Quantum turbulence in condensate collisions: an application of the classical field method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our non-perturbative method includes the effect of quantum noise, and provides for the first time a theoretical description of collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms are calculated from a single simulation, and show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms--a property which should be straightforwardly measurable.Comment: 5 pages, 3 figures: Rewritten text, replaced figure

Entanglement of formation for symmetric Gaussian states

We show that for a fixed amount of entanglement, two-mode squeezed states are those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact to determine the entanglement of formation for all symmetric Gaussian states corresponding to two modes. This is the first instance in which this measure has been determined for genuine continuous variable systems.Comment: 4 pages, revtex

Biased EPR entanglement and its application to teleportation

We consider pure continuous variable entanglement with non-equal correlations between orthogonal quadratures. We introduce a simple protocol which equates these correlations and in the process transforms the entanglement onto a state with the minimum allowed number of photons. As an example we show that our protocol transforms, through unitary local operations, a single squeezed beam split on a beam splitter into the same entanglement that is produced when two squeezed beams are mixed orthogonally. We demonstrate that this technique can in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure

Quadripartite continuous-variable entanglement via quadruply concurrent downconversion

We investigate an intra-cavity coupled down-conversion scheme to generate quadripartite entanglement using concurrently resonant nonlinearities. We verify that quadripartite entanglement is present in this system by calculating the output fluctuation spectra and then considering violations of optimized inequalities of the van Loock-Furusawa type. The entanglement characteristics both above and below the oscillation threshold are considered. We also present analytic solutions for the quadrature operators and the van Loock-Furusawa correlations in the undepleted pump approximation.Comment: 9 pages, 5 figure

Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement

We propose a cavity QED setup which implements a dissipative Lipkin-Meshkov-Glick model -- an interacting collective spin system. By varying the external model parameters the system can be made to undergo both first-and second-order quantum phase transitions, which are signified by dramatic changes in cavity output field properties, such as the probe laser transmission spectrum. The steady-state entanglement between pairs of atoms is shown to peak at the critical points and can be experimentally determined by suitable measurements on the cavity output field. The entanglement dynamics also exhibits pronounced variations in the vicinities of the phase transitions.Comment: 19 pages, 18 figures, shortened versio

Tripartite entanglement and threshold properties of coupled intracavity downconversion and sum-frequency generation

The process of cascaded downconversion and sum-frequency generation inside an optical cavity has been predicted to be a potential source of three-mode continuous-variable entanglement. When the cavity is pumped by two fields, the threshold properties have been analysed, showing that these are more complicated than in well-known processes such as optical parametric oscillation. When there is only a single pumping field, the entanglement properties have been calculated using a linearised fluctuation analysis, but without any consideration of the threshold properties or critical operating points of the system. In this work we extend this analysis to demonstrate that the singly pumped system demonstrates a rich range of threshold behaviour when quantisation of the pump field is taken into account and that asymmetric polychromatic entanglement is available over a wide range of operational parameters.Comment: 24 pages, 15 figure

The role of quantum fluctuations in the optomechanical properties of a Bose-Einstein condensate in a ring cavity

We analyze a detailed model of a Bose-Einstein condensate trapped in a ring optical resonator and contrast its classical and quantum properties to those of a Fabry-P{\'e}rot geometry. The inclusion of two counter-propagating light fields and three matter field modes leads to important differences between the two situations. Specifically, we identify an experimentally realizable region where the system's behavior differs strongly from that of a BEC in a Fabry-P\'{e}rot cavity, and also where quantum corrections become significant. The classical dynamics are rich, and near bifurcation points in the mean-field classical system, the quantum fluctuations have a major impact on the system's dynamics.Comment: 11 pages, 11 figures, submitted to PR

A comparative study of dynamical simulation methods for the dissociation of molecular Bose-Einstein condensates

We describe a pairing mean-field theory related to the Hartree-Fock-Bogoliubov approach, and apply it to the dynamics of dissociation of a molecular Bose-Einstein condensate (BEC) into correlated bosonic atom pairs. We also perform the same simulation using two stochastic phase-space techniques for quantum dynamics -- the positive P-representation method and the truncated Wigner method. By comparing the results of our calculations we are able to assess the relative strength of these theoretical techniques in describing molecular dissociation in one spatial dimension. An important aspect of our analysis is the inclusion of atom-atom interactions which can be problematic for the positive-P method. We find that the truncated Wigner method mostly agrees with the positive-P simulations, but can be simulated for significantly longer times. The pairing mean-field theory results diverge from the quantum dynamical methods after relatively short times.Comment: 11 pages, 7 figures, corrected typos, minor content change

Decoherence induced by a phase-damping reservoir

A phase damping reservoir composed by $N$-bosons coupled to a system of interest through a cross-Kerr interaction is proposed and its effects on quantum superpo sitions are investigated. By means of analytical calculations we show that: i-) the reservoir induces a Gaussian decay of quantum coherences, and ii-) the inher ent incommensurate character of the spectral distribution yields irreversibility . A state-independent decoherence time and a master equation are both derived an alytically. These results, which have been extended for the thermodynamic limit, show that nondissipative decoherence can be suitably contemplated within the EI D approach. Finally, it is shown that the same mechanism yielding decoherence ar e also responsible for inducing dynamical disentanglement.Comment: 8 pages, 3 figure

Diffraction limit of the sub-Planck structures

The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function, controlled by the sub-Planck structures arising from phase space interference, is obtained exactly. The validity of large phase space support, in which context the asymptotic limit is achieved, is discussed in detail. For large number of coherent states, uniformly located on a circle, it identically matches with the diffraction pattern for a circular ring with uniform angular source strength. This is in accordance with the van Cittert-Zernike theorem, where the overlap function, similar to the mutual coherence function matches with a diffraction pattern.Comment: 5 pages, 3 figure