We study the radiation emitted by a cavity moving in vacuum. We give a quantitative estimate of the photon production inside the cavity as well as of the photon flux radiated from the cavity. A resonance enhancement occurs not only when the cavity length is modulated but also for a global oscillation of the cavity. For a high finesse cavity the emitted radiation surpasses radiation from a single mirror by orders of magnitude.
We discuss the quantized field inside a general one-dimensional cavity system. We recognize the $SL(2,R)$ symmetry being the remainder of the conformal group. The explanation of the lack of the resonance production for the fundamental frequency is given and the asymptotic behavior of the cavity system is properly described.
We obtain explicit analytical expressions for the quadrature variances and the photon distribution functions of the electromagnetic field modes excited from vacuum or thermal states due to the non-stationary Casimir effect in an ideal one-dimensional Fabry--Perot cavity with vibrating walls, provided the frequency of vibrations is close to a multiple frequency of the fundamental unperturbed electromagnetic mode.
We present the study of parametric resonance in a one-dimensional cavity based on the analysis of classical optical paths. The recursive formulas for field energy are given. We separate the mechanism of particle production and the resonance amplification of radiation. The production of photons is a purely quantum effect described in terms of quantum anomalies in recursive formulas. The resonance enhancement is a classical phenomenon of focusing and amplifying beams of photons due to Döppler effect.
We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU(2) method, we obtain analytic formulae that give excellent descriptions of the geometric phase, energy, and wavefunction of the resonating system. In particular, we observe a sudden $π$-jump in the geometric phase when the system is in resonance. We found similar behaviors in the geometric phase of a spin-1/2 particle in a rotating magnetic field, for which we developed a geometrical model to help visualize its evolution…
The creation of TE-mode photons in a three-dimensional perfectly conducting cavity with one resonantly vibrating wall is studied numerically. We show that the creation of TE-mode photons in a rectangular cavity is related to the production of massive scalar particles on a time-dependent interval. The equations of motion are solved numerically which allows to take into account the intermode coupling. We compare the numerical results with analytical predictions and discuss the effects of the intermode coupling in detail. The numerical simulations reveal that photon creation in a three-dimensiona…
We present a general formalism allowing for efficient numerical calculation of the production of massless scalar particles from vacuum in a one-dimensional dynamical cavity, i.e. the dynamical Casimir effect. By introducing a particular parametrization for the time evolution of the field modes inside the cavity we derive a coupled system of first-order linear differential equations. The solutions to this system determine the number of created particles and can be found by means of numerical methods for arbitrary motions of the walls of the cavity. To demonstrate the method which accounts for t…
For one-dimensional vibrating cavity systems appearing in the standard illustration of the dynamical Casimir effect, we propose an approach to the construction of exact closed-form solutions. As new results, we obtain solutions that are given for arbitrary frequencies, amplitudes and time regions. In a broad range of parameters, a vibrating cavity model exhibits the general property of exponential instability. Marginal behavior of the system manifests in a power-like growth of radiated energy.
Two different quantum processes are considered in a perturbed vacuum cavity: time refraction and dynamical Casimir effect. They are shown to be physically equivalent, and are predicted to be unstable, leading to an exponential growth in the number of photons created in the cavity. The concept of an effective Unruh acceleration for these processes is also introduced, in order to make a comparison in terms of radiation efficiency, with the Unruh radiation associated with an accelerated frame in unbounded vacuum.
