arXiv subjects
Publications and source records attributed to V. V. Dodonov.
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 consider a relaxation of a single mode of the quantized field in a presence of one- and two-photon absorption and emission processes. Exact stationary solutions of the master equation for the diagonal elements of the density matrix in the Fock basis are found in the case of completely saturated two-photon emission. If two-photon processes dominate over single-photon ones, the stationary state is a mixture of phase averaged even and odd coherent states.
We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like {\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS) are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to {\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<π/(2g), being identically equal to zero for |x-kt|>π/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.
We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.
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 vacuum in the (j+ps)th mode goes asymptotically to a constant value $cp^2\sin^2(πj/p)\sqrt{ε^2-δ^2}/[πL_0 (j+ps)]$, the numbers of photons in the modes with indices p,2p,3p,... being the integrals of motion. The total number of photons in all the modes is proportional to $p^3(ε^2-δ^2) t^2$ in the short-time and in the long-time limits. In the case of strong detuning $|δ|>ε$ the total energy and the total number of photons generated from vacuum oscillate with the amplitudes decreasing as $(ε/δ)^2$ for $ε\ll|δ|$. The special cases of p=1 and p=2 are studied in detail.
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we apply the quantum singular time dependent oscillator model to describe the relative one dimensional motion of two ions in a trap. We argue that the model can be justified for low energy excited states with the quantum numbers $n\ll n_{max}\sim 100$, provided that the dimensionless constant characterizing the strength of the repulsive potential is large enough, $g_*\sim 10^5$. Time dependent Gaussian-like wave packets generalizing odd coherent states of the harmonic oscillator, and excitation number eigenstates are constructed. We show that the relative motion of the ions, in contradistinction to its center of mass counterpart, is extremely sensitive to the time dependence of the binding harmonic potential, since the large value of $g_*$ results in a significant amplification of the transition probabilities between energy eigenstate even for slow time variations of the frequency.
The problem of wave packet tunneling from a parabolic potential well through a barrier represented by a power potential is considered in the case when the barrier height is much greater than the oscillator ground state energy, and the difference between the average energy of the packet and the nearest oscillator eigenvalue is sufficiently small. The universal Poisson distribution of the partial tunneling rates from the oscillator energy levels is discovered. The explicit expressions for the tunneling rates of different types of packets (coherent, squeezed, even/odd, thermal, etc.) are given in terms of the exponential and modified Bessel functions. The tunneling rates turn out very sensitive to the energy distributions in the packets, and they may exceed significantly the tunneling rate from the energy state with the same average number of quanta.
The primary aim of the present paper is to attract the attention of particle physicists to new developments in studying squeezed and correlated states of the electromagnetic field as well as of those working on the latest topic to new findings about multiplicity distributions in quantum chromodynamics. The new types of nonclassical states used in quantum optics as squeezed states, correlated states, even and odd coherent states (Schrödinger cat states) for one--mode and multimode interaction are reviewed. Their distribution functions are analyzed according to the method used first for multiplicity distributions in high energy particle interactions. The phenomenon of oscillations of particle distribution functions of the squeezed fields is described and confronted to the phenomenon of oscillations of cumulant moments of some distributions for squeezed and correlated field states. Possible extension of the method to fields different from the electromagnetic field (gluons, pions, etc.) is speculated.
We study the Photon statistics in the superpositions of coherent states $|α\rangle$ and $|α^*\rangle$ named ``Schrödinger real and imaginary cat states''. The oscillatory character of photon distribution function (PDF) emerging due to the quantum interference between the two components is shown, and the phenomenon of the quadrature squeezing is observed for the moderate values of $|α|\sim 1$. Despite the quantity ${\langle\triangle n^2\rangle}/{\langle n\rangle}$ tends to the unit value (like in the Poissonian PDF) at $|α|\gg 1$, the photon statistics is essentially non-Poissonian for all values of $|α|$. The factorial moments and cumulants of the PDF are calculated, and the oscillations of their ratio are demonstrated.
Photon distribution function, means and dispersions are found explicitly for the nonclassical state of light which is created from the photon--added coherent state $\vert α,m \rangle$ due to a time--dependence of the frequency of the electromagnetic field oscillator. Generating function for factorial momenta is obtained. The Wigner function and Q--function are constructed explicitly for the excited photon--added coherent state of light. Influence of added photons on known oscillations of photon distribution function for squeezed light is demonstrated. oscillator are considered.
The cumulants and factorial moments of photon distribution for squeezed and correlated light are calculated in terms of Chebyshev, Legendre and Laguerre polynomials. The phenomenon of strong oscillations of the ratio of the cumulant to factorial moment is found.
The multimode even and odd coherent states (multimode Schroedinger cat states) are constructed for polymode parametric oscillators of the electromagnetic field. The evolution of the photon distribution function is evaluated explicitly. The distribution function is expressed in terms of the multivariable Hermite polynomials, its means and dispersions are calculated. The conditions for the existence of squeezing are formulated. The correlations among the different modes of Schroedinger cat states are studied.
The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for large values of indices are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.
The oscillations of photon distribution function for squeezed and correlated light are shown to decrease when the temperature increases.The influence of the squeezing parameter and photon quadrature correlation coefficient on the photon distribution oscillations at nonzero temperatures is studied. The connection of deformation of Planck distribution formula with oscillations of distribution for squeezed and correlated light is discussed.
For N-mode light described by the Wigner function of generic Gaussian form the photon distribution function is obtained explicitly and expressed in terms of Hermite polynomial of $2N$ variables with equal pairs of indices.The mean values and dispersions of photon numbers are obtained for this generic mixed state.Generating function for photon distribution is obtained explicitly. The expression for $N$-mode photon distribution function for squeezed photon number states in terms of Hermite polynomials of $2N$ variables and for squeezed coherent states in terms of Hermite polynomials of $N$ variables is discussed.
For one-mode light described by the Wigner function of generic Gaussian form the photon distribution function is obtained explicitly and expressed in terms of Hermite polynomials of two variables.The mean values and dispersions of photon numbers are obtained for this generic %mixed state.Generating function for photon distribution is discussed.Known partial cases of thermal state,correlated state,squeezed state and coherent state are considered.The connection of Schrodinger uncertainty relation for quadratures with photon distribution is demonstrated explicitly.