Transmission-line waveguides can mediate long-range fluctuation-induced forces between neutral objects. We present two approaches for the description of these forces between electric components embedded in transmission-line circuits. The first, following ordinary quantum electrodynamics (QED), consists of the quantization and scattering theory of voltage and current waves inside transmission lines. The second approach relies on a simple circuit analysis with additional noisy current sources due to resistors in the circuit, as per the fluctuation-dissipation theorem (FDT). We apply the latter approach to derive a general formula for the Casimir force induced by circuit fluctuations between any two impedances. The application of this formula, considering the sign of the resulting force, is discussed. While both QED and FDT approaches are equivalent, we conclude that the latter is simpler to generalize and solve.
We develop a QED approach to find the contribution of the quantum vacuum to the electromagnetic Abraham force. Semi-classical theories predict diverging contributions from the quantum vacuum. We show that the divergencies disappear by Kramers-Bethe mass-renormalization. The finite remainder is compared to the relativistic corrections to the Abraham force. This work generalizes an earlier paper [1], dedicated to the harmonic oscillator, to the hydrogen atom and corrects two subtle errors.
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.
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 investigate analytically and numerically the nonstationary circuit QED setup in which $N$ independent qubits interact with a single mode of the Electromagnetic field confined in a resonator. We consider the harmonic time modulation of some parameter (atomic transition frequency or the atom-field coupling strength) and derive the unitary dynamics up to the second order in the modulation depth for $N=1$ and $N\gg 1$. It is shown that all the resonant phenomena that occur for modulation frequencies $\sim 2ω_{0}$ (where $ω_{0}$ is the cavity frequency) also occur for the halved frequencies. How…
We consider Casimir-Polder and Casimir forces with finite dissipation by coupling heat baths to the dipoles introducing, this way, dissipation from 'first principles'. We derive a representation of the free energy as an integral over real frequencies, which can be viewd as an generalization of the 'remarkable formula' introduced by Ford et. al. 1985. For instance, we obtain a nonperturbative representation for the atom-atom and atom-wall interactions. We investigate several limiting cases. From the limit $T\to0$ we show that the third law of thermodynamics cannot be violated within the given a…
We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account in an implicit way. We prove that this formula is also valid when the surrounding medium is dissipative.
We study theoretically the non-stationary circuit QED system in which the artificial atom transition frequency has a small periodic modulation in time, prescribed externally. We show that, in the dispersive regime, when the modulation periodicity meets the `resonances', the dynamics may be described by the dynamical Casimir effect, Jaynes-Cummings or Anti-Jaynes-Cummings effective Hamiltonians. In the resonant atom-cavity regime, under the modulation `resonance' the dynamics resembles the behavior of the dynamical Casimir effect in a vibrating cavity containing a resonant two-level atom, and e…
Recent advances in nanotechnology and atomic physics may allow for a demonstration of the dynamical Casimir effect. An array of film bulk acoustic resonators (FBARs) coherently driven at twice the resonant frequency of a high-quality electromagnetic cavity can generate a stationary state of Casimir photons. These are detected using an alkali atom beam prepared in an inverted population of hyperfine states, with an induced superradiant burst producing a detectable radio-frequency signal. We describe here the results of the simulations of the dynamics of superradiance and superfluorescence, with…
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.
Vacuum fluctuations provide a fundamental source of dissipation for systems coupled to quantum fields by radiation pressure. In the dynamical Casimir effect, accelerating neutral bodies in free space give rise to the emission of real photons while experiencing a damping force which plays the role of a radiation reaction force. Analog models where non-stationary conditions for the electromagnetic field simulate the presence of moving plates are currently under experimental investigation. A dissipative force might also appear in the case of uniform relative motion between two bodies, thus leadin…
Based on a circuit QED qubit-cavity array a source of two-mode entangled microwave radiation is designed. Our scheme is rooted in the combination of external driving, collective phenomena and dissipation. On top of that the reflexion symmetry is broken via external driving permitting the appearance of chiral emission. Our findings go beyond the applications and are relevant for fundamental physics, since we show how to implement quantum lattice models exhibiting criticality driven by dissipation.
