Critical fluctuations and entanglement in the nondegenerate parametric oscillator

We present a fully quantum mechanical treatment of the nondegenerate optical parametric oscillator both below and near threshold. This is a nonequilibrium quantum system with a critical point phase transition, that is also known to exhibit strong yet easily observed squeezing and quantum entanglement. Our treatment makes use of the positive P representation and goes beyond the usual linearized theory. We compare our analytical results with numerical simulations and find excellent agreement. We also carry out a detailed comparison of our results with those obtained from stochastic electrodynamics, a theory obtained by truncating the equation of motion for the Wigner function, with a view to locating regions of agreement and disagreement between the two. We calculate commonly used measures of quantum behavior including entanglement, squeezing, and Einstein-Podolsky-Rosen (EPR) correlations as well as higher order tripartite correlations, and show how these are modified as the critical point is approached. These results are compared with those obtained using two degenerate parametric oscillators, and we find that in the near-critical region the nondegenerate oscillator has stronger EPR correlations. In general, the critical fluctuations represent an ultimate limit to the possible entanglement that can be achieved in a nondegenerate parametric oscillator.

Continuous-variable Einstein-Podolsky-Rosen paradox with traveling-wave second-harmonic generation

The Einstein-Podolsky-Rosen paradox and quantum entanglement are at the heart of quantum mechanics. Here we show that single-pass traveling-wave second-harmonic generation can be used to demonstrate both entanglement and the paradox with continuous variables that are analogous to the position and momentum of the original proposal.

Entanglement and the Einstein-Podolsky-Rosen paradox with coupled intracavity optical down-converters

We show that two evanescently coupled χ((2)) parametric down-converters inside a Fabry-Perot cavity provide a tunable source of quadrature squeezed light, Einstein-Podolsky-Rosen (EPR) correlations and quantum entanglement. Analyzing the operation in the below threshold regime, we show how these properties can be controlled by adjusting the coupling strengths and the cavity detunings. As this can be implemented with integrated optics, it provides a possible route to rugged and stable EPR sources.

Calculation of the microcanonical temperature for the classical Bose field

The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated by a time average over a sufficiently long period of dynamical evolution. In this paper, we describe in detail how to calculate the temperature and chemical potential from the dynamics of a microcanonical classical field, using the particular example of the classical modes of a Bose-condensed gas. The accurate determination of these thermodynamics quantities is essential in measuring the shift of the critical temperature of a Bose gas due to nonperturbative many-body effects.

Macroscopic quantum Schrdinger and Einstein-Podolsky-Rosen paradoxes

We propose macroscopic generalizations of the Einstein-Podolsky-Rosen paradox in which the completeness of quantum mechanics is contrasted with forms of macroscopic reality and macroscopic local reality defined in relation to Schrodinger's original 'cat' paradox.

Bright entanglement and the Einstein-Podolsky-Rosen paradox with coupled parametric oscillators

We show that two evanescently coupled chi((2)) parametric oscillators provide a tunable bright source of quadrature squeezed light, Einstein-Podolsky-Rosen correlations and quantum entanglement. Analysing the system in the above threshold regime, we demonstrate that these properties can be controlled by adjusting the coupling strengths and the cavity detunings. As this can be implemented with integrated optics, it provides a possible route to rugged and stable EPR sources. (C) 2005 Elsevier B.V. All rights reserved.

Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We compare theoretically the tripartite entanglement available from the use of three concurrent x(2) nonlinearities and three independent squeezed states mixed on beamsplitters, using an appropriate version of the van Loock-Furusawa inequalities. We also define three-mode generalizations of the Einstein-Podolsky-Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

Expansion tube operating conditions for studying nonequilibrium radiation relevant to Titan Aerocapture

The predictions of nonequilibrium radiation in the shock layer for a Titan aerocapture aeroshell vary significantly amongst Computational Fluid Dynamics (CFD) analyses and are limited by the physical models of the nonequilibrium flow processes. Of particular interest are nonequilibrium processes associated with the CN molecule which is a strong radiator. It is necessary to have experimental data for these radiating shock layers which will allow for validation of the CFD models. This paper describes the development of a test flow condition for subscale aeroshell models in a superorbital expansion tunnel. We discuss the need for a Titan gas condition that closely simulates the atmospheric composition and present experimental data of the free stream test flow conditions. Furthermore, we present finite-rate CFD calculations of the facility to estimate the remaining free stream conditions, which cannot be directly measured during experiments.

Interacting nonequilibrium systems with two temperatures

We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being interconnected with each other. Using generating functional analysis, commonly used in statistical mechanics, we find exactly soluble expressions for their individual magnetization that define a two-dimensional nonlinear map, the equations of which have the same form as those obtained for densely connected equilibrium systems. Steady states correspond to the fixed points of this map, separating the parameter space into a rich set of nonequilibrium phases that we analyze in asymptotically high and low (nonequilibrium) temperature limits. The theoretical formalism is shown to revert to the classical nonequilibrium steady state problem for two interacting systems with a nonzero heat transfer between them that catalyzes a phase transition between ambient nonequilibrium states. © 2013 American Physical Society.

Emergence of equilibriumlike domains within nonequilibrium Ising spin systems

Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibriumlike behavior in localized or nonlocalized domains within nonequilibrium Ising spin systems. Equilibrium domains are shown to emerge either abruptly or gradually depending on the system parameters and disappear, becoming indistinguishable from the remainder of the system for other parameter values. © 2013 American Physical Society.