arXiv subjects

Yvan Castin

Publications and source records attributed to Yvan Castin.

At least 73 records · Page 4Linked to original sources

arXiv2009

Spectrum of Light in a Quantum Fluctuating Periodic Structure

We address the general problem of the excitation spectrum for light coupled to scatterers having quantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginary part to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a way that we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice, on a J=0->J'=1 narrow atomic transition. As a side result, we resolve a controversy for the occurrence of a spectral gap in a fcc lattice.

cond-mat.other↗

arXiv2009

Fano-Hopfield model and photonic band gaps for an arbitrary atomic lattice

We study the light dispersion relation in a periodic ensemble of atoms at fixed positions in the Fano-Hopfield model (the atomic dipole being modeled with harmonic oscillators). Compared to earlier works, we do not restrict to cubic lattices, and we do not regularize the theory by hand but we renormalize it in a systematic way using a Gaussian cut-off in momentum space. Whereas no omnidirectional spectral gap is known for light in a Bravais atomic lattice, we find that, for a wide range of parameters, an omnidirectional gap occurs in a diamond atomic lattice, which may be realized in an experiment with ultra-cold atoms. The long-wavelength limit of the theory also provides a Lorentz-Lorenz (or Clausius-Mossotti) relation for an arbitrary lattice.

cond-mat.quant-gas↗

arXiv2009

Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory

We consider the grand potential $Ω$ of a two-dimensional weakly interacting homogeneous Bose gas at zero temperature. Building on a number-conserving Bogoliubov method for a lattice model in the grand canonical ensemble, we calculate the next order term as compared to the Bogoliubov prediction, in a systematic expansion of $Ω$ in powers of the parameter measuring the weakness of the interaction. Our prediction is in very good agreement with recent Monte Carlo calculations.

cond-mat.stat-mech↗

arXiv2009

Number of closed-channel molecules in the BEC-BCS crossover

Using a two-channel model, we show that the number of closed channel molecules in a two-component Fermi gas close to a Feshbach resonance is directly related to the derivative of the energy of the gas with respect to the inverse scattering length. We extract this quantity from the fixed node Monte-Carlo equation of state and we compare to the number of closed channel molecules measured in the Rice experiment with lithium [Partridge et al., Phys. Rev. Lett. 95, 020404 (2005)]. We also discuss the effect of a difference between the trapping potentials seen by a closed-channel molecule and by an open-channel pair of atoms in terms of an effective position-dependent scattering length.

cond-mat.other↗

arXiv2009

The truncated Wigner method for Bose condensed gases: limits of validity and applications

We study the truncated Wigner method (TWM) applied to a weakly interacting Bose condensed gas perturbed away from thermal equilibrium. The idea of the method is to generate an ensemble of classical fields which samples the Wigner function of the initial thermal density operator, and to evolve each field with the Gross-Pitaevskii equation (GPE). In the first part of the paper we improve the sampling technique over our previous work and we test its accuracy against the exactly solvable model of the ideal gas. In the second part of the paper we investigate the conditions of validity of the TWM. For short evolution times the time-dependent Bogoliubov approximation is valid for almost pure condensates. The requirement that the TWM reproduces the Bogoliubov prediction leads to the constraint that the number of field modes must be smaller than the number of particles.For longer times the nonlinear dynamics of the noncondensed modes plays an important role. To demonstrate this we analyse the case of a 3D spatially homogeneous Bose condensed gas and we test how well TWM reproduces Beliaev-Landau damping.We have identified the mechanism which limits the validity of the TWM: the initial classical fields, driven by the time-dependent GPE, thermalise to a classical field distribution at a temperature T_class larger than the initial temperature T. When T_class significantly exceeds T a spurious damping is observed in the simulation. This leads to the second condition for the TWM, T_class-T<<T, which requires that the maximum energy of the Bogoliubov modes does not exceed a few k_B T.

cond-mat.stat-mech↗

arXiv2008

Internal structure of a quantum soliton and classical excitations due to trap opening

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: From the Bethe ansatz solution we extract the internal correlation function of the particle positions in the quantum soliton, that is for a fixed center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: It deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.

cond-mat.other↗

arXiv2008

Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study

Within the classical field model, we find that the phase of a Bose-Einstein condensate undergoes a true diffusive motion in the microcanonical ensemble, the variance of the condensate phase change between time zero and time $t$ growing linearly in $t$. The phase diffusion coefficient obeys a simple scaling law in the double thermodynamic and Bogoliubov limit. We construct an approximate calculation of the diffusion coefficient, in fair agreement with the numerical results over the considered temperature range, and we extend this approximate calculation to the quantum field.