The Casimir friction problem for a pair of dielectric particles in relative motion is analyzed, utilizing a microscopic model in which we start from statistical mechanics for harmonically oscillating particles at finite temperature moving nonrelativistically with constant velocity. The use of statistical mechanics in this context has in our opinion some definite advantages, in comparison with the more conventional quantum electrodynamic description of media that involves the use of a refractive index. The statistical-mechanical description is physical and direct, and the oscillator model, in s…
The Casimir friction problem can be dealt with in a simplified way by considering two harmonic oscillators moving with constant relative velocity. Recently we calculated the energy dissipation for such a case, [EPL {\bf 91}, 60003 (2010); Europ. Phys. J. D {\bf 61}, 335 (2011)]. A recent study of Barton [New J. Phys. {\bf 12}, 113044 (2010)] seemingly leads to a different result for the dissipation. If such a discrepancy really were true, it would imply a delicate difficulty for the basic theory of Casimir friction. In the present note we show that the expressions for the dissipation are in fa…
This paper is a second in a series devoted to the study of a two-oscillator system in linear relative motion (the first one published as a letter in Europhys. Lett. 91, 60003 (2010)). The main idea behind considering this kind of system is to use it as a simple model for Casimir friction. In the present paper we extend our previous theory so as to obtain the change in the oscillator energy to second order in the perturbation, even though we employ first order perturbation theory only. The results agree with, and confirm, our earlier results obtained via different routes. The friction force is …
The frequencies of transitions between hyperfine levels of ground-state atoms can be measured with exquisite precision using magnetic-resonance techniques. This makes hyperfine transitions ideal probes of QED effects originating from the interaction of atoms with the quantized electromagnetic field. One of the most remarkable effects predicted by QED is the Casimir-Polder shift experienced by the energy levels of atoms placed near one or more dielectric objects. Here we compute the Casimir-Polder shift and the width of hyperfine transitions between ground-state Zeeman sub-levels of an hydrogen…
We study the Casimir force between a perfectly conducting and an infinitely permeable plate with the radiation pressure approach. This method illustrates how a repulsive force arises as a consequence of the redistribution of the vacuum-field modes corresponding to specific boundary conditions. We discuss also how the method of the zero-point radiation pressure follows from QED.
We investigate a two-level atom coupled to a cavity with a strong classical driving field in a dissipative environment and find an analytical expression of the time evolution density matrix for the system. The analytical density operator is then used to study the entanglement between the atom and cavity by considering the competing process between the atom-field interactions and the field-environment interactions. It is shown that there is an optimal interaction time for generating atom-cavity entanglement.
We present a feasible scheme to investigate the geometric phase for an atom trapped in an optical cavity induced by the effective decay process due to cavity photon loss. The cavity mode, together with the external driving fields, acts as the engineered environment of the atom. When the parameters of the reservoir is adiabatically and cyclically changed, the system initially in the nontrivial dark state of the effective Lindblad operator undergoes a cyclic evolution and acquires a geometric phase. The geometric phase can be observed with the atomic Ramsey interference oscillation in the decohe…
We study the spatial fluctuations of the Casimir-Polder force experienced by an atom or a small sphere moved above a metallic plate at fixed separation distance. We demonstrate that unlike the mean force, the magnitude of these fluctuations crucially relies on the relaxation of conduction electron in the metallic bulk, and even achieves values that differ by orders of magnitude depending on the amount of dissipation. We also discover that fluctuations suffer a spectacular decrease at large distances in the case of nonzero temperature.
We analyze the introduction of dissipative effects in the study of the dynamical Casimir effect. We consider a toy model for an electromagnetic cavity that contains a semiconducting thin shell, which is irradiated with short laser pulses in order to produce periodic oscillations of its conductivity. The coupling between the quantum field in the cavity and the microscopic degrees of freedom of the shell induces dissipation and noise in the dynamics of the field. We argue that the photon creation process should be described in terms of a damped oscillator with nonlocal dissipation and colored no…
Cavity and circuit QED study light-matter interaction at its most fundamental level. Yet, this interaction is most often neglected when considering the coupling of this system with an environment. In this paper, we show how this simplification, which leads to the standard quantum optics master equation, is at the root of unphysical effects. Including qubit relaxation and dephasing, and cavity relaxation, we derive a master equation that takes into account the qubit-resonator coupling. Special attention is given to the ultrastrong coupling regime, where the failure of the quantum optical master…
We investigate the magnetic dipole coupling between a metallic surface and an atom in a thermal state, ground state and excited hyperine state. This interaction results in a repulsive correction and - unlike the electrical dipole contribution - depends sensitively on the Ohmic dissipation in the material.
