Asymptotical photon distributions in the dissipative Dynamical Casimir Effect

Asymptotical formulas for the photon distribution function of a quantum oscillator with time-dependent frequency and damping coefficients, interacting with a thermal reservoir, are derived in the case of a large mean number of quanta. Different regimes of excitation of an initial thermal state with an arbitrary temperature are considered. New formulas are used to predict the statistical properties of the electromagnetic field created in the experiments on the Dynamical Casimir Effect which are now under preparation.Comment: 11 pages, accepted contribution to CEWQO 2009 proceedings (to appear in Physica Scripta

Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror

A "microscopic" justification of the "symmetric damping" model of a quantum oscillator with time-dependent frequency and time-dependent damping is given. This model is used to predict results of experiments on simulating the dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror. It is shown that the most general bilinear time-dependent coupling of a selected oscillator (field mode) to a bath of harmonic oscillators results in two equal friction coefficients for the both quadratures, provided all the coupling coefficients are proportional to a single arbitrary function of time whose duration is much shorter than the periods of all oscillators. The choice of coupling in the rotating wave approximation form leads to the "mimimum noise" model of the quantum damped oscillator, introduced earlier in a pure phenomenological way.Comment: 9 pages, typos corrected, corresponds to the published version, except for the reference styl

Photon creation from vacuum and interactions engineering in nonstationary circuit QED

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. In the resonant atom-cavity regime and under the resonant modulation, the dynamics is similar to the one occurring for a stationary two-level atom in a vibrating cavity, and an entangled state with two photons can be created from vacuum. Moreover, we consider the situation in which the atom-cavity coupling, the atomic frequency, or both have a small nonperiodic time modulation, and show that photons can be created from vacuum in the dispersive regime. Therefore, an analog of the dynamical Casimir effect can be simulated in circuit QED, and several photons, as well as entangled states, can be generated from vacuum due to the anti-rotating term in the Rabi Hamiltonian.Comment: 14 pages, 6 figures. Talk presented at the International Workshop "60 Years of Casimir Effect", 23 - 27 June, 2008, Brasili

Vibrating Cavities - A numerical approach

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 the intermode coupling we investigate the creation of massless scalar particles in a one-dimensional vibrating cavity by means of three particular cavity motions. We compare the numerical results with analytical predictions as well as a different numerical approach.Comment: 28 pages, 19 figures, accepted for publication in J. Opt. B: Quantum Semiclass. Op

Numerical approach to the dynamical Casimir effect

The dynamical Casimir effect for a massless scalar field in 1+1-dimensions is studied numerically by solving a system of coupled first-order differential equations. The number of scalar particles created from vacuum is given by the solutions to this system which can be found by means of standard numerics. The formalism already used in a former work is derived in detail and is applied to resonant as well as off-resonant cavity oscillations.Comment: 15 pages, 4 figures, accepted for publication in J. Phys. A (special issue: Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005

The Schrodinger particle in an oscillating spherical cavity

We study a Schrodinger particle in an infinite spherical well with an oscillating wall. Parametric resonances emerge when the oscillation frequency is equal to the energy difference between two eigenstates of the static cavity. Whereas an analytic calculation based on a two-level system approximation reproduces the numerical results at low driving amplitudes, epsilon, we observe a drastic change of behaviour when epsilon > 0.1, when new resonance states appear bearing no apparent relation to the eigenstates of the static system.Comment: 9 pages, 6 figures, corrected typo

Dynamical Casimir Effect in a Leaky Cavity at Finite Temperature

The phenomenon of particle creation within an almost resonantly vibrating cavity with losses is investigated for the example of a massless scalar field at finite temperature. A leaky cavity is designed via the insertion of a dispersive mirror into a larger ideal cavity (the reservoir). In the case of parametric resonance the rotating wave approximation allows for the construction of an effective Hamiltonian. The number of produced particles is then calculated using response theory as well as a non-perturbative approach. In addition we study the associated master equation and briefly discuss the effects of detuning. The exponential growth of the particle numbers and the strong enhancement at finite temperatures found earlier for ideal cavities turn out to be essentially preserved. The relevance of the results for experimental tests of quantum radiation via the dynamical Casimir effect is addressed. Furthermore the generalization to the electromagnetic field is outlined.Comment: 48 pages, 8 figures typos corrected & references added and update

Dynamical Casimir effect at finite temperature

Thermal effects on the creation of particles under the influence of time-dependent boundary conditions are investigated. The dominant temperature correction to the energy radiated by a moving mirror is derived by means of response theory. For a resonantly vibrating cavity the thermal effect on the number of created photons is obtained non-perturbatively. Finite temperatures can enhance the pure vacuum effect by several orders of magnitude. The relevance of finite temperature effects for the experimental verification of the dynamical Casimir effect is addressed.Comment: 9 LaTex page

Properties of Squeezed-State Excitations

The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op