We investigate the dynamics of coherence and entanglement of vibrating qubits. Firstly, we consider a single trapped ion qubit inside a perfect cavity and successively we use it to construct a bipartite system made of two of such subsystems, taken identical and noninteracting. As a general result, we find that qubit vibration can lead to prolonging initial coherence in both single-qubit and two-qubit system. However, despite of this coherence preservation, we show that the decay of the entanglement between the two qubits is sped up by the vibrational motion of the qubits. Furthermore, we highl…
Acceleration radiation - or Unruh radiation - the thermal radiation observed by an ever accelerating observer or detector, although having similarities to Hawking radiation, so far has proved extremely challenging to observe experimentally. One recent suggestion is that, in the presence of a mirror, constant acceleration of an atom in its ground state can excite the atom while at the same time cause it to emit a photon in an Unruh-type process. In this work we show that merely by shaking the atom, in simple harmonic motion for example, can have the same effect. We calculate the transition rate…
The problem of photon creation from vacuum due to the nonstationary Casimir effect in an ideal one-dimensional Fabry--Perot cavity with vibrating walls is solved in the resonance case, when the frequency of vibrations is close to the frequency of some unperturbed electromagnetic mode: $ω_w=p(πc/L_0)(1+δ)$, $|δ|\ll 1$, (p=1,2,...). An explicit analytical expression for the total energy in all the modes shows an exponential growth if $|δ|$ is less than the dimensionless amplitude of vibrations $ε\ll 1$, the increment being proportional to $p\sqrt{ε^2-δ^2}$. The rate of photon generation from vac…
It has previously been shown theoretically that the exchange of linear momentum between the light field in an optical cavity and a vibrating end mirror can entangle the electromagnetic field with the vibrational motion of that mirror. In this paper we consider the rotational analog of this situation and show that radiation torque can similarly entangle a Laguerre-Gaussian cavity mode with a rotating end mirror. We examine the mirror-field entanglement as a function of ambient temperature, radiation detuning and orbital angular momentum carried by the cavity mode.
We consider the motion of the end mirror of a cavity inside which a two-level atom trapped. The fast vibrating mirror induces nonlinear couplings between the cavity field and the atom. We analyze this optical effect by showing the population of the atom in its internal degrees of freedom as a function of time. On the other side, fast atom-field variables result in an additional potential for the atomic center-of-mass motion and the mirror vibration, leading to entanglement in the motion and the vibration. The entanglement has been numerically simulated and discussed.
We study the optomechanical behaviour of a driven Fabry-Pérot cavity containing two vibrating dielectric membranes. We characterize the cavity-mode frequency shift as a function of the two-membrane positions, and report a $\sim 2.47$ gain in the optomechanical coupling strength of the membrane relative motion with respect to the single membrane case. This is achieved when the two membranes are properly positioned to form an inner cavity which is resonant with the driving field. We also show that this two-membrane system has the capability to tune the single-photon optomechanical coupling on de…
We consider the dynamics of a vibrating and rotating end-mirror of an optical Fabry-P{érot} cavity that can sustain Laguerre-Gaussian modes. We demonstrate theoretically that since the intra-cavity field carries linear as well as angular momentum, radiation pressure can create bipartite entanglement between a vibrational and a rotational mode of the mirror. Further we show that the ratio of vibrational and rotational couplings with the radiation field can easily be adjusted experimentally, which makes the generation and detection of entanglement robust to uncertainties in the cavity manufactur…
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.
When ground state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The cavity field at steady state is described by a thermal density matrix under most conditions. However, under some conditions gain is possible, and when the atoms are injected in a regular fashion, the radiation can be produced in a squeezed state.
