Dynamical Casimir Effect Research Articles

Quantum entanglement due to a modulated dynamical Casimir effect

We study the creation and entanglement of quasiparticle pairs due to a periodic variation of the mode frequencies of a homogeneous quantum system. Depending on the values of the parameters describing the periodic modulation, the number of created pairs either oscillates or, in a narrow resonant frequency interval, grows exponentially in time. For a system initially in a thermal state, we determine in which cases the final state is quantum mechanically entangled, i.e., where the bipartite state is nonseparable. We include some weak dissipation, expected to be found in any experimental setup, and study the corresponding reduction of the quantum entanglement. Our findings are used to interpret the results of two recent experiments.

Exotic states in the dynamical Casimir effect

We consider the interaction of a qubit with a single mode of the quantized electromagnetic field and show that, in the ultrastrong coupling regime and when the qubit-field interaction is switched on abruptly, the dynamical Casimir effect leads to the generation of a variety of exotic states of the field, which cannot be simply described as squeezed states. Such effect is a consequence of the intrinsic nonlinearity of the qubit and also appears when initially both the qubit and the field are in their ground state. The non-classicality of the obtained exotic states is characterized by means of a parameter based on the volume of the negative part of the Wigner function. A transition to non-classical states is observed by changing either the interaction strength or the interaction time. The observed phenomena appear as a general feature of nonadiabatic quantum gates, so that the dynamical Casimir effect can be the origin of a fundamental upper limit to the maximum speed of quantum computation and communication protocols.

Smith-Purcell radiation from surface waves

We consider the radiation from an electron in flight over a surface wave of an arbitrary profile excited in a plane interface. For an electron bunch the conditions are specified under which the overall radiation essentially exceeds the incoherent part. In particular, it is shown that the radiation from the bunch with asymmetric density distribution of electrons in the longitudinal direction is partially coherent for waves with wavelengths much shorter than the characteristic longitudinal size of the bunch. The quantum radiation due to the dynamical Casimir effect induced by surface waves excited on a plane boundary is discussed.

The dynamic Casimir effect within a vibrating metal photonic crystal

The lattice-vibrating metal photonic crystal is exactly a system of dynamical Casimir effect connected in series, and so we can expect that a dynamical Casimir effect is enhanced by the photonic band effect. In the present study, when an electromagnetic field between metal plates is in the ground state in a one-dimensional metal photonic crystal, the radiation of electromagnetic wave in excited states has been investigated by artificially introducing lattice vibration to the photonic crystal. In this case as well as a dynamical Casimir effect, it has been shown that the harmonics of a ground state are generated just by vibrating a photonic crystal even without an incident wave. The dependencies of the radiating power on the number of layers and on the wavenumber of the lattice vibration are remarkable. It has been found that the radiation amplitude on lower excited states is not necessarily large and radiation on specific excited levels is large.

Dynamical Casimir effect in ultra-cold matter with a time-dependent effective charge

We propose a new scheme for observing the phonon analogue of the dynamical Casimir effect (DCE) in a gas of laser-cooled atoms. Namely, the emission of phonon pairs from vacuum can happen due to periodic variations of the effective charge of atoms, caused by a small intensity modulation of laser beams used for cooling and trapping the atoms. Then the ‘temporal Bragg diffraction’ results in phonon backscattering in time, equivalent to the DCE.

A computer algebra package for calculation of the energy density produced via the dynamical Casimir effect in one-dimensional cavities

We present a Maple package for calculation of the exact value of the energy density for a real massless scalar quantum field in a two-dimensional space–time, inside a cavity with a moving mirror, arbitrary choices for the law of motion of the boundary and initial field state. Program summaryProgram title: DynamicCasimirPackageCatalogue identifier: AESR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1430No. of bytes in distributed program, including test data, etc.: 63390Distribution format: tar.gzProgramming language: Maple.Computer: Any computer running Maple 10 or later.Operating system: Any operating system running Maple 10 or later.RAM: (recommended): 4.0 GB or 6.0 GB MbClassification: 5, 11.4, 18.Nature of problem:Calculation of the exact value of the energy density for a real massless scalar quantum field in a two-dimensional space–time, inside a cavity with a moving boundary, arbitrary choices for the law of motion of the boundary and initial field state.Solution method:The routines are based on the exact numerical approach proposed by Cole and Schieve (Phys. Rev. A 52 (1995) 4005), and also on the extension of this approach to an arbitrary initial field state, developed by the present authors, in collaboration with Lima and Silva (Phys. Rev. D 81 (2010) 025016).Restrictions:One-dimensional cavities with just one moving boundary.Running time:Depends on the type of the problem (small ≈ seconds, large ≈ hours). The worksheet takes ≈30 min to execute.

