index of dielectric materials by strong laser beams, we study some aspects of the quantum radiation created by such refractive index perturbations.
A boundary undergoing relativistic motion can create particles from quantum vacuum fluctuations in a phenomenon known as the dynamical Casimir effect. We examine the creation of particles, and more generally the transformation of quantum field states, due to boundary motion in curved spacetime. We provide a novel method enabling the calculation of the effect for a wide range of trajectories and spacetimes. We apply this to the experimental scenario used to detect the dynamical Casimir effect, now adopting the Schwarzschild metric, and find novel resonances in particle creation as a result of t…
Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a weak gravitational field. Such a force is here evaluated and is found to have opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is analyzed and experimental detection is discussed, bearing in mind the current technological resources.
We will use Fisher information to properly analyze the quantum weak equivalence principle. We argue that gravitational waves will be partially reflected by superconductors. This will occur as the violation of the weak equivalence principle in Cooper pairs is larger than the surrounding ionic lattice. Such reflections of virtual gravitational waves by superconductors can produce a gravitational Casimir effect, which may be detected using currently available technology.
We discuss the possibility of verifying the equivalence principle for the zero-point energy of quantum electrodynamics, by evaluating the force, produced by vacuum fluctuations, acting on a rigid Casimir cavity in a weak gravitational field. The resulting force has opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is derived and experimental feasibility is discussed, taking into account current technological resources.
It has been demonstrated that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. We here add further support to this conclusion by considering parallel semitransparent plates, that is, delta-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates (tau,x,y,xi). Fixed xi in such a spacetime represents uniform acceleration. We calculate the force on systems consisting of one or two such plates at fixed values of xi. In the limit of larg…
We propose a generalization of the superconducting circuit simulation of the dynamical Casimir effect where we consider relativistically moving boundary conditions following different trajectories. We study the feasibility of the setup used in the past to simulate the dynamical Casimir effect to reproduce richer relativistic trajectories differing from purely sinusoidal ones. We show how different relativistic oscillatory trajectories of the boundaries of the same period and similar shape produce a rather different spectrum of particles characteristic of their respective motions.
We present the status of an experimental test for gravitational strength forces below 1 mm. Our experiment uses small 1 kilohertz oscillators as test masses, with a stiff counducting shield between them to suppress backgrounds. At the present sensitivity of approximately 1000 times gravitational strength, we see no evidence for new forces with interaction ranges between 75 microns and 1 mm. While the Casimir background is not expected to be significant at this range, an extension of the shielding technique we employ may be useful for reducing this background in experiments below a few microns.…
It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This conclusion holds independently of the orientation of the plates. We review these arguments and add further support to this conclusion by considering parallel semitransparent plates, that is, $δ$-function potentials, acting on a massless scalar field, in a spacetime defined by Rindler coordinates. We calculate the force on systems consisting of one or two such plates …
We present an approach to studying the Casimir effects by means of the effective theory. An essential point of our approach is replacing the mirror separation into the size of space S^1 in the adiabatic approximation. It is natural to identify the size of space S^1 with the scale factor of the Robertson-Walker-type metric. This replacement simplifies the construction of a class of effective models to study the Casimir effects. To check the validity of this replacement we construct a model for a scalar field coupling to the two-dimensional gravity and calculate the Casimir effects by the effect…
After reviewing some essential features of the Casimir effect and, specifically, of its regularization by zeta function and Hadamard methods, we consider the dynamical Casimir effect (or Fulling-Davis theory), where related regularization problems appear, with a view to an experimental verification of this theory. We finish with a discussion of the possible contribution of vacuum fluctuations to dark energy, in a Casimir like fashion, that might involve the dynamical version.