We calculate the number of photons produced by the parametric resonance in a cavity with vibrating walls. We consider the case that the frequency of vibrating wall is $n ω_1 (n=1,2,3,...)$ which is a generalization of other works considering only $2 ω_1$, where $ω_1$ is the fundamental-mode frequency of the electromagnetic field in the cavity. For the calculation of time-evolution of quantum fields, we introduce a new method which is borrowed from the time-dependent perturbation theory of the usual quantum mechanics. This perturbation method makes it possible to calculate the photon number for…
The hopping mechanism plays a key role in collective phenomena emerging in many-body physics. The ability to create and control systems that display this feature is important for next generation quantum technologies. Here we study two cavities separated by a vibrating two-sided perfect mirror and show that, within currently available experimental parameters, this system displays photon-pair hopping between the two electromagnetic resonators. In particular, the two-photon hopping is not due to tunneling, but rather to higher order resonant processes. Starting from the classical problem, where t…
We show that an atom can be coupled to a mechanical oscillator via quantum vacuum fluctuations of a cavity field enabling energy transfer processes between them. In a hybrid quantum system consisting of a cavity resonator with a movable mirror and an atom, these processes are dominated by two pair-creation mechanisms: the counterrotating (atom-cavity system) and dynamical Casimir interaction terms (optomechanical system). Because of these two pair-creation mechanisms, the resonant atom-mirror coupling is the result of high-order virtual processes with different transition paths well described …
Analysis of the spontaneously induced correlation on atom-radiation entanglement in an ensemble of two-level atoms initially prepared in the upper level and placed in a cavity containing a squeezed radiation employing the method of evaluating the coherent-state propagator is presented. It is found that the cavity radiation exhibits squeezing which is directly attributed to the squeezed radiation in the cavity. The intensity of the cavity radiation increases with the squeeze parameter and interaction time. It is also shown that substantial degree of entanglement between the atomic states and ra…
A scheme of generating recently introduced fan-states | α, 2k>_F (αis complex, k=1,2,3,...) is proposed basing on a Λ-type atom-cavity field interaction. We show that with suitable atomic preparations and measurements a passage of a sequence of N atoms through a cavity may transform an initial field coherent state | α> to a fan-state | α, 2k>_F with k=2^{N-2}.
In the present contribution we analyse a simple thought process at T = 0 in an idealized heat engine having partitions made of a material with an upper frequency cut-off and bathed in zero-point (ZP) electromagnetic radiation. As a result, a possible mechanism of filling real cavities with ZP radiation based on Doppler's effect has been suggested and corresponding entropy changes are discussed.
We propose a method to entangle two distant vibrating microsize mirrors (i.e., mechanical oscillators) in a cavity optomechanical system. In this scheme, we discuss both the resonant and large-detuning conditions, and show that the entanglement of two mechanical oscillators can be achieved with the assistance of a two-level atom and cavity-radiation pressure. In the resonant case, the operation time is relatively short, which is desirable to minimize the effects of decoherence. While in the large-detuning case, the cavity is only virtually excited during the interaction. Therefore, the decay o…
We theoretically study the radiation-induced interaction between the mechanical motion of an oscillating mirror and a remotely trapped atomic cloud. When illuminated by continuous-wave radiation, the mirror motion will induce red and blue sideband radiation, which respectively increases and reduces motional excitation. We find that by suitably driving $Λ$-level atoms, the mirror correlation with a specific radiation sideband could be converted from the outgoing to the incoming radiation. Such process allows us to manipulate the heating and cooling effects. Particularly, we develop an optomecha…
Effect of biased noise fluctuations on the degree of squeezing as well as the intensity of a radiation generated by a one-photon coherent beat laser is presented. It turns out that the radiation exhibits squeezing inside and outside the cavity under certain conditions. The degree of squeezing is enhanced by the biased noise input significantly in both regions. Despite the presence of the biased environment modes outside the cavity, the degree of squeezing outside the cavity can be greater than or equal to or even less than the cavity radiation depending on the initial preparation of the atomic…
We study Stokes and anti-Stokes processes in cavity optomechanics in the regime of strong coupling. The Stokes and anti-Stokes signals exhibit prominently the normal-mode splitting. We report gain for the Stokes signal. We also report lifetime splitting when the pump power is less than the critical power for normal-mode splitting. The nonlinear Stokes processes provide a useful method for studying strong coupling regime of cavity optomechanics. We also investigate the correlations between the Stokes and anti-Stokes photons produced spontaneously by the optomechanical system. At zero temperatur…
We calculate the photon emission of a high finesse cavity moving in vacuum. The cavity is treated as an open system. The field initially in the vacuum state accumulates a dephasing depending on the mirrors motion when bouncing back and forth inside the cavity. The dephasing is not linearized in our calculation, so that qualitatively new effects like pulse shaping in the time domain and frequency up-conversion in the spectrum are found. Furthermore we predict the existence of a threshold above which the system should show self-sustained oscillations.
