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.

Bright entanglement in the intracavity nonlinear coupler

We show that the intracavity Kerr nonlinear coupler is a potential source of bright continuous variable entangled light beams which are tunable and spatially separated. We use a linearized fluctuation analysis to calculate the necessary correlations in regimes where it is valid. This means that we are treating regimes where the system exhibits Gaussian statistics so that well-known criteria are both necessary and sufficient to demonstrate entanglement. This system may be realized with integrated optics and thus provides a potentially rugged and stable source of bright entangled beams.

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.

Continuous variable tripartite entanglement from twin nonlinearities

In this work, we analyse and compare the continuous variable tripartite entanglement available from the use of two concurrent or cascaded X (2) nonlinearities. We examine both idealized travelling-wave models and more experimentally realistic intracavity models, showing that tripartite entangled outputs are readily producible. These may be a useful resource for applications such as quantum cryptography and teleportation.

Critical Temperature of a Trapped Bose Gas: Comparison of Theory and Experiment

We apply the projected Gross-Pitaevskii equation (PGPE) formalism to the experimental problem of the shift in critical temperature T-c of a harmonically confined Bose gas as reported in Gerbier , Phys. Rev. Lett. 92, 030405 (2004). The PGPE method includes critical fluctuations and we find the results differ from various mean-field theories, and are in best agreement with experimental data. To unequivocally observe beyond mean-field effects, however, the experimental precision must either improve by an order of magnitude, or consider more strongly interacting systems. This is the first application of a classical field method to make quantitative comparison with experiment.

Gaussian operator bases for correlated fermions

We formulate a general multi-mode Gaussian operator basis for fermions, to enable a positive phase-space representation of correlated Fermi states. The Gaussian basis extends existing bosonic phase-space methods to Fermi systems and thus allows first-principles dynamical or equilibrium calculations in quantum many-body Fermi systems. We prove the completeness of the basis and derive differential forms for products with one- and two-body operators. Because the basis satisfies fermionic superselection rules, the resulting phase space involves only c-numbers, without requiring anticommuting Grassmann variables. Furthermore, because of the overcompleteness of the basis, the phase-space distribution can always be chosen positive. This has important consequences for the sign problem in fermion physics.

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multimode 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 behavior 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.

Generation of a frequency comb of squeezing in an optical parametric oscillator

The multimode operation of an optical parametric oscillator (OPO) operating below threshold is calculated. We predict that squeezing can be generated in a comb that is limited only by the phase matching bandwidth of the OPO. Effects of technical noise on the squeezing spectrum are investigated. It is shown that maximal squeezing can be obtained at high frequency even in the presence of seed laser noise and cavity length fluctuations. Furthermore the spectrum obtained by detuning the laser frequency off OPO cavity resonance is calculated.

Homodyne measurement of the average photon number

We describe a scheme for measurement of the mean photon flux at an arbitrary optical sideband frequency using homodyne detection. Experimental implementation of the technique requires an acousto-optic modulator in addition to the homodyne detector, and does not require phase locking. The technique exhibits polarization and frequency and spatial mode selectivity, as well as much improved speed, resolution, and dynamic range when compared to linear photodetectors and avalanche photodiodes, with potential application to quantum-state tomography and information encoding using an optical frequency basis. Experimental data also support a quantum-mechanical description of vacuum noise.

Signatures for generalized macroscopic superpositions

We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.

Three-body recombination of ultracold Bose gases using the truncated Wigner method

We apply the truncated Wigner method to the process of three-body recombination in ultracold Bose gases. We find that within the validity regime of the Wigner truncation for two-body scattering, three-body recombination can be treated using a set of coupled stochastic differential equations that include diffusion terms, and can be simulated using known numerical methods. As an example we investigate the behavior of a simple homogeneous Bose gas, finding a very slight increase of the loss rate compared to that obtained by using the standard method.

Mean-field phase diagrams of imbalanced Fermi gases near a Feshbach resonance

We propose phase diagrams for an imbalanced (unequal number of atoms or Fermi surface in two pairing hyperfine states) gas of atomic fermions near a broad Feshbach resonance using mean-field theory. Particularly, in the plane of interaction and polarization we determine the region for a mixed phase composed of normal and superfluid components. We compare our prediction of phase boundaries with the recent measurement and find a good qualitative agreement.

Temperature of a trapped unitary Fermi gas at finite entropy

We present theoretical predictions for the equation of state of a harmonically trapped Fermi gas in the unitary limit. Our calculations compare Monte Carlo results with the equation of state of a uniform gas using three distinct perturbation schemes. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conversion into the weakly interacting limit of molecular BEC. We predict the entropy dependence of the equation of state.

Practical limitations in optical entanglement purification

Entanglement purification protocols play an important role in the distribution of entangled systems, which is necessary for various quantum information processing applications. We consider the effects of photodetector efficiency and bandwidth, channel loss and mode mismatch on the operation of an optical entanglement purification protocol. We derive necessary detector and mode-matching requirements to facilitate practical operation of such a scheme, without having to resort to destructive coincidence-type demonstrations.