arXiv subjects

Patrick Navez

Publications and source records attributed to Patrick Navez.

33 records · Page 2Linked to original sources

arXiv2010

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

We study the quench from the Mott to the superfluid phase in the Bose-Hubbard model and investigate the spatial-temporal growth of phase coherence, i.e., 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 diffusion-like growth rate.

quant-ph↗

arXiv2010

Manifestation of a gap due to the exchange energy in a spinor condensate

We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between results obtained in the Bogoliubov-Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We argue that the GRPA is superior since, contrary to the BPA, it preserves the SU(2) symmetry and the f-sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap.

cond-mat.stat-mech↗

arXiv2010

Gap and screening in Raman scattering of a Bose condensed gas

We propose different spectroscopic methods to explore the nature of the thermal excitations of a trapped Bose condensed gas: 1) a four photon process to probe the uniform region in the trap center: 2) a stimulated Raman process in order to analyze the influence of a momentum transfer in the resulting scattered atom momentum distribution. We apply these methods to address specifically the energy spectrum and the scattering amplitude of these excitations in a transition between two hyperfine levels of the gas atoms. In particular, we exemplify the potential offered by these proposed techniques by contrasting the spectrum expected, from the {\it non conserving} Bogoliubov approximation valid for weak depletion, to the spectrum of the finite temperature extensions like the {\it conserving} generalized random phase approximation (GRPA). Both predict the existence of the Bogoliubov collective excitations but the GRPA approximation distinguishes them from the single atom excitations with a gapped and parabolic dispersion relation and accounts for the dynamical screening of any external perturbation applied to the gas. We propose two feasible experiments, one concerns the observation of the gap associated to this second branch of excitations and the other deals with this screening effect.

cond-mat.stat-mech↗

arXiv2009

Probing the thermal atoms of a Bose gas through Raman transition

We explore the many body physics of a Bose condensed atom gas at finite temperature through the Raman transition between two hyperfine levels. Unlike the Bragg scattering where the phonon-like nature of the collective excitations has been observed, a different branch of thermal atom excitation is found theoretically in the Raman scattering. This excitation is predicted in the generalized random phase approximation (GRPA) and has a gapped and parabolic dispersion relation. The gap energy results from the exchange interaction and is released during the Raman transition. The scattering rate is determined versus the transition frequency $ω$ and the transferred momentum $\vc{q}$ and shows the corresponding resonance around this gap. Nevertheless, the Raman scattering process is attenuated by the superfluid part of the gas. The macroscopic wave function of the condensate deforms its shape in order to screen locally the external potential displayed by the Raman light beams. This screening is total for a condensed atom transition in order to prevent the condensate from incoherent scattering. The experimental observation of this result would explain some of the reasons why a superfluid condensate moves coherently without any friction with its surrounding.

cond-mat.other↗

arXiv2007

Bose Condensed Gas in Strong Disorder Potential With Arbitrary Correlation Length

We study the properties of a dilute Bose condensed gas at zero temperature in the presence of a strong random potential with arbitrary correlation length. Starting from the underlying Gross-Pitaevskii equation, we use the random phase approximation in order to get a closed integral equation for the averaged density distribution which allows to determine both the condensate and the superfluid density. The obtained results generalize those of Huang and Meng (HM) to strong disorder. In particular, we find the critical value of the disorder strength, where the superfluid phase disappears by a first-order phase transition. We show how this critical value changes as a function of the correlation length.

cond-mat.dis-nn↗

arXiv2005

Subsonic critical velocity at finite temperature

Based on the dielectric formalism in the generalised random phase approximation, we generalise the description of a Bose condensed gas to allow for a relative velocity between the superfluid and normal fluid. In this model, we determine the critical velocity dynamically as the transition point between stable and unstable dynamics. Unlike the zero temperature case, at finite temperature the relative critical velocity of a dilute Bose gas is lower than the sound velocity. This result illustrates one relevant difference that exists between a conserving and gapless approximation and other approaches.

cond-mat.stat-mech↗

arXiv2004

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

We 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 \cite{condenson}. In this approach, the condensate influences the binary collisional process between the 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. PACS numbers:03.75.Hh, 03.75.Kk, 05.30.-d

cond-mat.stat-mech↗

arXiv2004

Collisionless dynamics of the condensate predicted in the random phase approximation