Detailed derivation of the master equation and the corresponding time evolution of the cavity radiation of a coherent beat laser when the atoms are initially prepared in a partial coherent superposition is presented. It turns out that the quantum features and intensity of the cavity radiation are considerably modified by the phase fluctuation arising due to the practical incapability of preparing atoms in the intended coherent superposition. New terms having an opposite sign with the contribution of the driving radiation emerged in the master equation. This can be taken as an indication for a …
We introduce a time-dependent perturbation method to calculate the number of created particles in a 1D cavity with an oscillating wall of the frequency $Ω. $ This method makes it easy to find the dominant part of the solution which results from the parametric resonance. The maximal number of particles are created at the mode frequency $Ω/2 . $ Using the Floquet theory, we discuss the long-time behavior of the particle creation.
Analysis of the dynamics of the cavity radiation of a coherently pumped correlated emission laser is presented. The phase fluctuation and dephasing are found to affect the time evolution of the two-mode squeezing and intensity of the cavity radiation significantly. The intensity and degree of the two-mode squeezing increase at early stages of the process with time, but this trend changes rapidly afterwards. It is also shown that they increase with phase fluctuation and dephasing in the strong driving limit, however the situation appears to be opposite in the weak driving limit. This essentiall…
A quantum system composed of a cavity radiation field interacting with a movable mirror is considered and quantum statistical properties of the field are studied. Such a system can serve in principle as an idealized meter for detection of a weak classical force coupled to the mirror which is modelled by a quantum harmonic oscillator. It is shown that the standard quantum limit on the measurement of the mirror position arises naturally from the properties of the system during its dynamical evolution. However, the force detection sensitivity of the system falls short of the corresponding standar…
We present a way to engineer an effective anti-Jaynes-Cumming and a Jaynes-Cumming interaction between an atomic system and a single cavity mode and show how to employ it in reservoir engineering processes. To construct the effective Hamiltonian, we analyse considered the interaction of an atomic system in a \{Lambda} configuration, driven by classical fields, with a single cavity mode. With this interaction, we firstly show how to generate a decoherence-free displaced squeezed state for the cavity field. In our scheme, an atomic beam works as a reservoir for the radiation field trapped inside…
We consider a cavity with a vibrating end mirror and coupled to a Bose-Einstein condensate. The cavity field mediates the interplay between mirror and collective oscillations of the atomic density. We study the implications of this dynamics and the possibility of an indirect diagnostic. Our predictions can be observed in a realistic setup that is central to the current quest for mesoscopic quantumness.
Using resonant interaction between atoms and the field in a high quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasi-probability distributions and demonstrate the nonclassicality of the superposition in terms of the zeroes of the Q-function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by Auffeves et al [Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.
The effective mass that approximately describes the effect of a classical homogeneous gravitational field on an interacting atom-radiation field system is determined within the framework of the Jaynes-Cummings model. By taking into account both the atomic motion and gravitational field, a full quantum treatment of the internal and external dynamics of the atom is presented. By solving exactly the Schrodinger equation in the interaction picture, the evolving state of the system is found. Influence of a classical homogeneous gravitational field on the energy eigenvalues, the effective mass of at…
We consider the coherent state radiation field inside a micromaser cavity and study the entanglement mediated by it on a pair of two level atoms passing though the cavity one after the other. We then investigate the effects of squeezing of the cavity field on the atomic entanglement. We compute the entanglement of formation for the emerging mixed two-atom state and show that squeezing of the cavity radiation field can increase the atomic entanglement.
