Wave mixing of optical pulses and Bose-Einstein condensates

We investigate theoretically the four-wave mixing of optical and matter waves resulting from the scattering of a short light pulse off an atomic Bose-Einstein condensate, as recently demonstrated by D. Schneble {\em et al.} [ Science {\bf 300}, 475 (2003)]. We show that atomic ``pair production'' from the condensate results in the generation of both forward- and backward-propagating matter waves. These waves are characterized by different phase-matching conditions, resulting in different angular distributions and temporal evolutions.Comment: 4+\epsilon pages, 3 figure

Quantification of Macroscopic Quantum Superpositions within Phase Space

Based on phase-space structures of quantum states, we propose a novel measure to quantify macroscopic quantum superpositions. Our measure simultaneously quantifies two different kinds of essential information for a given quantum state in a harmonious manner: the degree of quantum coherence and the effective size of the physical system that involves the superposition. It enjoys remarkably good analytical and algebraic properties. It turns out to be the most general and inclusive measure ever proposed that it can be applied to any types of multipartite states and mixed states represented in phase space.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

A temperature behavior of the frustrated translational mode of adsorbate and the nature of the "adsorbate-substrate" interaction

A temperature behavior of the frustrated translational mode (T-mode) of a light particle, coupled by different regimes of ohmicity to the surface, is studied within a formalism of the generalized diffusion coefficients. The memory effects of the adsorbate motion are considered to be the main reason of the T-mode origin. Numerical calculations yield a thermally induced shift and broadening of the T-mode, which is found to be linear in temperature for Ohmic and super-Ohmic systems and nonlinear for strongly sub-Ohmic ones. We obtain analytical expressions for the T-mode shift and width at weak coupling for the systems with integer "ohmicity" indexes n=0-2 in zero temperature and high temperature limits. We provide an explanation of the experimentally observed blue- or red-shifts of the T-mode on the basis of a comparative analysis of two typical times of the system evolution: a time of decay of the "velocity-velocity" autocorrelation function, and a correlation time of the thermal bath random forces. A relation of the T-mode to the multiple jumps of the adsorbate is discussed, and generalization of conditions of the multiple hopping to the case of quantum surface diffusion is performed.Comment: 12 pages, 4 figure

Non-Markovian disentanglement dynamics of two-qubit system

We investigated the disentanglement dynamics of two-qubit system in Non-Markovian approach. We showed that only the couple strength with the environment near to or less than fine-structure constant 1/137, entanglement appear exponential decay for a certain class of two-qubit entangled state. While the coupling between qubit and the environment is much larger, system always appears the sudden-death of entanglement even in the vacuum environment.Comment: 17 pages, 3 figure

Prescription for experimental determination of the dynamics of a quantum black box

We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient conditions for this to be possible, and illustrate the general theory by considering specifically one and two quantum bit systems. These procedures may be useful in the comparative evaluation of experimental quantum measurement, communication, and computation systems.Comment: 6 pages, Revtex. Submitted to J. Mod. Op

Second Virial Coefficient for Noncommutative Space

The second virial coefficient $B_{2}^{nc}(T)$ for non-interacting particles moving in a two-dimensional noncommutative space and in the presence of a uniform magnetic field $\vec B$ is presented. The noncommutativity parameter \te can be chosen such that the $B_{2}^{nc}(T)$ can be interpreted as the second virial coefficient for anyons of statistics \al in the presence of $\vec B$ and living on the commuting plane. In particular in the high temperature limit \be\lga 0, we establish a relation between the parameter \te and the statistics \al. Moreover, $B_{2}^{nc}(T)$ can also be interpreted in terms of composite fermions.Comment: 11 pages, misprints corrected and references adde

On the critical exponent of a quantum noise driven phase transition: the open system Dicke-model

The quantum phase transition of the Dicke-model has been observed recently in a system formed by motional excitations of a laser-driven Bose--Einstein condensate coupled to an optical cavity [1]. The cavity-based system is intrinsically open: photons can leak out of the cavity where they are detected. Even at zero temperature, the continuous weak measurement of the photon number leads to an irreversible dynamics towards a steady-state which exhibits a dynamical quantum phase transition. However, whereas the critical point and the mean field is only slightly modified with respect to the phase transition in the ground state, the entanglement and the critical exponents of the singular quantum correlations are significantly different in the two cases.Comment: 7 page

Bell inequalities for Continuous-Variable Measurements

Tests of local hidden variable theories using measurements with continuous variable (CV) outcomes are developed, and a comparison of different methods is presented. As examples, we focus on multipartite entangled GHZ and cluster states. We suggest a physical process that produces the states proposed here, and investigate experiments both with and without binning of the continuous variable. In the former case, the Mermin-Klyshko inequalities can be used directly. For unbinned outcomes, the moment-based CFRD inequalities are extended to functional inequalities by considering arbitrary functions of the measurements at each site. By optimising these functions, we obtain more robust violations of local hidden variable theories than with either binning or moments. Recent inequalities based on the algebra of quaternions and octonions are compared with these methods. Since the prime advantage of CV experiments is to provide a route to highly efficient detection via homodyne measurements, we analyse the effect of noise and detection losses in both binned and unbinned cases. The CV moment inequalities with an optimal function have greater robustness to both loss and noise. This could permit a loophole-free test of Bell inequalities.Comment: 17 pages, 6 figure

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behaviour in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.Comment: More references and examples. Much less mathematical materia

Comparison of Quantum and Classical Local-field Effects on Two-Level Atoms in a Dielectric

The macroscopic quantum theory of the electromagnetic field in a dielectric medium interacting with a dense collection of embedded two-level atoms fails to reproduce a result that is obtained from an application of the classical Lorentz local-field condition. Specifically, macroscopic quantum electrodynamics predicts that the Lorentz redshift of the resonance frequency of the atoms will be enhanced by a factor of the refractive index n of the host medium. However, an enhancement factor of (n*n+2)/3 is derived using the Bloembergen procedure in which the classical Lorentz local-field condition is applied to the optical Bloch equations. Both derivations are short and uncomplicated and are based on well-established physical theories, yet lead to contradictory results. Microscopic quantum electrodynamics confirms the classical local-field-based results. Then the application of macroscopic quantum electrodynamic theory to embedded atoms is proved false by a specific example in which both the correspondence principle and microscopic theory of quantum electrodynamics are violated.Comment: Published version with rewritten abstract and introductio