Dynamical Casimir Emission from Polariton Condensates

We study theoretically the dynamical Casimir effect in an exciton-polariton condensate that is suddenly created by an ultrashort laser pulse at normal incidence. As a consequence of the abrupt change of the quantum vacuum, Bogoliubov excitations are generated. The subsequent evolution, governed by polariton interactions and losses, is studied within a linearized truncated Wigner approximation. We focus in particular on the momentum distribution and spatial coherence. The limiting behavior at large and small momenta is determined analytically. A simple scaling relation for the final condensate depletion as a function of the system parameters is found and the correlation length is shown to depend linearly on the condensate depletion.

Amplifying the Hawking Signal in BECs

We consider simple models of Bose-Einstein condensates to study analog pair-creation effects, namely, the Hawking effect from acoustic black holes and the dynamical Casimir effect in rapidly time-dependent backgrounds. We also focus on a proposal by Cornell to amplify the Hawking signal in density-density correlators by reducing the atoms’ interactions shortly before measurements are made.

Time Crystals in Ultracold Matter

We consider the formation of time crystals in a gas of laser-cooled atoms. We show that the phonon frequency is shifted inside a time crystal, and the phonon backscattering resulting from a temporal Bragg diffraction can be observed. A quantum-field description allows us to demonstrate that these effects are accompanied by emission of the phonon pairs from vacuum. The same description can be used for the dynamical Casimir effect, which, in some sense, is as a special case of the time crystal with similar quantum vacuum properties. Due to its low temperature and low noise level, a gas of ultracold atoms seems promising for experimental studies in quantum vacuum phenomena, such as those associated with time crystals.

Dynamical Casimir effect in superradiant light scattering by Bose—Einstein condensate in an optomechanical cavity

We investigate the effects of dynamical Casimir effect in superradiant light scattering by Bose—Einstein condensate in an optomechanical cavity. The system is studied using both classical and quantized mirror motions. The cavity frequency is harmonically modulated in time for both the cases. The main quantity of interest is the number of intracavity scattered photons. The system has been investigated under the weak and strong modulations. It has been observed that the amplitude of the scattered photons is more for the classical mirror motion than the quantized mirror motion. Also, initially, the amplitude of scattered photons is high for lower modulation amplitude than higher modulation amplitude. We also found that the behavior of the plots are similar under strong and weak modulations for the quantized mirror motion.

ROTATING WAVE APPROXIMATION OF THE LAW'S EFFECTIVE HAMILTONIAN ON THE DYNAMICAL CASIMIR EFFECT

In this paper, we treat the Law's effective Hamiltonian of the dynamical Casimir effect (DCE) in a cavity and construct an analytic approximate solution of the time-dependent Schrödinger equation under the general setting through a kind of rotating wave approximation (RWA). To the best of our knowledge this is the finest analytic approximate solution.

Linking the Dynamical Casimir Effect to the Collective Excitation Effect at Finite Temperature

Thermal effects on the dynamical Casimir effect and the collective excitation effect are investigated in a resonantly vibrating cavity filled with an ensemble of two-level atoms. The results show that the moving mirror of the cavity results in the dynamical Casimir effect and the collective excitation effect of the two-level atoms,and the finite temperature enhances the number of created photons and created excitons by several orders of magnitude. The relevance experiments of the finite-temperature effects for the dynamical Casimir effect and the collective excitation effect are addressed.

Relativistic bands in the spectrum of created particles via the dynamical Casimir effect

We present a general analytical approach to investigate relativistic corrections in the dynamical Casimir effect (DCE). Particularly, we discuss the behavior of the additional frequency bands that appear in the spectral distribution of the created particles when the first relativistic corrections are taken into account. We do that in the context of circuit QED, by analyzing the setup used in the first measurement of the DCE, where a system with a time-dependent boundary condition simulates the mechanical motion of a single mirror in 1+1 dimensions. Our method is applicable to a large class of systems with oscillatory time-dependent parameters and can be generalized to higher dimensions and other fields.