We show that one can cool a micro-mechanical oscillator to its quantum ground state using radiation pressure in an appropriately detuned cavity (self-cooling). From a simple theory based on Heisenberg-Langevin equations we find that optimal self-cooling occurs in the good cavity regime, when the cavity bandwidth is smaller than the mechanical frequency, but still larger than the effective mechanical damping. In this case the intracavity field and the vibrational mechanical mode coherently exchange their fluctuations. We also present dynamical calculations which show how to access the mirror fi…
We consider the problem of photon creation from vacuum inside an ideal cavity with vibrating walls in the resonance case, taking into account the interaction between the resonant field mode and a detector modeled by a quantum harmonic oscillator. The frequency of wall vibrations is taken to be twice the cavity normal frequency, modified due to the coupling with the detector. The dynamical equations are solved with the aid of the multiple scales method. Analytical expressions are obtained for the photon mean numbers and their variances for the field and detector modes, which are supposed to be …
We consider the electromagnetic vacuum field inside a perfect plane cavity with moving mirrors, in the nonrelativistic approximation. We show that low frequency photons are generated in pairs that satisfy simple properties associated to the plane geometry. We calculate the photon generation rates for each polarization as functions of the mechanical frequency by two independent methods: on one hand from the analysis of the boundary conditions for moving mirrors and with the aid of Green functions; and on the other hand by an effective Hamiltonian approach. The angular and frequency spectra are …
We investigate the effects of parity-deformed radiation fields on the dynamics of entanglement transfer to distant noninteracting atom qubits. These qubits are embedded in two separated lossy cavities connected by a leaky fiber, which acts as a cavity buffer with delocalized modes. The process is studied within a single-excitation subspace, the parity-deformed cavity photons allowing the introduction of static local classical fields which function as a control. The mechanism of state transfer is analyzed in comparison to the uncontrolled case. We find that the transfer evolution exhibits an as…
We present and investigate an analogue model for a controllable photon geberation via the dynamical Casimir effect (DCE) in a cavity containing a degenerate optical amplifier (OPA) which is pumed by an amplitude-modulated field. The time modulation of the pump field in the model OPA system is equivalent to a periodic modulation of the cavity length, which is responsible for the generation of the Casimir radiation. By taking into account the rapidly oscillating terms of the modulation frequency, the effects of the corresponding counter-rotating terms (CRTs) on the analogue Casimir radiation eme…
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.…
Optomechanical systems have been attracting intensive attention in various physical experiments. With an optomechanical system, the displacement of or the force acting on a mechanical oscillator can be precisely measured by utilizing optical interferometry. As a mechanical oscillator, a suspended mirror is often used in over milligram scale optomechanical systems. However, the tiny suspended mirror in a linear cavity can be unstable in its yaw rotational degree of freedom due to optical radiation pressure. This instability curbs the optical power that the cavity can accumulate in it, and impos…
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…
A cavity optomechanical system is initiated by a radiation pressure of a cavity field onto a mirror element acting as a quantum resonator. This radiation pressure can control the thermodynamic character of the mirror to some extent, such as cooling its effective temperature. Here we show that by properly engineering the spectral density of a thermal heat bath that interacts with a quantum system, the evolution of the quantum system can be effectively turned on and off. Inside a cavity optomechanical system, when the heat bath is realized by a multi-mode oscillator modeling of the mirror, this …
Thermal or chaotic light sources emit radiation characterized by a slightly enhanced probability of emitting photons in bunches, described by a zero-delay second-order correlation function $g^{(2)}(0) = 2$. Here we explore photon-coincidence counting statistics of thermal cavities in the ultrastrong coupling regime, where the atom-cavity coupling rate becomes comparable to the cavity resonance frequency. We find that, depending on the system temperature and coupling rate, thermal photons escaping the cavity can display very different statistical behaviors, characterised by second-order correla…
In this work we propose an approach to deal with radiation field states which incorporates damping effects at zero temperature. By using some well known results on dissipation of a cavity field state, obtained by standard ab-initio methods, it was possible to infer through a phenomenological way the explicit form for the evolution of the state vector for the whole system: the cavity-field plus reservoir. This proposal turns out to be of extreme convenience to account for the influence of the reservoir over the cavity field. To illustrate the universal applicability of our approach we consider …