We show that even small nonlinearities significantly affect particle production in the dynamical Casimir effect at large evolution times. To that end, we derive the effective Hamiltonian and resum leading loop corrections to the particle flux in a massless scalar field theory with time-dependent Dirichlet boundary conditions and quartic self-interaction. To perform the resummation, we assume small deviations from the equilibrium and employ a kind of rotating wave approximation. Besides that, we consider a quantum circuit analog of the dynamical Casimir effect, which is also essentially nonline…
We consider the three-body Casimir-Polder interaction between three atoms during their dynamical self-dressing. We show that the time-dependent three-body Casimir-Polder interaction energy displays nonlocal features related to quantum properties of the electromagnetic field and to the nonlocality of spatial field correlations. We discuss the measurability of this intriguing phenomenon and its relation with the usual concept of stationary three-body forces.
The resonant scalar particle generation for a swinging cavity resonator in the Casimir vacuum is examined. It is shown that the number of particles grows exponentially when the cavity rotates at some specific external frequency.
Motivated by a recent proposal for an experimental verification of the dynamical Casimir effect, the macroscopic electromagnetic field within a perfect cavity containing a thin slab with a time-dependent dielectric permittivity is quantized in terms of the dual potentials. For the resonance case, the number of photons created out of the vacuum due to the dynamical Casimir effect is calculated for both polarizations (TE and TM). PACS: 42.50.Lc, 03.70.+k, 42.50.Dv, 42.60.Da.
This is a brief review of different aspects of the so-called Dynamical Casimir Effect and the proposals aimed at its possible experimental realizations. A rough classification of these proposals is given and important theoretical problems are pointed out.
We report a theoretical study of the optical properties of a three-level emitter embedded in an optical cavity including the non-rotating wave terms of the light-matter interaction Hamiltonian. Rabi oscillations induced by a continuous wave drive laser are responsible for a periodic time-modulation of the effective cavity resonance, which results in a significant dynamical Casimir emission. A clear signature of the back-action effect of the dynamical Casimir emission onto the drive laser is visible as a sizable suppression of its absorption.
This work deals with the problem of photon detection generated from the mirror-induced Dynamical Casimir Effect. Particularly we are interested in measurement of those statistical characteristics of a generated intracavity field which may confirm its nonthermal properties. Here an indirect protocol for quadrature dispersion measurement is presented.
The Casimir force is the ultimate background in ongoing searches of extra-gravitational forces in the micrometer range. Eccentric cylinders offer favorable experimental conditions for such measurements as spurious gravitational and electrostatic effects can be minimized. Here we report on the evaluation of the exact Casimir interaction between perfectly conducting eccentric cylinders using a mode summation technique, and study different limiting cases of relevance for Casimir force measurements, with potential implications for the understanding of mechanical properties of nanotubes.
We consider the Casimir-Polder interaction between two atoms, one in the ground state and the other in its excited state. The interaction is time-dependent for this system, because of the dynamical self-dressing and the spontaneous decay of the excited atom. We calculate the dynamical Casimir-Polder potential between the two atoms using an effective Hamiltonian approach. The results obtained and their physical meaning are discussed and compared with previous results based on a time-independent approach which uses a non-normalizable dressed state for the excited atom.
We develop a dynamical approach to study the Casimir-Polder force between a initially bare molecule and a magnetodielectric body at finite temperature. Switching on the interaction between the molecule and the field at a particular time, we study the resulting temporal evolution of the Casimir-Polder interaction. The dynamical self-dressing of the molecule and its population-induced dynamics are accounted for and discussed. In particular, we find that the Casimir-Polder force between a chiral molecule and a perfect mirror oscillates in time with a frequency related to the molecular transition …
We study analytically the photon generation from vacuum due to the Dynamical Casimir effect in a cavity with a two-level atom, prepared initially in an arbitrary pure state. Performing small unitary transformations we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant/dispersive regimes.