Parametric excitation of a cavity field mode coupled to a harmonic oscillator detector

We study the parametric resonance in a system of two coupled quantum harmonic oscillators when the frequency of one of them (describing the field mode) is modulated at exactly twice the unperturbed eigenfrequency (the case of ‘unshifted resonance’). The coordinate–momentum coupling between the two oscillators is chosen in order to simulate the dynamical Casimir effect in a cavity containing a harmonic oscillator detector (LC-contour). Analytical solutions are obtained with the aid of the multiple scales method. For the field mode and detector initially prepared in thermal squeezed states, we calculate the mean numbers of quanta in both modes, as well as the invariant squeezing coefficients, purity and photon distribution functions, analyzing the influence of coupling strength and frequency modulation depth on the dynamics of these quantities. We show that the system goes to strongly squeezed states even for high temperature initial states of the detector. Depending on the relative strength of coupling coefficient and the parametric modulation amplitude, initially separable states go to permanently entangled states or they show periodic appearance and disappearance of entanglement.

Dynamical Casimir effect in dissipative media: When is the final state nonseparable?

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 stimulated and spontaneous emission are clearly identified. We then study how dissipation modifies this competition.

Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall

We consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casimir potential energy between the cavity walls. We also find a change of the field energy density in the cavity, particularly relevant in the proximity of the mobile wall, yielding a correction to the Casimir-Polder interaction with a polarizable body placed inside the cavity. Similarities and differences of our results with the dynamical Casimir effect are also discussed.

Quantum Interference of Dual-Channel Excited Magnons in Spin-1 Bose—Einstein Condensates Atomic Chain

We investigate the quantum interference of spin wave excitations of a spin-1 atomic Bose condensate confined in an optical lattice. Single-channel and dual-channel interactions are employed in our system, and their induced excitations are compared. Also we consider the interplay of magneto-optical excitations, which leads to a constructive or destructive effect for the creation of magnons based on background excitations. The population distributions of excited magnons can be well controlled by steering the long-range dipole-dipole interactions. Such a scheme can be used to demonstrate conventional quantum-optical phenomena like dynamical Casimir effect at finite temperatures.

Mode-mixing quantum gates and entanglement without particle creation in periodically accelerated cavities

We show that mode-mixing quantum gates can be produced by non-uniform relativistic acceleration. Periodic motion in cavities exhibits a series of resonant conditions producing entangling quantum gates between different frequency modes. The resonant condition associated with particle creation is the main feature of the dynamical Casimir effect which has been recently demonstrated in superconducting circuits. We show that a second resonance, which has attracted less attention since it implies negligible particle production, produces a beam splitting quantum gate leading to a resonant enhancement of entanglement which can be used as the first evidence of acceleration effects in mechanical oscillators. We propose a desktop experiment where the frequencies associated with this second resonance can be produced mechanically.

Spontaneous conversion from virtual to real photons in the ultrastrong-coupling regime.

We show that a spontaneous release of virtual photon pairs can occur in a quantum optical system in the ultrastrong coupling regime. In this regime, which is attracting interest both in semiconductor and superconducting systems, the light-matter coupling rate Ω(R) becomes comparable to the bare resonance frequency of photons ω(0). In contrast to the dynamical Casimir effect and other pair creation mechanisms, this phenomenon does not require external forces or time dependent parameters in the Hamiltonian.

Entanglement generation in relativistic cavity motion

We analyse particle creation and mode mixing for a quantum field in an accelerated cavity, assuming small accelerations but allowing arbitrary velocities, travel times and travel distances, and in particular including the regime of relativistic velocities. As an application, we identify a desktop experimental scenario where the mode mixing resonance frequency in linear sinusoidal motion or in uniform circular motion is significantly below the particle creation resonance frequencies of the Dynamical Casimir Effect, and arguably at the threshold of current technology. The mode mixing acts as a beamsplitter quantum gate, experimentally detectable not only via fluxes or particle numbers but also via entanglement generation.