Patrick Navez

Non-Gaussian cloning of quantum coherent states is optimal

We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. Both optimal fidelities are attained for phase space translation covariant cloners. Remarkably, the joint fidelity is maximized by a Gaussian cloner, whereas the single-clone fidelity can be enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can achieve a single-clone fidelity of approximately 0.6826, perceivably higher than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can be realized by means of an optical parametric amplifier supplemented with a particular source of non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.

Cloning a real d-dimensional quantum state on the edge of the no-signaling condition

We investigate the class of quantum cloning machines that equally duplicate all real states in a Hilbert space of arbitrary dimension. By using the no-signaling condition, namely, that cloning cannot make superluminal communication possible, we derive an upper bound on the fidelity of this class of quantum cloning machines. Then, for each dimension d, we construct an optimal symmetric cloner whose fidelity saturates this bound. Similar calculations can also be performed in order to recover the fidelity of the optimal universal cloner in d dimensions.

Emergence of coherence in the Mott--superfluid quench of the Bose-Hubbard model

We study the quench from the Mott-insulator to the superfluid phase in the Bose-Hubbard model and investigate the spatial-temporal growth of phase coherence, that is, phase locking between initially uncorrelated sites. To this end, we establish a hierarchy of correlations via a controlled expansion into inverse powers of the coordination number 1/Z. It turns out that the off-diagonal long-range order spreads with a constant propagation speed, forming local condensate patches, whereas the phase correlator follows a diffusionlike growth rate.

Cloning quantum entanglement in arbitrary dimensions

We have found a quantum cloning machine that optimally duplicates the entanglement of a pair of d-dimensional quantum systems prepared in an arbitrary isotropic state. It maximizes the entanglement of formation contained in the two copies of any maximally entangled input state, while preserving the separability of unentangled input states. Moreover, it cannot increase the entanglement of formation of isotropic states. For large d, the entanglement of formation of each clone tends to one-half the entanglement of the input state, which corresponds to a classical behavior. Finally, we investigate a local entanglement cloner, which yields entangled clones with one-fourth the input entanglement in the large-d limit.

Sauter-Schwinger-like tunneling in tilted Bose-Hubbard lattices in the Mott phase

We study the Mott phase of the Bose-Hubbard model on a tilted lattice. On the (Gutzwiller) mean-field level, the tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive a quantitative analogy to the Sauter-Schwinger effect, i.e., electron-positron pair creation out of the vacuum by an electric field. For large tilts, we obtain resonant tunneling related to Bloch oscillations.

Propagation of quantum correlations after a quench in the Mott-insulator regime of the Bose-Hubbard model

We study a quantum quench in the Bose-Hubbard model where the tunneling rate J is suddenly switched from zero to a finite value in the Mott regime. In order to solve the many-body quantum dynamics far from equilibrium, we consider the reduced density matrices for a finite number of lattice sites and split them up into on-site density operators, i.e., the mean field, plus two-point and three-point correlations etc. Neglecting three-point and higher correlations, we are able to numerically simulate the time-evolution of the on-site density matrices and the two-point quantum correlations (e.g., their effective light-cone structure) for a comparably large number O(103) of lattice sites.

Quasi-particle approach for lattice Hamiltonians with large coordination numbers

In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this linearization should be justified by an expansion into the powers of some small control parameter. Here, we present a method for general lattice Hamiltonians with large coordination numbers Z 1, which is based on an expansion into the powers of 1/Z. In order to demonstrate the generality of our method, we apply it to various spin systems, as well as the Bose and Fermi–Hubbard model.

Phase diagram of quasi-two-dimensional bosons in a laser-speckle potential

We have studied the phase diagram of a quasi-two-dimensional interacting Bose gas at zero temperature in the presence of random potential created by laser speckles. The superfluid fraction and the fraction of particles with zero momentum are obtained within the mean-field Gross-Pitaevskii theory and in diffusion Monte Carlo simulations. We find a transition from the superfluid to the insulating state when the strength of the disorder grows. Estimations of the critical parameters are compared with the predictions of the percolation theory in the Thomas-Fermi approximation. Analytical expressions for the zero-momentum fraction and the superfluid fraction are derived in the limit of weak disorder and weak interactions within the framework of the Bogoliubov theory. Limits of validity of various approximations are discussed.

Collisionless dynamics of the condensate predicted in the random phase approximation

From the microscopic theory, we derive a number conserving quantum kinetic equation, for a dilute Bose gas valid at any temperature, in which the binary collisions between the quasi-particles are mediated by the Bogoliubov collective excitations. This different approach starts from the many-body Hamiltonian of a Boson gas and uses, in an appropriate way, the generalized random phase approximation. As a result, the collision term of the kinetic equation contains higher order contributions in the expansion in the interaction parameter. The major interest of this particular mechanism is that, in a regime where the condensate is stable, the collision process between condensed and noncondensed particles is totally blocked due to a total annihilation of the mutual interaction potential induced by the condensate itself. As a consequence, the condensate is not constrained to relax and can be superfluid. Furthermore, a Boltzmann-like H-theorem for the entropy exists for this equation and allows to distinguish between dissipative and nondissipative phenomena (like vortices). We also illustrate the analogy between this approach and the kinetic theory for a plasma, in which the collective excitations correspond precisely to a plasmon. The spectrum of these excitations and their damping are exactly the ones obtained from the gapless and conserving equilibrium dielectric formalism developed in Fliesser et al. [Phys. Rev. A 64 (2001) 013609]. Finally, we recover the Bogoliubov results for the ground state energy and the particle momentum distribution. This work contains more details of the summary presented in Navez [J. Low Temp. Phys., 138 (2005) 705–710].

Kinetic theory and dynamic structure factor of a condensate in the random phase approximation

No HeadingWe present the microscopic kinetic theory of a homogeneous dilute Bose condensed gas in the generalized random phase approximation (GRPA), which satisfies the following requirements: 1) the mass, momentum and energy conservation laws; 2) the H-theorem; 3) the superfluidity property and 4) the recovery of the Bogoliubov theory at zero temperature 1. In this approach, the condensate influences the binary collisional process between two normal atoms, in the sense that their interaction force results from the mediation of a Bogoliubov collective excitation traveling throughout the condensate. Furthermore, as long as the Bose gas is stable, no collision happens between condensed and normal atoms. In this paper, we show how the kinetic theory in the GRPA allows to calculate the dynamic structure factor at finite temperature and when the normal and superfluid are in a relative motion. The obtained spectrum for this factor provides a prediction which, compared to the experimental results, allows to validate the GRPA.