We show that oscillations of a homogeneous medium with constant material coefficients produce pairs of photons. Classical analysis of an oscillating medium reveals regions of parametric resonance where the electromagnetic waves are exponentially amplified. The quantum counterpart of parametric resonance is an exponentially growing number of photons in the same parameter regions. This process may be viewed as another manifestation of the dynamical Casimir effect. However, in contrast to the standard dynamical Casimir effect, photon production here takes place in the entire volume and is not due…
We theoretically investigate the dynamical Casimir effect in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose to implement a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum interference devices (SQUIDs) that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free s…
By means of two simple examples: phase and amplitude damping, the impact of decoherence on the dynamical Casimir effect is investigated. Even without dissipating energy (i.e., pure phase damping), the amount of created particles can be diminished significantly via the coupling to the environment (reservoir theory) inducing decoherence. For a simple microscopic model, it is demonstrated that spontaneous decays within the medium generate those problems -- Rabi oscillations are far more advantageous in that respect. These findings are particularly relevant in view of a recently proposed experimen…
We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicalilty indicators could give further evidence of …
We explore the interplay between acceleration radiation and the dynamical Casimir effect (DCE) in the field of superconducting quantum technologies, analyzing the generation of entanglement between two qubits by means of the DCE in several states of qubit motion. We show that the correlated absorption and emission of photons is crucial for entanglement, which in some cases can be linked to the notion of simultaneity in special relativity.
We consider the problem of motion-induced photon creation from quantum vacuum inside closed, perfectly conducting cavities with time-dependent geometries. These include one dimensional Fabry-Perrot resonators with Dirichlet or Neumann boundary conditions, three dimensional cylindrical waveguides, and a spherical shell. The number of Casimir TE, TM and TEM photons is computed. We also present a classical mechanical analogue of the one dimensional dynamical Casimir effect.
We give a short review on the static and dynamical Casimir effects, recalling their historical prediction, as well as their more recent experimental verification. We emphasise on the central role played by so-called {\it dynamical boundary conditions} (for which the boundary condition depends on a second time derivative of the field) in the experimental verification of the dynamical Casimir effect by Wilson et al. We then go on to review our previous work on the static Casimir effect with dynamical boundary conditions, providing an overview on how to compute the so-called local Casimir energy,…
The problem of nonlocality in the dynamical three-body Casimir-Polder interaction between an initially excited and two ground-state atoms is considered. It is shown that the nonlocal spatial correlations of the field emitted by the excited atom during the initial part of its spontaneous decay may become manifest in the three-body interaction. The observability of this new phenomenon is discussed.
In this paper we study an optomechnical system enclosed by an optical cavity with one mirror attached to a spring as a closed quantum system. We provide a different angle of studying the phenomenons related to the dynamical Casimir effect via Feynman diagram technique. Dressing effects of phonon, photon and coupling strength are discussed. The energy shift of ground state is obtained. The dynamical Casimir effect is modeled by the scattering processes converting phonons to photons and the corresponding scattering amplitudes are computed. The force-force correlation function of the radiation pr…
We propose to use quantum coherence as ultimate proof of quantum nature in the radiation that appears by means of the Dynamical Casimir Effect in experiments with superconducting microwave waveguides. We show that, unlike previously considered measurements of quantum correlations such as entanglement and discord, quantum coherence does not require a threshold value of the external pump amplitude and is highly robust to thermal noise.
We study the dynamical Casimir effect in the presence of a finite coherence time, which is associated with a finite quality factor of the optical cavity. We use the time refraction model, where a fixed cavity with a modulated optical medium, replaces the empty cavity with a vibrating mirror. Temporal coherence is described with the help of cavity quasi-mode operators. Asymptotic expressions for the number of photon pairs generated from vacuum are derived.
We study analytically and numerically the dynamical Casimir effect in a cavity containing two stationary 2-level atoms that interact with the resonance field mode via the Tavis-Cummings Hamiltonian. We determine the modulation frequencies for which the field and atomic excitations are generated and study the corresponding dynamical behaviors in the absence of damping. It is shown that the two-atom setup allows for monitoring of photon generation without interrupting the growth, and different entangled states can be generated during the process.
In the present paper, we show that a partially reflecting static mirror with time-dependent properties can produce, via dynamical Casimir effect in the context of a massless scalar field in $1+1$ dimensions, a larger number of particles than a perfectly reflecting one. As particular limits, our results recover those found in the literature for a perfect static mirror imposing a generalized or an usual time-dependent Robin boundary condition.
