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We show two examples in which the dynamical Casimir effect can be achieved by modulating the Kerr or higher order nonlinearities. In the first case the cavity field is coupled to an arbitrary number of qubits or an harmonic oscillator via the dipole interaction. In the second case, the modulation of the nonlinearities is accompanied by the off-resonance modulation of the cavity frequency. We present the analytic description of the phenomenon and supplement it with numeric simulations, demonstrating that photons can be created from vacuum and the resulting hyper-Poissonian photon statistics is very different from the squeezed vacuum state., Comment: 8 pages, 5 figures

We consider a quantum spinless nonrelativistic charged particle moving in the $xy$ plane under the action of a time-dependent magnetic field, described by means of the linear vector potential ${\bf A}=B(t)\PG{-y(1+\alpha),x(1-\alpha)}/2$, with two fixed values of the gauge parameter $\alpha$: $\alpha=0$ (the circular gauge) and $\alpha =1$ (the Landau gauge). Although the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for $\alpha=0$ and straight lines for $\alpha=1$. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function $B(t)$. They are expressed in terms of solutions to the classical equation of motion $\ddot\vep +\omega_{\alpha}^2(t) \vep=0$, with $\omega_1=2\omega_0$. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions $B(t)$, when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case, as well. The case of slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value., Comment: 50 pages, 24 figures. The title and text are expanded. This version is close to the published paper (except for formatting)

Exact solutions of the time-dependent Schrodinger equation for a quantum oscillator subject to periodical frequency delta-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.

This is a brief review of various families of coherent and squeezed states (and their generalizations) for a charged particle in a magnetic field, that have been constructed for the past 50 years. Although the main attention is paid to the Gaussian states, various families of non-Gaussian states are also discussed, and the list of relevant references is provided., Comment: 21 pages, 162references. This is a chapter for the book of proceedings of the CIRM workshop (November 2016) "Coherent States and their Applications: A Contemporary Panorama", to be published by Springer

New sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. One of consequences is the new inequality, giving a nonzero lower bound for the product of two variances in the case of zero mean value of the commutator between the related operators. Moreover, explicit examples show that in some cases this new bound can be better than the known Robertson--Schr\"odinger one., Comment: 6 pages, submitted to PRA

A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of the two-dimensional pure Gaussian state is considered as an example., Comment: 5 pages, accepted for publication in International Journal of Quantum Information (special issue Torino-2017)

The strong coupling constant $\alpha_s(M_Z)$ is determined from inclusive jet and dijet cross sections in neutral-current deep-inelastic $ep$ scattering (DIS) measured at HERA by the H1 collaboration using next-to-next-to-leading order (NNLO) QCD predictions. The dependence of the NNLO predictions and of the resulting value of $\alpha_s(M_Z)$ at the $Z$-boson mass $m_Z$ are studied as a function of the choice of the renormalisation and factorisation scales. Using inclusive jet and dijet data together, the strong coupling constant is determined to be $\alpha_s(M_Z)=0.1166\,(19)_{\rm exp}\,(24)_{\rm th}$. Complementary, $\alpha_s(M_Z)$ is determined together with parton distribution functions of the proton (PDFs) from jet and inclusive DIS data measured by the H1 experiment. The value $\alpha_s(M_Z)=0.1147\,(25)_{\rm tot}$ obtained is consistent with the determination from jet data alone. The impact of the jet data on the PDFs is studied. The running of the strong coupling is tested at different values of the renormalisation scale and the results are found to be in agreement with expectations., Comment: 45 pages, 17 figures, with changes discussed in an erratum submitted to EPJ C

The paper deals with fractal characteristics (Hurst exponent) and wavelet-scaleograms of the information distribution model, suggested by the authors. The authors have studied the effect of Hurst exponent change depending upon the model parameters, which have semantic meaning. The paper also considers fractal characteristics of real information streams. It is described, how the Hurst exponent dynamics depends on these information streams state in practice, Comment: 10 pages, 5 figures