We perform the matching required to compute the leading effective boundary contribution to the QED lagrangian in the presence of a conducting surface, once the electron is integrated out. Our result resolves a confusion in the literature concerning the interpretation of the leading such correction to the Casimir energy. It also provides a useful theoretical laboratory for brane-world calculations in which kinetic terms are generated on the brane, since a lot is known about QED near boundaries.
Based on a unified approach to macroscopic QED that allows for the inclusion of amplification in a limited space and frequency range, we study the Casimir force as a Lorentz force on an arbitrary partially amplifying system of linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate that the force on a weakly polarisable/magnetisable amplifying object in the presence of a purely absorbing environment can be expressed as a sum over the Casimir--Polder forces on the excited atoms inside the body. As an example, the resonant force between a plate consisting of a dilute gas o…
When an incident light beam is scattered off a sample of ultracold atoms trapped in an optical lattice, the statistical properties of the retro-reflected field contain information about the quantum state of the atoms, and permit for example to distinguish between atoms in a superfluid and a Mott insulator state. This paper extends our previous analysis of this problem to include the effects of cavity damping. We use a Monte Carlo wave function method to determine the two-time correlation function and time-dependent physical spectrum of the retro-reflected field in the case of a simple two-well…
A critical look is taken at the calculation of the Casimir effect. The boundary conditions play an important role and should be imposed in a physical way. An acceptable result for the vacuum energy is only obtained when different regularization schemes yield the same result. Radiative corrections to the Casimir force between two parallel plates due to electromagnetic vacuum fluctuations have been obtained both in full QED and in a low-energy, effective field theory with conflicting results. Including surface terms in the effective Lagrangian, the QED result can be understood. Finally, a proble…
We study theoretically the nonstationary circuit QED system in which the artificial atom transition frequency, or the atom-cavity coupling, have a small periodic time modulation, prescribed externally. The system formed by the atom coupled to a single cavity mode is described by the Rabi Hamiltonian. We show that, in the dispersive regime, when the modulation periodicity is tuned to the `resonances', the system dynamics presents the dynamical Casimir effect, resonant Jaynes-Cummings or resonant Anti-Jaynes-Cummings behaviors, and it can be described by the corresponding effective Hamiltonians.…
We examine recent prescriptions for estimating the thermal Casimir force between two metallic plates from the point of view of their consistency with the Bohr-van Leeuwen theorem of classical statistical physics. We find that prescriptions including the effect of ohmic dissipation satisfy the theorem, while prescriptions that neglect ohmic dissipation do not.
We discuss the Casimir effect between two identical, parallel slabs, emphasizing the role of dissipation and temperature. Starting from quite general assumptions, we analyze the behavior of the Casimir entropy in the limit T->0 and link it to the behavior of the slab's reflection coefficients at low frequencies. We also derive a formula in terms of a sum over modes, valid for dissipative slabs that can be interpreted in terms of a damped quantum oscillator.
We propose the use of a tunneling electromechanical transducer to dynamically detect Casimir forces between two conducting surfaces. The maximum distance for which Casimir forces should be detectable with our method is around $1 μ$m, while the lower limit is given by the ability to approach the surfaces. This technique should permit to study gravitational forces on the same range of distances, as well as the vacuum friction provided that very low dissipation mechanical resonators are used.
Based on a generalization of the Lifshiftz theory we calculate Casimir forces involving magnetodielectric and possibly anisotropic metamaterials, focusing on the possibility of repulsive forces. It is found that Casimir repulsion decreases with magnetic dissipation, and even a small Drude background in metallic-based metamaterials acts to make attractive a Casimir force that would otherwise be predicted to be repulsive. The sign of the force also depends sensitively on the degree of optical anisotropy of the metamaterial, and on the form of the frequency-dependency of the magnetic response.