We consider the nonstationary circuit QED architecture, where a single artificial two-level atom interacts with a cavity field mode under external modulation of one or more system parameters. Two different approaches are employed to study the effects of Markovian dissipation on modulation-induced transitions between the atom-field dressed states: the standard master equation of Quantum Optics and the recently formulated dressed-picture master equation. We estimate the associated transition rates and show that photon generation from vacuum ("dynamical Casimir effect", DCE) and coherent photon a…
We present a quantum description of photon creation via dynamical Casimir effect based on the standard Hamiltonian formulation. The particle representation is constructed in the expansion of field operators fixed with the initial modes. The Hamiltonian is presented in terms of the creation and annihilation operators with the time-varying couplings which originate from the external properties such as an oscillating boundary or a plasma mirror of a semiconductor slab. Some consideration is also made for the experimental realization with a semiconductor plasma mirror.
We demonstrate, in the regime of ultrastrong matter-field coupling, the strong connection between the dynamical Casimir effect (DCE) and the performance of quantum information protocols. Our results are illustrated by means of a realistic quantum communication channel and show that the DCE is a fundamental limit for quantum computation and communication and that novel schemes are required to implement ultrafast and reliable quantum gates. Strategies to partially counteract the DCE are also discussed.
Cavities with periodically oscillating mirrors have been predicted to excite photon pairs out of the quantum vacuum in a process known as the Dynamical Casimir effect. Here we propose and analyse an experimental layout that can provide an efficient modulation of the effective optical length of a cavity mode in the near-infrared spectral region. An analytical model of the dynamical Casimir emission is developed and compared to the predictions of a direct numerical solution of Maxwell's equations in real time. A sizeable intensity of dynamical Casimir emission is anticipated for realistic operat…
Asymptotical formulas for the photon distribution function of a quantum oscillator with time-dependent frequency and damping coefficients, interacting with a thermal reservoir, are derived in the case of a large mean number of quanta. Different regimes of excitation of an initial thermal state with an arbitrary temperature are considered. New formulas are used to predict the statistical properties of the electromagnetic field created in the experiments on the Dynamical Casimir Effect which are now under preparation.
Nonlinear terms in the equations of motion can induce secularly growing loop corrections to correlation functions. Recently such corrections were shown to affect the particle production by a nonuniformly moving ideal mirror. We extend this conclusion to the cases of ideal vibrating cavity and single semitransparent mirror. These models provide natural IR and UV scales and allow a more accurate study of the loop behavior. In both cases we confirm that two-loop correction to the Keldysh propagator quadratically grows with time. This growth indicates a breakdown of the semiclassical approximation…
We discuss the prospects of employing an NbN superconducting microwave stripline resonator for studying the dynamical Casimir effect experimentally. Preliminary experimental results, in which optical illumination is employed for modulating the resonance frequencies of the resonator, show that such a system is highly promising for this purpose. Moreover, we discuss the undesirable effect of heating which results from the optical illumination, and show that degradation in noise properties can be minimized by employing an appropriate design.
We study a stochastic version of the dynamical Casimir effect, computing the particle creation inside a cavity produced by a random motion of one of its walls. We first present a calculation perturbative in the amplitude of the motion. We compare the stochastic particle creation with the deterministic counterpart. Then we go beyond the perturbative evaluation using a stochastic version of the multiple scale analysis, that takes into account stochastic parametric resonance. We stress the relevance of the coupling between the different modes induced by the stochastic motion. In the single-mode a…
We analyse the generation of quantum discord by means of the dynamical Casimir effect in superconducting waveguides modulated by superconducting quantum interferometric devices. We show that for realistic experimental parameters, the conditions for the existence of quantum discord are less demanding than the previously considered for quantum entanglement or non-classicality. The states with non-zero discord and zero entanglement generated by the dynamical Casimir effect are a useful resource for quantum cryptography.
