Dynamical Casimir Effect Research Articles

Dynamical Casimir effect via four- and five-photon transitions using a strongly detuned atom

The scenario of a single-mode cavity with harmonically modulated frequency is revisited in the presence of strongly detuned qubit or cyclic qutrit. It is found that when the qubit frequency is close to $3\ensuremath{\nu}$ there is a peak in the photon generation rate via four-photon transitions for the modulation frequency $4\ensuremath{\nu}$, where $\ensuremath{\nu}$ is the average cavity frequency. Effective five-photon processes can occur for the modulation frequency $5\ensuremath{\nu}$ in the presence of a cyclic qutrit, and the corresponding transition rates exhibit series of peaks. Closed analytical description is derived for the unitary evolution, and numeric simulations indicate the feasibility of multiphoton dynamical Casimir effect under weak dissipation.

Motion induced radiation and quantum friction for a moving atom

We study quantum dissipative effects that result from the non-relativistic motion of an atom, coupled to a quantum real scalar field, in the presence of a static imperfect mirror. Our study consists of two parts: in the first, we consider accelerated motion in free space, namely, switching off the coupling to the mirror. This results in motion induced radiation, which we quantify via the vacuum persistence amplitude. In the model we use, the atom is described by a quantum harmonic oscillator (QHO). We show that its natural frequency poses a threshold which separates different regimes, involving or not the internal excitation of the oscillator, with the ulterior emission of a photon. At higher orders in the coupling to the field, pairs of photons may be created by virtue of the Dynamical Casimir Effect (DCE). In the second part, we switch on the coupling to the mirror, which we describe by localized microscopic degrees of freedom. We show that this leads to the existence of quantum contactless friction as well as to corrections to the free space emission considered in the first part. The latter are similar to the effect of a dielectric on the spontaneous emission of an excited atom. We have found that, when the atom is accelerated and close to the plate, it is crucial to take into account the losses in the dielectric in order to obtain finite results for the vacuum persistence amplitude.

Vacuum fluctuation effects due to an Abelian gauge field in 2 + 1 dimensions, in the presence of moving mirrors

We study the Dynamical Casimir Effect (DCE) due to an Abelian gauge field in 2+1 dimensions, in the presence of semitransparent, zero-width mirrors, which may move or deform in a time-dependent way. We obtain general expressions for the probability of motion-induced pair creation, which we render in a more explicit form, for some relevant states of motion.

Conversion of mechanical noise into correlated photon pairs: Dynamical Casimir effect from an incoherent mechanical drive

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 effect. We also calculate cavity emission spectra both in the resonant and the dispersive regimes, providing useful information on the emission process.

Optical analogue of the dynamical Casimir effect in a dispersion-oscillating fibre

The dynamical Casimir effect is the generation of pairs of real particles or photons from the vacuum as a result of a non-adiabatic change of a system parameter or boundary condition. As opposed to standard parametric amplification where the modulation occurs both in space and in time, this fundamental process requires a pure modulation in time, which makes its detection particularly challenging at optical frequencies. In this paper we experimentally demonstrate a realization of the analogue dynamical Casimir effect in the near-infrared optical regime in a dispersion-oscillating photonic crystal fibre. The experiments are based on the equivalence of the spatial modulation of the fibre core diameter to a pure temporal modulation when this is considered in the co-moving frame of the travelling pump pulse. We provide evidence of optical dynamical Casimir effect by measuring quantum correlations between the spectrally resolved photon pairs and prove their non-classical nature with photon anti-bunching.

Asymmetric quantum correlations in the dynamical Casimir effect

Considering the current available experimental studies on the dynamical Casimir effect (DCE) in superconducting microwave waveguides, we study asymmetric quantum correlations in microwave radiation. The asymmetric quantum correlations are created by the presence of detuning in the DCE. We study the asymmetric quantum steering and determine the parameter regions of one- and two-way quantum steering. It shows that steering from Bob to Alice is more difficult than steering from Alice to Bob. Moreover, we find regions that represent states that, although entangled, cannot be used for teleporting coherent states; however, the steerable states are appropriate for quantum teleportation. We investigate how the teleportation fidelity functions as an indicator of the quality of EPR steering in the DCE.

From the moving piston to the dynamical Casimir effect: Explorations with shaken condensates

Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform for studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this paper we discuss theoretically two types of experiments with interacting one dimensional condensates with moving boundaries. Our analysis is based on the Luttinger liquid model which utilizes the emergent conformal symmetry of the low energy sector of the Lieb-Liniger model. The first system we consider is a variable length interferometer with two Y-junctions connected back to back. We demonstrate that dynamics of the relative phase between the two arms of the interferometer can be analyzed using the formalism developed by Moore in the problem of electromagnetic vacuum squeezing in a cavity with moving mirrors. The second system we discuss is a single condensate in a box potential with periodically moving walls. This system exhibits classical excitation of the mode resonant with the drive as well as nonlinear generation of off-resonant modes. In addition we find strong parametric multimode squeezing between modes whose energy difference matches integer multiples of the drive frequency.

