V. V. Dodonov

Current status of the dynamical Casimir effect

This is a brief review of different aspects of the so-called dynamical Casimir effect and the proposals aimed at its possible experimental realizations. A rough classification of these proposals is given and important theoretical problems are pointed out.

Quantum phenomena in resonators with moving walls

New solutions for the mode functions of the electromagnetic field in ideal cavity which boundary oscillates at a resonance frequency are obtained in the long‐time limit. The rate of photons creation from initial vacuum state is shown to be time independent and proportional to the amplitude of oscillations and the resonance frequency. Temperature corrections are evaluated. The squeezing coefficients for the quantum states of the field generated are calculated, as well as the backward reaction of the field on the vibrating wall.

Photon creation and excitation of a detector in a cavity with a resonantly vibrating wall

Abstract The problem of photon generation inside an ideal 3D cavity with resonantly vibrating walls is studied. The possibility of creating from a vacuum up to 104 photons in a cavity with a Q-factor of about 3 × 1010 is predicted. Different responses of detectors modeled by a harmonic oscillator and by a two-level atom are demonstrated.

Exact propagators for time-dependent Coulomb, delta and other potentials

Abstract A new formula relating the propagators of the Schrodinger equation with certain time-dependent potentials to the propagator of the same equation with time-dependent potentials is derived on the basis of the integral of motion found by Berry and Klein. The examples considered include the non-stationary harmonic oscillator, the singular oscillator, the Coulomb potential, the delta potential and the particle in a box problem.

Hilbert-Schmidt distance and non-classicality of states in quantum optics

Abstract The Hilbert—Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states. Unitary transformations of both states with the same unitary operator (e.g. the displacement of both states in the phase plane by the same displacement vector and squeezing of both states) do not change this distance. The nearest distance of a given state to the whole set of coherent states is proposed as a quantitative measure of non-classicality of the state which is identical when considering the coherent states as the most classical ones among pure states and the deviations from them as non-classicality. The connection to other definitions of the non-classicality of states is discussed. The notion of distance can also be used for the definition of a neighbourhood of considered states. Inequalities for the distance of states to Fock states are derived. For given neighbourhoods, they restrict common characteristics of the state as the dispersion of the number operator and the squared deviation of the mean values of the number operator for the considered state and the Fock state. Possible modifications in the definition of non-classicality for mixed states with dependence on the impurity parameter and by including the displaced thermal states as the most classical reference states are discussed.

RESONANCE PHOTON GENERATION IN A VIBRATING CAVITY

The problem of photon creation from vacuum due to the non-stationary 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: , , ( is the mean distance between the walls). An explicit analytical expression for the total energy in all the modes shows an exponential growth if is less than the dimensionless amplitude of vibrations , the increment being proportional to . The rate of photon generation from vacuum in the th mode goes asymptotically to a constant value , the numbers of photons in the modes with indices being the integrals of motion. The total number of photons in all the modes is proportional to in the short-time and in the long-time limits. In the case of strong detuning the total energy and the total number of photons generated from vacuum oscillate with the amplitudes decreasing as for . The special cases of p = 1 and p = 2 are studied in detail.

Quantum particle in a box with moving walls

The analytical expressions for the energy gain and transition probabilities between energy levels of a nonrelativistic quantum particle confined in a box with uniformly moving walls, including the cases of adiabatic motion and a sudden change of the size of the box was obtained.

Correlated states in quantum electronics (resonant circuit)

Coherent and correlated states of a Josephson junction are constructed. Quantum current and voltage noises are calculated. The influence of an external current and of parametric buildup on the Josephson junction is discussed. The feasibility in principle of exciting correlated and coherent states in a Josephson junction is suggested.

Photon generation from vacuum in nondegenerate cavities with regular and random periodic displacements of boundaries

We study the influence of fluctuations in periodic motion of boundaries of an ideal three-dimensional cavity on the rate of photon generation from vacuum due to the nonstationary Casimir effect.

Time-dependent oscillator with Kronig-Penney excitation

Abstract Exact solutions of the time-dependent Schrodinger equation for a quantum oscillator subject to periodical frequency δ-kicks are obtained. We show that the oscillator occurs in the squeezed state and calculate the corresponding squeezing coefficients and the energy increase rate in terms of Chebyshev polynomials.