In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode expansion of the electromagnetic fields in free space to allow for the presence of absorbing bodies. We show that macroscopic quantum electrodynamics provides the link between isolated atomic systems and magnetoelectric bodies, and serves as an important tool for the understanding of surface-assisted atomic relaxation effects and the intimately connected positi…
In this paper we give fully analytical description of the dynamics of a collection of $N$-Frenkel excitons in high density regime dispersively coupled to a single mode cavity field, in the presence of both exciton and cavity-field dissipations. By using excitonic operators as q-deformed bosonic operators for the system, we solve analytically the Liouville equation for the density operator at zero temperature and investigate the influence of the number of excitons and the effect of both dissipations on dynamical behavior of the system. We use the solution of master equation to explore the dissi…
We establish a general relation between dispersion forces. First, based on QED in causal media, leading-order perturbation theory is used to express both the single-atom Casimir-Polder and the two-atom van der Waals potentials in terms of the atomic polarizabilities and the Green tensor for the body-assisted electromagnetic field. Endowed with this geometry-independent framework, we then employ the Born expansion of the Green tensor together with the Clausius-Mosotti relation to prove that the macroscopic Casimir-Polder potential of an atom in the presence of dielectric bodies is due to an inf…
We demonstrate how a time-dependent dissipative environment may be used as a tool for controlling the quantum state of a two-level atom. In our model system the frequency and coupling strength associated with microscopic reservoir modes are modulated, while the principal features of the reservoir structure remain fixed in time. Physically, this may be achieved by containing a static atom-cavity system inside an oscillating external bath. We show that it is possible to dynamically decouple the atom from its environment, despite the fact that the two remain resonant at all times. This can lead t…
We investigate the influence of temperature and dissipation on the Landau-Zener transition probability in circuit QED. Dissipation is modelled by coupling the transmission line to a bath of harmonic oscillators. The reduced description for the density operator is treated within Bloch-Redfield theory. A phase-space representation allows an efficient numerical implementation of the resulting master equation. It provides reliable results which are valid even for rather low temperatures. We find that the spin-flip probability as a function of temperature and dissipation strength exhibits a non-mon…
We compute the Casimir interaction between a plane and a sphere, the configuration employed in the most precise experiments. The scattering formula is developed by taking a suitably chosen plane-wave and multipole basis and is valid for arbitrary values of the sphere radius, inter-plate distance, temperature and arbitrary dielectric functions for both sphere and plate. Our analytical and numerical results for metallic surfaces show a non-trivial interplay between the effects of curvature, temperature, finite conductivity and dissipation.
The role played by zero-point contribution, also called quantum noise or vacuum fluctuations, in the quantum expression of the fluctuation-dissipation theorem (FDT) is a long-standing open problem widely discussed by the physicist community since its announcement by Callen and Welton pioneer paper of 1951 [1]. From one hand, it has the drawbacks of: (i) the expectation value of its energy is infinite, (ii) it produces an ultraviolet catastrophe of the noise power spectral density and, (iii) it lacks of an experimental validation under thermal equilibrium conditions. From another hand, by impos…
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…
We study photon condensation phenomena in a driven and dissipative array of superconducting microwave resonators. Specifically, we show that by using an appropriately designed coupling of microwave photons to superconducting qubits, an effective dissipative mechanism can be engineered, which scatters photons towards low-momentum states while conserving their number. This mimics a tunable coupling of bosons to a low temperature bath, and leads to the formation of a stationary photon condensate in the presence of losses and under continuous-driving conditions. Here we propose a realistic experim…
We report the experimental observation, and a theoretical explanation, of collective suppression of linewidths for multiple superconducting qubits coupled to a good cavity. This demonstrates how strong qubit-cavity coupling can significantly modify the dephasing and dissipation processes that might be expected for individual qubits, and can potentially improve coherence times in many-body circuit QED.
