Tripartite and bipartite entanglement in continuous-variable tripartite systems

We examine one asymmetric adnd two fully symmetric Gaussian continuous-variable systems in terms of their tripartite and bipartite entanglement properties. We treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models, and standard beamsplitter relations for a model that mixes the outputs of optical parametric oscillators. Our two symmetric systems exhibit perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, all three systems exhibit both tripartite and bipartite entanglement. We conclude that none of the outputs are completely analogous to either GHZ or W states, but there are parameter regions where they produce T states introduced by Adesso \etal The qualitative differences in the output states for different interaction parameters indicate that continuous-variable tripartite quantum information systems offer a versatility not found in bipartite systems.Comment: 18 pages, 6 figures. arXiv admin note: text overlap with arXiv:1510.0182

Improved quantum correlations in second harmonic generation with a squeezed pump

We investigate the effects of a squeezed pump on the quantum properties and conversion efficiency of the light produced in single-pass second harmonic generation. Using stochastic integration of the two-mode equations of motion in the positive-P representation, we find that larger violations of continuous-variable harmonic entanglement criteria are available for lesser effective interaction strengths than with a coherent pump. This enhancement of the quantum properties also applies to violations of the Reid-Drummond inequalities used to demonstrate a harmonic version of the Einstein-Podolsky-Rosen paradox. We find that the conversion efficiency is largely unchanged except for very low pump intensities and high levels of squeezing.Comment: 19 pages, 7 figure

Quantum field effects in coupled atomic and molecular Bose-Einstein condensates

This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive-P representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The model includes all interactions between the particles, background gas losses, two-body losses and the numerical simulations are performed in three dimensions. It is found that it is possible to differentiate the quantum and semiclassical behaviour when the particle density is sufficiently low and the coupling is sufficiently strong.Comment: 4 postscript figure

Quantum-field-theoretical techniques for stochastic representation of quantum problems

We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic difference equations in discretised time

Pairing mean-field theory for the dynamics of dissociation of molecular Bose-Einstein condensates

We develop a pairing mean-field theory to describe the quantum dynamics of the dissociation of molecular Bose-Einstein condensates into their constituent bosonic or fermionic atoms. We apply the theory to one, two, and three-dimensional geometries and analyze the role of dimensionality on the atom production rate as a function of the dissociation energy. As well as determining the populations and coherences of the atoms, we calculate the correlations that exist between atoms of opposite momenta, including the column density correlations in 3D systems. We compare the results with those of the undepleted molecular field approximation and argue that the latter is most reliable in fermionic systems and in lower dimensions. In the bosonic case we compare the pairing mean-field results with exact calculations using the positive-$P$ stochastic method and estimate the range of validity of the pairing mean-field theory. Comparisons with similar first-principle simulations in the fermionic case are currently not available, however, we argue that the range of validity of the present approach should be broader for fermions than for bosons in the regime where Pauli blocking prevents complete depletion of the molecular condensate.Comment: 16 pages, 10 figure

Generating controllable atom-light entanglement with a Raman atom laser system

We introduce a scheme for creating continuous variable entanglement between an atomic beam and an optical field, by using squeezed light to outcouple atoms from a BEC via a Raman transition. We model the full multimode dynamics of the atom laser beam and the squeezed optical field, and show that with appropriate two-photon detuning and two-photon Rabi frequency, the transmitted light is entangled in amplitude and phase with the outcoupled atom laser beam. The degree of entanglement is controllable via changes in the two-photon Rabi frequency of the outcoupling process.Comment: 4 pages, 4 figure