Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction

A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium ($\chi^{(3)}$ non-linearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are discussed. We provide examples of quantum interference, sub-Planck phase space structures, and Gaussian versus non-Gaussian dynamical evolution of the state. The results also apply to the description of a nanomechanical resonator with an intrinsic Duffing nonlinearity.Comment: 10 pages, 11 figure

Sudden vanishing and reappearance of nonclassical effects: General occurrence of finite-time decays and periodic vanishings of nonclassicality and entanglement witnesses

Analyses of phenomena exhibiting finite-time decay of quantum entanglement have recently attracted considerable attention. Such decay is often referred to as sudden vanishing (or sudden death) of entanglement, which can be followed by its sudden reappearance (or sudden rebirth). We analyze various finite-time decays (for dissipative systems) and analogous periodic vanishings (for unitary systems) of nonclassical correlations as described by violations of classical inequalities and the corresponding nonclassicality witnesses (or quantumness witnesses), which are not necessarily entanglement witnesses. We show that these sudden vanishings are universal phenomena and can be observed: (i) not only for two- or multi-mode but also for single-mode nonclassical fields, (ii) not solely for dissipative systems, and (iii) at evolution times which are usually different from those of sudden vanishings and reappearances of quantum entanglement.Comment: 10 pages, 3 figure

Atomic Squeezing under Collective Emission

Atomic squeezing is studied for the case of large systems of radiating atoms, when collective effects are well developed. All temporal stages are analyzed, starting with the quantum stage of spontaneous emission, passing through the coherent stage of superradiant emission, and going to the relaxation stage ending with stationary solutions. A method of governing the temporal behaviour of the squeezing factor is suggested. The influence of a squeezed effective vacuum on the characteristics of collective emission is also investigated.Comment: Latex file, 21 page, 9 figure

Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]

The quantization of phase is still an open problem. In the approach of Susskind and Glogower so called cosine and sine operators play a fundamental role. Their eigenstates in the Fock representation are related with the Chebyshev polynomials of the second kind. Here we introduce more general cosine and sine operators whose eigenfunctions in the Fock basis are related in a similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1]. To each polynomial set defined in terms of a weight function there corresponds a pair of cosine and sine operators. Depending on the symmetry of the weight function we distinguish generalized or extended operators. Their eigenstates are used to define cosine and sine representations and probability distributions. We consider also the inverse arccosine and arcsine operators and use their eigenstates to define cosine-phase and sine-phase distributions, respectively. Specific, numerical and graphical results are given for the classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure

The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators

We develop a method for the determination of thecdynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the quantum-classical correspondence. Using this method, we find analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.Comment: 15 pages, RevTEX (EPSF-style), 3 figs. Replaced with final version (stylistic corrections

Direct sampling of exponential phase moments of smoothed Wigner functions

We investigate exponential phase moments of the s-parametrized quasidistributions (smoothed Wigner functions). We show that the knowledge of these moments as functions of s provides, together with photon-number statistics, a complete description of the quantum state. We demonstrate that the exponential phase moments can be directly sampled from the data recorded in balanced homodyne detection and we present simple expressions for the sampling kernels. The phase moments are Fourier coefficients of phase distributions obtained from the quasidistributions via integration over the radial variable in polar coordinates. We performed Monte Carlo simulations of the homodyne detection and we demonstrate the feasibility of direct sampling of the moments and subsequent reconstruction of the phase distribution.Comment: RevTeX, 8 pages, 6 figures, accepted Phys. Rev.

Quantum-scissors device for optical state truncation: A proposal for practical realization

We propose a realizable experimental scheme to prepare superposition of the vacuum and one-photon states by truncating an input coherent state. The scheme is based on the quantum scissors device proposed by Pegg, Phillips, and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] and uses photon-counting detectors, a single-photon source, and linear optical elements. Realistic features of the photon counting and single-photon generation are taken into account and possible error sources are discussed together with their effect on the fidelity and efficiency of the truncation process. Wigner function and phase distribution of the generated states are given and discussed for the evaluation of the proposed scheme.Comment: 11 pages, 12 figures, the final version to appear in Phys. Rev. A64, 0638xx (2001

Response of a two-level atom to a narrow-bandwidth squeezed-vacuum excitation

Using the coupled-system approach we calculate the optical spectra of the fluorescence and transmitted fields of a two-level atom driven by a squeezed vacuum of bandwidths smaller than the natural atomic linewidth. We find that in this regime of squeezing bandwidths the spectra exhibit unique features, such as a hole burning and a three-peak structure, which do not appear for a broadband excitation. We show that the features are unique to the quantum nature of the driving squeezed vacuum field and donor appear when the atom is driven by a classically squeezed field. We find that a quantum squeezed-vacuum field produces squeezing in the emitted fluorescence field which appears only in the squeezing spectrum while there is no squeezing in the total field. We also discuss a nonresonant excitation and find that depending on the squeezing bandwidth there is a peak or a hole in the spectrum at a frequency corresponding to a three-wave-mixing process. The hole appears only for a broadband excitation and results from the strong correlations between squeezed-vacuum photons

Quantum entanglement and disentanglement of multi-atom systems

We present a review of recent research on quantum entanglement, with special emphasis on entanglement between single atoms, processing of an encoded entanglement and its temporary evolution. Analysis based on the density matrix formalism are described. We give a simple description of the entangling procedure and explore the role of the environment in creation of entanglement and in disentanglement of atomic systems. A particular process we will focus on is spontaneous emission, usually recognized as an irreversible loss of information and entanglement encoded in the internal states of the system. We illustrate some certain circumstances where this irreversible process can in fact induce entanglement between separated systems. We also show how spontaneous emission reveals a competition between the Bell states of a two qubit system that leads to the recently discovered "sudden" features in the temporal evolution of entanglement. An another problem illustrated in details is a deterministic preparation of atoms and atomic ensembles in long-lived stationary squeezed states and entangled cluster states. We then determine how to trigger the evolution of the stable entanglement and also address the issue of a steered evolution of entanglement between desired pairs of qubits that can be achieved simply by varying the parameters of a given system.Comment: Review articl