The paper provides a agent-based model, which describes distribution of informative messages, containing links to informational resources in the Internet. The results of modeling have been confirmed by studying a real network of Twitter microblogs. The paper describes stages of building a corporate system of monitoring network informational resources, the content of which is determined by links in microblogs. The advantages of such approach are set forth., Comment: 6 pages, 3 figures

An exact infinite set of coupled ordinary differential equations, describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity, containing a thin slab with the time-dependent conductivity $\sigma(t)$ and dielectric permittivity $\varepsilon(t)$, is derived for the dispersion-less media. This problem is analyzed in connection with the attempts to simulate the so called Dynamical Casimir Effect in three-dimensional electromagnetic cavities, containing a thin semiconductor slab, periodically illuminated by strong laser pulses. Therefore it is assumed that functions $\sigma(t)$ and $\delta\varepsilon(t)=\varepsilon(t)-\varepsilon(0)$ are different from zero during short time intervals (pulses) only. The main goal is to find the conditions, under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). Approximate solutions to the dynamical equations are obtained in the cases of "small" and "big" maximal values of the functions $\sigma(t)$ and $\delta\varepsilon(t)$. It is shown, that the single-mode approximation, used in the previous studies, can be justified in the case of "small" perturbations. But the initially excited field mode cannot be amplified in this case, if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximal values of conductivity and the concentration of free carries (the model of "almost ideal conductor"), created inside the slab, under the crucial condition, that the function $\delta\varepsilon(t)$ is {\em negative}. This result follows from a simple approximate analytical solution, and it is confirmed by exact numerical calculations. However, the evaluations show, that the necessary energy of laser pulses must be, probably, unrealistically high., Comment: 15 pages, 3 figures; accepted for publication in Journal of Russian Laser Research

We study two-dimensional quantum Gaussian packets with a fixed value of mean angular momentum. This value is the sum of two independent parts: the `external' momentum related to the motion of the packet center and the `internal' momentum due to quantum fluctuations. The packets minimizing the mean energy of an isotropic oscillator with the fixed mean angular momentum are found. They exist for `co-rotating' external and internal motions, and they have nonzero correlation coefficients between coordinates and momenta, together with some (moderate) amount of quadrature squeezing. Variances of angular momentum and energy are calculated, too. Differences in the behavior of `co-rotating' and `anti-rotating' packets are shown. The time evolution of rotating Gaussian packets is analyzed, including the cases of a charge in a homogeneous magnetic field and a free particle. In the latter case, the effect of initial shrinking of packets with big enough coordinate-momentum correlation coefficients (followed by the well known expansion) is discovered. This happens due to a competition of `focusing' and `de-focusing' in the orthogonal directions., Comment: 23 pages, 2 figures, to appear in Journal of Physics A

We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty product. Also, we calculate the "stationarity time" for mixed Gaussian states of a quantum harmonic oscillator, showing explicitly that pure quantum states are "more fragile" than mixed ones with the same value of the energy dispersion. The problems of quantum evolution speed limits, time operators and measurements of energy and time are briefly discussed, too., Comment: 39 pages, 2 figures, 300 references, to appear in the special issue of Physica Scripta "150 years of Margarita and Vladimir Man'ko"

We study the tunneling of slow quantum packets through a high Coulomb barrier. We show that the transmission coefficient can be quite different from the standard expression obtained in the plane wave (WKB) approximation (and larger by many orders of magnitude), even if the momentum dispersion is much smaller than the mean value of the momentum., Comment: 3 pages, 3 figures, accepted for publication in Physics Letters A

We study the evolution of the most general initial Gaussian packet with nonzero correlation coefficient between the coordinate and momentum operators in the presence of a repulsive delta potential barrier, using the known exact propagator of the time-dependent Schr\"odinger equation. For the initial packet localized far enough from the barrier, we define the transmission coefficient as the probability of discovering the particle in the whole semi-axis on the other side of the barrier. It appears that the asymptotical transmission coefficient (calculated in the large time limit) depends on two dimensionless parameters: the normalized ratio of the potential strength to the initial mean value of momentum and the ratio of the initial momentum dispersion to the initial mean value of momentum. For small values of the second parameter the result is reduced to the well known formula for the transparency of the delta barrier, obtained in the plane wave approximation by solving the stationary Schr\"odinger equation. For big values of the second parameter, the transmission coefficient can be much bigger than that calculated in the plane wave approximation. For a fixed initial spread of the packet in the coordinate space, the initial correlation coefficient influences the transparency of the barrier only indirectly, through the increase of the initial momentum dispersion., Comment: 10 pages, 2 figures, to appear in Journal of Russian Laser Research, Vol. 35, issue 1