Study of the combined effects of a Kerr nonlinearity and a two-level atom upon a single nonstationary cavity mode

We study a simple version of the dynamical Casimir effect in a single electromagnetic cavity mode containing a Kerr medium and a two-level atom. We obtain approximate expressions for the time-evolution operator valid at short times and/or low average photon number. We have found an interplay between the effect of the nonlinear Kerr medium, which is to decrease the growth of photon generation from the vacuum state, and that of the two-level atom, which is to increase the photon generation. We explore an ample range of Hamiltonian parameters going from the resonant to the dispersive regimes.

Entanglement through qubit motion and the dynamical Casimir effect

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.

Quantum work distributions associated with the dynamical Casimir effect

We study the joint probability distribution function of the work and the change of photon number of the nonequilibrium process of driving the electromagnetic (EM) field in a three-dimensional cavity with an oscillating boundary. The system is initially prepared in a grand canonical equilibrium state and we obtain the analytical expressions of the characteristic functions of work distributions in the single-resonance and multiple-resonance conditions. Our study demonstrates the validity of the fluctuation theorems of the grand canonical ensemble in nonequilibrium processes with particle creation and annihilation. In addition, our work illustrates that in the high temperature limit, the work done on the quantized EM field approaches its classical counterpart; while in the low temperature limit, similar to Casimir effect, it differs significantly from its classical counterpart.

Floquet dynamics of classical and quantum cavity fields

We show that the time-dependence of electromagnetic field in a periodically modulated cavity can be effectively analyzed using a Floquet map. The map relates the field states separated by one period of the drive; iterative application of the map allows to determine field configuration after arbitrary number of drive periods. For resonant and near-resonant drives, the map has stable and unstable fixed points, which are the loci of infinite energy concentration in the long time limit. The Floquet map method can be applied both to classical and quantum massless field problems, including the dynamical Casimir effect. The stroboscopic time evolution implemented by the map can be interpreted in terms of the wave propagation in a curved space, with the fixed points of the map corresponding to the black hole and white hole horizons. More practically, the map can be used to design protocols for signal compression/decompression, cooling, and sensing.

Revealing the Presence of Potential Crossings in Diatomics Induced by Quantum Cavity Radiation.

We propose an experiment to find evidence of the formation of light-induced crossings provoked by cavity quantum radiation on simple molecules by using state-of-the-art optical cavities, molecular beams, pump-probe laser schemes, and velocity mapping detectors for fragmentation. The procedure is based on prompt excitation and subsequent dissociation in a three-state scheme of a polar diatomic molecule, with two ^{1}Σ states (ground and first excited) coupled first by the UV pump laser and then by the cavity radiation, and a third fully dissociative state ^{1}Π coupled through the delayed UV/V probe laser. The observed enhancement of photodissociation yields in the ^{1}Π channel at given time delays between the pump and probe lasers unambiguously indicates the formation of a light-induced crossing between the two ^{1}Σ field-dressed potential energy curves of the molecule. Also, the production of cavity photons out of the vacuum field state via nonadiabatic effects represents a showcase of a molecular dynamical Casimir effect. To simulate the experiment outcome, we perform abinitio coherent quantum dynamics of the molecule LiF subject to external lasers and quantum cavity interactions in the strong coupling regime, using a product grid representation of the total polaritonic wave function for both vibrational and photon degrees of freedom.

Explosive particle creation by instantaneous change of boundary conditions

We investigate the dynamic Casimir effect (DCE) of a $1+1$ dimensional free massless scalar field in a finite or semi-infinite cavity for which the boundary condition (BC) instantaneously changes from the Neumann to Dirichlet BC or reversely. While this setup is motivated by the gravitational phenomena such as the formation of strong naked singularities or wormholes, and the topology change of spacetimes or strings in quantum gravity, the analysis is quite general. For the Neumann-to-Dirichlet cases, we find two components of diverging flux emanate from the point where the BC changes. We carefully compare this result with that of Ishibashi and Hosoya (2002) obtained in the context of a quantum version of cosmic censorship hypothesis, and show that one of the diverging components was overlooked by them and is actually non-renormalizable, suggesting to bring non-negligible backreaction or semiclassical instability. On the other hand, for the Dirichlet-to-Neumann cases, we reveal for the first time that only one component of diverging flux emanates, which is the same kind as that overlooked in the Neumann-to-Dirichlet cases. This result suggests not only the robustness of the appearance of diverging flux in instantaneous limits of DCE but also that the type of divergence sensitively depends on the combination of initial and final BCs.

Interaction of Mechanical Oscillators Mediated by the Exchange of Virtual Photon Pairs.