We study the consequences of dissipation in homogeneous media when the system is subject to a sudden change, thereby producing pairs of correlated quasi-particles with opposite momenta. We compute both the modifications of the spectrum, and those of the correlations. In particular, we compute the final coherence level, and identify the regimes where the state is non-separable. To isolate the role of dissipation, we first consider dispersive media and study the competition between the intensity of the jump which induces some coherence, and the temperature which reduces it. The contributions of …
Based on macroscopic QED in linear, causal media, we present a consistent theory for the Casimir-Polder force acting on an atom positioned near dispersing and absorbing magnetodielectric bodies. The perturbative result for the van-der-Waals energy is shown to exhibit interesting new features in the presence of magnetodielectric bodies. To go beyond perturbation theory, we start with the center-of-mass equation of motion and derive a dynamical expression for the Casimir-Polder force acting on an atom prepared in an arbitrary electronic state. For a non-driven atom in the weak coupling regime, t…
The nonlocal response functions to quantum fluctuations are used to find asymptotic expressions for the Casimir free energy and entropy at arbitrarily low temperature in the configuration of two parallel metallic plates. It is shown that by introducing an alternative nonlocal response to the off-the-mass-shell fluctuations the Lifshitz theory is brought into agreement with the requirements of thermodynamics. According to our results, the Casimir entropy calculated using the nonlocal response functions, which take into account dissipation of conduction electrons, remains positive and monotonous…
QED vacua under the influence of external conditions (background fields, finite temperature, boundary conditions) can be considered as dispersive media whose complex behaviour can no longer be described in terms of a single universal vacuum velocity of light c. Beginning in the early 1950's (J.S. Toll), quantum field theoretic investigations have led to considerable insight into the relation between the vacuum structure and the propagation of light. Recent years have witnessed a significant growth of activity in this field of research. After a short overview, two characteristic situations are …
The situation with the temperature corrections to the Casimir force between real metals of finite conductivity is reported. It is shown that the plasma dielectric function is well adapted to the Lifshitz formula and leads to reasonable results for real conductors. The Drude dielectric function which describes media with dissipation is found not to belong to the application range of the Lifshitz formula at nonzero temperature. For Drude metals the special modification of the zero-frequency term of this formula is suggested. The contradictory results on the subject in recent literature are analy…
We propose an experimental setup, feasible with present day technology, involving two highquality- factor cavities, one Ramsey zone and a two-level atom which interacts with them. The dynamics in the cavities is modeled by a dissipative dispersive Jaynes-Cummings model. Analytical expresions for the evolution superoperator in each part of the proposed setup and for the concurrence between the atom and the first cavity are given, and the pairwise entanglement of the subsystems is calculated numerically. We consider initial separable states given by the tensor product of a superposition of the t…
A general theory of the Casimir-Polder interaction of single atoms with dispersing and absorbing magnetodielectric bodies is presented, which is based on QED in linear, causal media. Both ground-state and excited atoms are considered. Whereas the Casimir-Polder force acting on a ground-state atom can conveniently be derived from a perturbative calculation of the atom-field coupling energy, an atom in an excited state is subject to transient force components that can only be fully understood by a dynamical treatment based on the body-assisted vacuum Lorentz force. The results show that the Casi…
We explore an analogy between the thermodynamics of a free dissipative quantum particle and that of an electromagnetic field between two mirrors of finite conductivity. While a free particle isolated from its environment will effectively be in the high-temperature limit for any nonvanishing temperature, a finite coupling to the environment leads to quantum effects ensuring the correct low-temperature behavior. Even then, it is found that under appropriate circumstances the entropy can be a nonmonotonic function of the temperature. Such a scenario with its specific dependence on the ratio of te…
The Casimir effect in quantum electrodynamics (QED) is perhaps the best-known example of fluctuation-induced long-ranged force acting on objects (conducting plates) immersed in a fluctuating medium (quantum electromagnetic field in vacuum). A similar effect emerges in statistical physics, where the force acting, e.g., on colloidal particles immersed in a binary liquid mixture is affected by the classical thermal fluctuations occurring in the surrounding medium. The resulting Casimir-like force acquires universal features upon approaching a critical point of the medium and becomes long-ranged a…