It was predicted some time ago that the cavity dynamical Casimir effect (generation of photons from the initial vacuum state in a cavity with moving walls) might be observed if a boundary vibrates at the double frequency of some selected cavity mode. However, to register the created photons one has to couple the cavity mode with some detector. Considering the harmonic oscillator model of a detector, we analyze how different coupling regimes can affect the statistics of the created quanta., Comment: 10 pages, 2 figures, to appear in the Topical Issue of Physica Scripta: Proceedings of CEWQO-2012

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 initially in the vacuum quantum states. We analyze different regimes of excitation, depending on the ratio of the modulation depth of the time-dependent cavity eigenfrequency to the coupling strength between the cavity mode and detector. We show that statistical properties of the detector quantum state (variances of the photon numbers, photon distribution function, and the degree of quadrature squeezing) can be quite different from that of the field mode. Besides, the mean number of quanta in the detector mode increases with some time delay, compared with the field mode.

We study the photon generation from vacuum via the Dynamical Casimir Effect in a cavity containing a N-level detector in equally-spaced resonant ladder configuration or N-1 identical resonant two-level atoms. If the modulation frequency equals exactly twice the unperturbed cavity frequency, the photon growth goes on steadily for odd N, while for even N at most N-2 photons can be generated. This finding is corroborated by numerical calculations. In the limit $N\to\infty$ we obtain the harmonic oscillator model of the detector, which admits analytical results., Comment: 4+ pages, 3 figures

We study analytically and numerically the dynamical Casimir effect in a cavity containing two stationary 2-level atoms that interact with the resonance field mode via the Tavis-Cummings Hamiltonian. We determine the modulation frequencies for which the field and atomic excitations are generated and study the corresponding dynamical behaviors in the absence of damping. It is shown that the two-atom setup allows for monitoring of photon generation without interrupting the growth, and different entangled states can be generated during the process., Comment: 4+ pages, 2 figures

We consider the scenario in which a damped three-level atom in the ladder or V configurations is coupled to a single cavity mode whose vacuum state is amplified by dint of the dynamical Casimir effect. We obtain approximate analytical expressions and exact numerical results for the time-dependent probabilities, demonstrating that the presence of the third level modifies the photon statistics and its population can serve as a witness of photon generation from vacuum., Comment: 7 pages, 4 figures

Exact and approximate formulas for the upper bound of the relative energy difference of two Gaussian states with the fixed fidelity between them are derived. The reciprocal formulas for the upper bound of the fidelity for the fixed value of the relative energy difference are obtained as well. The bounds appear higher for pure states than for mixed ones, and their maximal values correspond to squeezed vacuum states. In particular, to guarantee the relative energy difference less than 10%, for quite arbitrary Gaussian states, the fidelity between them must exceed the level 0.998866., Comment: 9 pages, accepted for publication in Journal of Physics A

We study analytically the photon generation from vacuum due to the Dynamical Casimir effect in a cavity with a two-level atom, prepared initially in an arbitrary pure state. Performing small unitary transformations we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant/dispersive regimes., Comment: 5 pages, 2 figures

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., Comment: 12 pages, the text corresponds to the final published version, except for the layout and reference style

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)

We propose an experimental scheme to probe the form of one-count operation used in the theory of continuous photodetection in cavities. Two main steps are: 1) an absorption of a single photon by an atom passing through a high-Q cavity containing electromagnetic field in a thermal or coherent state, 2) a subsequent measurement of the photon statistics in the new field state arising after the photon absorption. Then comparing the probabilities of finding 0 and 1 photons in the initial and final states of the field, one can make conclusions on the form of the one-count operation. This method can be readily applied in the microwave cavity QED with present technology., Comment: 5 pages, 4 figures. New references and discussion added