From the microscopic theory, we derive a number conserving quantum kinetic equation, valid for a dilute Bose gas at any temperature, in which the binary collisions between the quasi-particles are mediated by phonon-like excitations (called ``condenson''). 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. This different expansion shows up that a scattering involves the emission and the absorption of a phonon-like excitation. The major interest of this particular mechanism is that, in a regime where the condensate is stable, the collision process between condensed and non condensed 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 non dissipative phenomena (like vortices). We also illustrate the analogy between this approach and the kinetic theory for a plasma, in which the excitations correspond precisely to a plasmon. Finally, we show the equivalence of this theory with the non-number conserving Bogoliubov theory at zero temperature.

cond-mat.stat-mech↗

arXiv2003

Cloning the entanglement of a pair of quantum bits

It is shown that any quantum operation that perfectly clones the entanglement of all maximally-entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests that some approximate cloning of entanglement is nevertheless allowed by quantum mechanics. We investigate a separability-preserving optimal cloning machine that duplicates all maximally-entangled states of two qubits, resulting in 0.285 bits of entanglement per clone, while a local cloning machine only yields 0.060 bits of entanglement per clone.

quant-ph↗

arXiv2003

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

We investigate a new 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.

quant-ph↗

arXiv2002

Frequency down conversion through Bose condensation of light

We propose an experimental set up allowing to convert an input light of wavelengths about $1-2 μm$ into an output light of a lower frequency. The basic principle of operating relies on the nonlinear optical properties exhibited by a microcavity filled with glass. The light inside this material behaves like a 2D interacting Bose gas susceptible to thermalise and create a quasi-condensate. Extension of this setup to a photonic bandgap material (fiber grating) allows the light to behave like a 3D Bose gas leading, after thermalisation, to the formation of a Bose condensate. Theoretical estimations show that a conversion of $1 μm$ into $1.5 μm$ is achieved with an input pulse of about $1 ns$ with a peak power of $10^3 W$, using a fiber grating containing an integrated cavity of size about $500 μm \times 100 μm^2$.

quant-ph↗

arXiv2001

A " quantum public key " based cryptographic scheme for continuous variables

By analogy to classical cryptography, we develop a "quantum public key" based cryptographic scheme in which the two public and private keys consist in each of two entangled beams of squeezed light. An analog message is encrypted by modulating the phase of the beam sent in public. The knowledge of the degree of non classical correlation between the beam quadratures measured in private and in public allows only the receiver to decrypt the message. Finally, in a view towards absolute security, we formally prove that any external intervention of an eavesdropper makes him vulnerable to any subsequent detection.

quant-ph↗

arXiv2000

Spatial entanglement of twin quantum images

We show that spatial entanglement of two twin images obtained by parametric down-conversion is complete, i.e. concerns both amplitude and phase. This is realised through a homodyne detection of these images which allows for measurement of the field quadrature components. EPR correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase of the local oscillator field (LO) in the area of maximal amplification. The results for quadrature components hold unchanged even in absence of any input image i.e. for pure parametric fluorescence. In this case they are not related to intensity and phase fluctuations.

quant-ph↗

arXiv1999

Thermodynamic identities and particle number fluctuations in weakly interacting Bose--Einstein condensates

We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean-square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of {\it auxiliary partition functions} for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, at variance with the anomalous scaling behavior V^{4/3} of the fluctuations in the ideal Bose gas.

cond-mat↗

arXiv1998

Bose-Einstein Condensate: A Superposition of Macroscopically Squeezed States

We study the ground state of a uniform Bose gas at zero temperature in the Hartree-Fock-Bogoliubov (HFB) approximation. We find a solution of the HFB equations which obeys the Hugenholtz-Pines theorem. This solution imposes a macroscopic squeezing to the condensed state and as a consequence displays large particle number fluctuations. Particle number conservation is restored by building the appropriate U(1) invariant ground state via the superposition of the squeezed states. The condensed particle number distribution of this new ground state is calculated as well as its fluctuations which present a normal behavior.

cond-mat↗