Two close parallel mirrors attract due to a small force (Casimir effect) originating from the quantum vacuum fluctuations of the electromagnetic field. These vacuum fluctuations can also induce motional forces exerted upon one mirror when the other one moves. Here, we consider an optomechanical system consisting of two vibrating mirrors constituting an optical resonator. We find that motional forces can determine noticeable coupling rates between the two spatially separated vibrating mirrors. We show that, by tuning the two mechanical oscillators into resonance, energy is exchanged between them at the quantum level. This coherent motional coupling is enabled by the exchange of virtual photon pairs, originating from the dynamical Casimir effect. The process proposed here shows that the electromagnetic quantum vacuum is able to transfer mechanical energy somewhat like an ordinary fluid. We show that this system can also operate as a mechanical parametric down-converter even at very weak excitations. These results demonstrate that vacuum-induced motional forces open up new possibilities for the development of optomechanical quantum technologies.

Dynamical Casimir effect meets material science

The aim of this study is to analyze attempts to observe the so called Dynamical Casimir effect in cavities, changing their optical lengths by means of fast time variations of material properties (dielectric permeability or conductivity) of thin slabs attached to the cavity walls. The emphasis is made on the case of semiconductor slabs excited by short laser pulses. Considering the evolution of the classical electromagnetic field in this case, an approximate analytical solution for an infinite set of coupled ordinary differential equations for the mode amplitudes is derived under certain simplifying assumptions. According to this solution, an amplification of the initial field can be made, provided the induced dielectric permeability can become negative with a large absolute value. Evaluations of the feasibility of such a scenario are given.

Quantum radiation from a shaken two-level atom in vacuum

We present a non-relativistic theory of quantum radiation generated by shaking a two-level atom in vacuum. Such radiation has the same origin of photon emission in dynamical Casimir effect. By performing a time-dependent "dressing" transformation to the Hamiltonian, we derive an interaction term that governs the radiation. In particular, we show that photon pairs can be generated, not only by shaking the position of the atom, but also by changing the internal states of the atom. As applications of our theory, we calculate the emission rate from an oscillating atom, and the multi-photon state generated in a single-photon scattering process.

The Dynamical Behaviors of the Two-Atom and the Dynamical Casimir Effect in a Non-Stationary Cavity

We study the dynamical Casimir effect and the dynamical behaviors of the two-atom in a non-stationary cavity containing two two-level atoms. By solving the problem in a matrix method, we obtain an analytic solution. The results show that the larger of the atom-field coupling coefficients and the coupling coefficient of atoms, the fewer photons generated, but the probability of double excitation of the two-atom increases with the coupling coefficients. The squeezed coefficient enhances the generation rate of the created photons and the possibility of the atoms in the excited states.

Unruh-DeWitt detectors as mirrors: Dynamical reflectivity and Casimir effect

We demonstrate that the Unruh-DeWitt harmonic-oscillator detectors in (1+1) dimensions derivative-coupled with a massless scalar field can mimic the atom mirrors in free space. Without introducing the Dirichlet boundary condition to the field, the reflectivity of our detector/atom mirror is dynamically determined by the interaction of the detector's internal oscillator and the field. When the oscillator-field coupling is strong, a broad frequency range of the quantum field can be mostly reflected by the detector mirror at late times. Constructing a cavity model with two such detector mirrors, we can see how the quantum field inside the cavity evolves from a continuous to a quasi-discrete spectrum which gives a negative Casimir energy density at late times. In our numerical calculations, the Casimir energy density in the cavity does not converge until the UV cutoff is sufficiently large, with which the two internal oscillators are always separable.

The Dynamical Casimir Effect in Squeezed Vacuum State

The dynamical Casimir effect (DCE) tells that the photons can be generated in the vacuum cavity. We here show how the squeezing of the cavity mode and the coupling between the atoms and cavity influence the DCE. We show that the atoms can be served as probe to detect the DCE. Our results show that the photon number increases with the increasing of the photonic squeezing but decreases with the atom-cavity coupling. The excitation number of the atom increases with both of the increasing of the squeezing and the atom-cavity coupling strength.

Applications of Picard and Magnus expansions to the Rabi model

We apply the Picard and Magnus expansions to both the semiclassical and the quantum Rabi model, with a switchable matter-field coupling. The case of the quantum Rabi model ia a paradigmatic example of finite-time quantum electrodynamics (QED), and in this case we build an intuitive diagrammatic representation of the Picard series. In particular, we show that regular oscillations in the mean number of photons, ascribed to the dynamical Casimir effect (DCE) for the the generation of photons and to the anti-DCE for their destruction, take place at twice the resonator frequency $\omega$. Such oscillations, which are a clear dynamical "smoking gun" of the ultrastrong coupling regime, can be predicted by first-order Picard expansion. We also show that the Magnus expansion can be used, through concatenation, as an efficient numerical integrator for both the semiclassical and the quantum Rabi model. In the first case, we find distinctive features in the Fourier spectrum of motion, with a single peak at the Rabi frequency $\Omega$ and doublets at frequencies $2n\omega\pm\Omega$, with $n$ positive integer. We explain these doublets, which are a feature beyond the rotating wave approximation (RWA), on the basis of the Picard series.