We examine some aspects of the continuous photodetection model for photocounting processes in cavities. First, we work out a microscopic model that describes the field-detector interaction and deduce a general expression for the Quantum Jump Superoperator (QJS), that shapes the detector's post-action on the field upon a detection. We show that in particular cases our model recovers the QJSs previously proposed ad hoc in the literature and point out that by adjusting the detector parameters one can engineer QJSs. Then we set up schemes for experimental verification of the model. By taking into account the ubiquitous non-idealities, we show that by measuring the lower photocounts moments and the mean waiting time one can check which QJS better describes the photocounting phenomenon., Comment: 12 pages, 7 figures. Contribution to the conference Quantum Optics III, Pucon - Chile, November 27-30, 2006

We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an environment can be simulated by two classical stochastic forces. This family is determined by three time-dependent correlation functions (besides the frequency and damping coefficients), and it includes as special cases the known master equations, whose dissipative part is bilinear with respect to the operators of coordinate and momentum., Comment: 10 pages, no figures

Some non-ideal effects as non-unit quantum efficiency, dark counts, dead time and cavity losses that occur in experiments are incorporated within the continuous photodetection model by using the analytical quantum trajectories approach. We show that in standard photocounting experiments the validity of the model can be verified, and the formal expression for the quantum jump superoperator can also be checked.

We study the back-action of a single photon detector on the electromagnetic field upon a photodetection by considering a microscopic model in which the detector is constituted of a sensor and an amplification mechanism. Using the quantum trajectories approach we determine the Quantum Jump Superoperator (QJS) that describes the action of the detector on the field state immediately after the photocount. The resulting QJS consists of two parts: the bright counts term, representing the real photoabsorptions, and the dark counts term, representing the amplification of intrinsic excitations inside the detector. First we compare our results for the counting rates to experimental data, showing a good agreement. Then we point out that by modifying the field frequency one can engineer the form of QJS, obtaining the QJS's proposed previously in an ad hoc manner.

We discuss the quantum jump operation in an open system, and show that jump super-operators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with 2-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that derived quantum jump super-operators have `nonlinear' form which depends on assumptions made about the interaction between the system and the detector. A continuous transition to the standard Srinivas--Davies form of the quantum jump super-operatoris shown.

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., Comment: 14 pages, 6 figures, LaTex; to appear in Physics Letters A

We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used., Comment: 12 pages, 4 figures

We introduce a simple measure of "classicality" of pure and mixed quantum states as a maximum value of the Hilbert-Schmidt "scalar products" between the renormalized statistical operators of the state concerned and all displaced thermal states. Choosing Fock states as the reference set, we introduce the measure of "anticlassicality". Both measures are illustrated for the Fock, coherent phase, and generic mixed Gaussian states. Gaussian states are shown to be the closest to thermal states possessing the same degree of quantum purity. On the contrary, Fock states appear to be more close to mixed thermal states than to pure coherent states., Comment: LaTex, 10 p., 3 PS figures; to appear in Physics Letters A

We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a possibility of using the Fokker-Planck equation to describe this evolution. Studying different interaction Hamiltonians, we show that unambiguous reduction to the Fokker-Planck equation is possible only within the framework of the so called rotating-wave approximation. As special cases we consider in detail the evolution of two coupled oscillators and relaxation of a charged oscillator in a uniform magnetic field., Comment: LaTex, 22 pages. This is the third part (pages 32-56) of the paper by the authors entitled "Quantum nonstationary oscillator: models and applications"

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropic coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered: a three-dimensional cavity possessing eigenfrequencies $\omega_3=3\omega_1$, whose wall oscillates at the frequency $\omega_w=2\omega_1$, and a one-dimensional (Fabry--Perot) cavity with an equidistant spectrum $\omega_n= n\omega_1$, when the distance between perfect mirrors oscillates at the frequencies $\omega_1$ and $2\omega_1$. The behaviour of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except for some specific situations, where the covariance entanglement coefficient, based on traces of covariance submatrices, seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field are considered: vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states., Comment: 23 pages, 10 figures; to appear in Journal of Russian Laser Research