The problem of photon creation from vacuum in an ideal cavity with vibrating walls is studied in the resonance case, when the frequency of vibrations equals twice the frequency of some unperturbed electromagnetic mode. Analytical solutions are obtained in two cases: for the one-dimensional model (scalar electrodynamics) and for the three-dimensional (3D) cavity. In the first example, we have a strong intermode interaction; nonetheless, an explicit solution in terms of the complete elliptic integrals is found. The rate of photon generation in the principal mode rapidly assumes a constant value proportional to the product of the frequency by the dimensionless amplitude of oscillations. The total amount of photons created in all the modes increases in time as ${\mathit{t}}^2$. In the second example, the eigenmode spectrum is nonequidistant and the problem can be reduced to the problem of a single harmonic oscillator with a time-dependent frequency. The number of photons in the resonant mode of a 3D cavity increases exponentially in time and the field appears in a highly squeezed state with a strongly oscillating photon distribution function. The problem of detecting the created photons is analyzed in the framework of a simplified model, when a detector is replaced with a harmonic oscillator. It turns out that the presence of the detector changes the picture drastically: both the detector and the field mode occur in highly mixed (nonthermal) quantum states, with identical nonoscillating photon distribution functions. The detector gains exactly half of the total energy of excitation inside the cavity. The estimations show a possibility of creating up to several hundred or even thousand photons, provided that the cavity’s Q factor exceeds ${10}^{10}$ and the amplitude of the wall’s oscillations is greater than ${10}^{\mathrm{-}10}$ cm at a frequency of the order of 10 GHz. © 1996 The American Physical Society.

We study the physical implementation of a qutrit quantum computer in the context of trapped ions. Qutrits are defined in terms of electronic levels of trapped ions. We concentrate our attention on a universal two-qutrit gate, which corresponds to a controlled-NOT gate between qutrits. Using this gate and a general gate of an individual qutrit, any gate can be decomposed into a sequence of these gates. In particular, we show how this works for performing the quantum Fourier transform for n qutrits.

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The problem of electromagnetic-field quantization in time-dependent nonuniform linear nondispersive media is investigated. The explicit formulas for the number of photons generated from the initial vacuum state due to the change in time of dielectric permeability of the medium are obtained in the case when the spatial and temporal dependences are factorized. The concrete time dependences include adiabatic and sudden changes of permeability, the parametric resonance at twice the eigenfrequency of the mode, Epstein’s symmetric and transition profiles, ‘‘temporal Fabry-Pérot resonator,’’ and some others. The upper and lower bounds for the squeezing and correlation coefficients of the field in the final state are given in terms of the reflection coefficient from an equivilent potential barrier or the number of created quanta. The problem of impulse propagation in a spatially uniform but time-dependent dielectric medium is discussed.

We comprehensively review the quantum theory of the polarization properties of light. In classical optics, these traits are characterized by the Stokes parameters, which can be geometrically interpreted using the Poincaré sphere. Remarkably, these Stokes parameters can also be applied to the quantum world, but then important differences emerge: now, because fluctuations in the number of photons are unavoidable, one is forced to work in the three-dimensional Poincaré space that can be regarded as a set of nested spheres. Additionally, higher-order moments of the Stokes variables might play a substantial role for quantum states, which is not the case for most classical Gaussian states. This brings about important differences between these two worlds that we review in detail. In particular, the classical degree of polarization produces unsatisfactory results in the quantum domain. We compare alternative quantum degrees and put forth that they order various states differently. Finally, intrinsically nonclassical states are explored, and their potential applications in quantum technologies are discussed.