Thermal effects on the creation of particles under the influence of time-dependent boundary conditions are investigated. The dominant temperature correction to the energy radiated by a moving mirror is derived by means of response theory. For a resonantly vibrating cavity the thermal effect on the number of created photons is obtained non-perturbatively. Finite temperatures can enhance the pure vacuum effect by several orders of magnitude. The relevance of finite temperature effects for the experimental verification of the dynamical Casimir effect is addressed.
We recently proposed a new approach to analyze the parametric resonance in a vibrating cavity based on the analysis of classical optical paths. This approach is used to examine various models of cavities with moving walls. We prove that our method is useful to extract easily basic physical outcome.
Quantum vacuum fluctuations are a direct manifestation of Heisenberg's uncertainty principle. The dynamical Casimir effect allows for the observation of these vacuum fluctuations by turning them into real, observable photons. However, the observation of this effect in a cavity QED experiment would require the rapid variation of the length of a cavity with relativistic velocities, a daunting challenge. Here, we propose a quantum simulation of the dynamical Casimir effect using an ion chain confined in a segmented ion trap. We derive a discrete model that enables us to map the dynamics of the mu…
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…
The moving-mirror problem is microscopically formulated without invoking the external boundary conditions. The moving mirrors are described by the quantized matter field interacting with the photon field, forming dynamical cavity polaritons: photons in the cavity are dressed by electrons in the moving mirrors. The effective Hamiltonian for the polariton is derived, and corrections to the results based on the external boundary conditions are discussed.
We study the dynamical Casimir effect in an electromagnetic cavity containing a Kerr medium. We obtain approximate expressions for the time evolution operator as well as for the number operator in the Heisenberg representation. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. The nonlinear medium produces a saturation effect in the photon generation which shows strong oscillations whose frequency increases with the intensity…
Electromagnetic field quantization in the presence of two semi-infinite dielectrics with moving interface is investigated in $1+1$-dimensional space-time. The moving interface is modeled for small displacements and the field equation is solved perturbatively. Input-output relations and spectral distribution of emitted photons are obtained and the effect of small transitions trough the interface discussed.
The dynamical Casimir effect for a massless scalar field in 1+1-dimensions is studied numerically by solving a system of coupled first-order differential equations. The number of scalar particles created from vacuum is given by the solutions to this system which can be found by means of standard numerics. The formalism already used in a former work is derived in detail and is applied to resonant as well as off-resonant cavity oscillations.
We show that the dynamical Casimir effect in an optomechanical system can be achieved under incoherent mechanical pumping. We adopt a fully quantum-mechanical approach for both the cavity field and the oscillating mirror. The dynamics is then evaluated using a recently-developed master equation approach in the dressed picture, including both zero and finite temperature photonic reservoirs. This analysis shows that the dynamical Casimir effect can be observed even when the mean value of the mechanical displacement is zero. This opens up new possibilities for the experimental observation of this…
It was predicted some time ago that the cavity dynamical Casimir effect (generation of photons from the initial vacuum state in a cavity with moving walls) might be observed if a boundary vibrates at the double frequency of some selected cavity mode. However, to register the created photons one has to couple the cavity mode with some detector. Considering the harmonic oscillator model of a detector, we analyze how different coupling regimes can affect the statistics of the created quanta.
The phenomenon of particle creation within a resonantly vibrating lossy cavity is investigated for the example of a massless scalar field at finite temperature. Leakage is provided by insertion of a dispersive mirror into a larger ideal cavity. Via the rotating wave approximation we demonstrate that for the case of parametric resonance the exponential growth of the number of created particles and the strong enhancement at finite temperatures are preserved in the presence of reasonable losses. The relevance for experimental tests of quantum radiation via the dynamical Casimir effect is addresse…
We discuss the role of the proximity force approximation in deriving limits to the existence of Yukawian forces - predicted in the submillimeter range by many unification models - from Casimir force experiments using the sphere-plane geometry. Two forms of this approximation are discussed, the first used in most analyses of the residuals from the Casimir force experiments performed so far, and the second recently discussed in this context in R. Decca et al. [Phys. Rev. D 79, 124021 (2009)]. We show that the former form of the proximity force approximation overestimates the expected Yukawa forc…