The ultrastrongly coupling (USC) system has very important research significance in quantum simulation and quantum computing. In this paper, the ultranarrow spectrum of a circuit QED system with two qubits ultrastrongly coupled to a single-mode cavity is studied. In the regime of USC, the JC model breaks down and the counter-rotating terms in the quantum Rabi Hamiltonian leads to the level anti-crossing in the energy spectrum. Choosing a single-photon driving field at the point of avoided-level crossing, we can get an equivalent four-level dressed state model, in which the dissipation of the t…
Near-field heat radiation and transfer are rich in various exciting effects, in particular, regarding the amplification due to the geometrical configuration of the system. In this paper, we study heat exchange in situations where the objects are confined by additional objects so that the dimensionality of heat flow is reduced. In particular, we compute the heat transfer for spherical point particles placed between two parallel plates. The presence of the plates can enhance or reduce the transfer compared to the free case and provides a slower power-law decay for large distance. We also compute…
Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard the cooperative radiation as a manifested effect secondary to the intrinsic synchronization among the atoms and propose a time-resolved measure of synchronization on a cavity-coupled dual-qubit system using multipartite concurrence. Comparing the variation of the concurrence over time with that of an asynchronicity measure, we find that the synchronization between the qubits features a time delay characteristic to the initiation of superfluorescent pulses. The delay coincides w…
We propose a method for the detection of a dynamical Casimir effect. Assuming that the Casimir photons are being generated in an electromagnetic cavity with a vibrating wall (dynamical Casimir effect), we consider electrons passing through the cavity to be interacting with the intracavity field. We show that the dynamical Casimir effect can be observed via the measurement of the change in the average or in the variance of the electron kinetic energy. We point out that the enhancement of the effect due to finite temperatures makes it easier to detect the Casimir photons.
We describe and demonstrate a method to control a detuned movable-mirror Fabry-Perot cavity using radiation pressure in the presence of a strong optical spring. At frequencies below the optical spring resonance, self-locking of the cavity is achieved intrinsically by the optomechanical (OM) interaction between the cavity field and the movable end mirror. The OM interaction results in a high rigidity and reduced susceptibility of the mirror to external forces. However, due to a finite delay time in the cavity, this enhanced rigidity is accompanied by an anti-damping force, which destabilizes th…
In large ensembles of identical atoms or spins, the interaction with a mode of the electromagnetic radiation field concentrates in a single superradiant degree of freedom with a collectively enhanced coupling. Given a controllable inhomogeneous broadening, such ensembles may be used for multi-mode storage of quantum states of the radiation field with applications in quantum communication networks and quantum computers. In this paper we analyze how the width and shape of the inhomogeneous broadening influence the collective enhancement and the dynamics of the cavity-ensemble system with focus o…
We theoretically investigate the three-photon blockade phenomenon in a two atoms cavity QED system, where two atoms are driven by a coherent field. In the case of in-phase radiations, we show that the three-photon blockade with bunched two photons can be realized in a small regime of the driving field Rabi frequency. However, in the case of out-of-phase radiations, the one-photon excitations are prohibited due to the destructive interference, and three-photon blockade can be realized in a wide regime of driving field Rabi frequency. In addition, the three-photon blockade phenomenon can be sign…
We describe the transfer of quantum information and entanglement from three flying (radiation) to three localized (atomic) qubits via cavity modes resonantly coupled to the atoms, in the presence of a common reservoir. Upon addressing the full dynamics of the resulting nine-qubit open system, we find that once the cavities are fed, fidelity and transferred entanglement are optimal, while their peak values exponentially decrease due to dissipative processes. The external radiation is then turned off and quantum correlations oscillate between atomic and cavity qubits. For a class of mixtures of …
An effective toy model for an ideal one-dimensional nonstationary cavity is taken to be the starting point to derive a fitting markovian master equation for the corresponding leaky cavity. In the regime where the generation of photons via the dynamical Casimir effect is bounded, the master equation thus constructed allows us to investigate the effects of decoherence on the average number of Casimir photons and their quantum fluctuations through the second-order correlation function.