cond-mat.other↗

arXiv2008

Creation and detection of a mesoscopic gas in a non-local quantum superposition

We investigate the scattering of a quantum matter wave soliton on a barrier in a one dimensional geometry and we show that it can lead to mesoscopic Schrödinger cat states, where the atomic gas is in a coherent superposition of being in the half-space to the left of the barrier and being in the half-space to the right of the barrier. We propose an interferometric method to reveal the coherent nature of this superposition and we discuss in details the experimental feasibility.

cond-mat.other↗

arXiv2008

A Wave Function approach to dissipative processes

Due to growing interest in quantum measurement, control and feedback, we reproduce a manuscript from 1992, presenting a simple physical and mathematical derivation of stochastic differential equations for wave functions of probed quantum systems. V. P. Belavkins seminal quantum filtering theory with similar equations, developed in the 1980es, was not known to the authors at the time of writing of the present manuscript.

quant-ph↗

arXiv2008

Three fully polarized fermions close to a p-wave Feshbach resonance

We study the three-body problem for three atomic fermions, in the same spin state, experiencing a resonant interaction in the p-wave channel via a Feshbach resonance represented by a two-channel model. The rate of inelastic processes due to recombination to deeply bound dimers is then estimated from the three-body solution using a simple prescription. We obtain numerical and analytical predictions for most of the experimentally relevant quantities that can be extracted from the three-body solution: the existence of weakly bound trimers and their lifetime, the low-energy elastic and inelastic scattering properties of an atom on a weakly bound dimer (including the atom-dimer scattering length and scattering volume), and the recombination rates for three colliding atoms towards weakly bound and deeply bound dimers. The effect of "background" non-resonant interactions in the open channel of the two-channel model is also calculated and allows to determine which three-body quantities are `universal' and which on the contrary depend on the details of the model.

cond-mat.other↗

arXiv2007

Three fermions in a box at the unitary limit: universality in a lattice model

We consider three fermions with two spin components interacting on a lattice model with an infinite scattering length. Low lying eigenenergies in a cubic box with periodic boundary conditions, and for a zero total momentum, are calculated numerically for decreasing values of the lattice period. The results are compared to the predictions of the zero range Bethe-Peierls model in continuous space, where the interaction is replaced by contact conditions. The numerical computation, combined with analytical arguments, shows the absence of negative energy solution, and a rapid convergence of the lattice model towards the Bethe-Peierls model for a vanishing lattice period. This establishes for this system the universality of the zero interaction range limit.

cond-mat.other↗

arXiv2007

A semi-classical field method for the equilibrium Bose gas and application to thermal vortices in two dimensions

We develop a semi-classical field method for the study of the weakly interacting Bose gas at finite temperature, which, contrarily to the usual classical field model, does not suffer from an ultraviolet cut-off dependence. We apply the method to the study of thermal vortices in spatially homogeneous, two-dimensional systems. We present numerical results for the vortex density and the vortex pair distribution function. Insight in the physics of the system is obtained by comparing the numerical results with the predictions of simple analytical models. In particular, we calculate the activation energy required to form a vortex pair at low temperature.

cond-mat.other↗

arXiv2007

Basic theory tools for degenerate Fermi gases

This is an introductory lecture to the theory of degenerate Fermi gases, in the context of present experiments on atomic Fermi gases. In part one, some properties of the ideal Fermi gas are presented, including a discussion of the fluctuations of the number of fermions in a given spatial zone in 1D, 2D and 3D. In part two, two-body aspects of the interaction potential are discussed and several possible models for the interaction are analyzed, including the two-channel model for the Feshbach resonance. In part three, basic predictions of zero temperature BCS theory are presented, including a derivation of superfluid hydrodynamic equations from time dependent BCS theory.

cond-mat.other↗

arXiv2007

Non-diffusive phase spreading of a Bose-Einstein condensate at finite temperature

We show that the phase of a condensate in a finite temperature gas spreads linearly in time at long times rather than in a diffusive way. This result is supported by classical field simulations, and analytical calculations which are generalized to the quantum case under the assumption of quantum ergodicity in the system. This super-diffusive behavior is intimately related to conservation of energy during the free evolution of the system and to fluctuations of energy in the prepared initial state.

cond-mat.other↗

arXiv2006

The unitary gas in an isotropic harmonic trap: symmetry properties and applications

We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, and relations between the moments of the trapping potential energy and the moments of the total energy.

cond-mat.other↗

arXiv2006

Three-dimensional strong localization of matter waves by scattering from atoms in a lattice with a confinement-induced resonance

The possibility of using ultracold atoms to observe strong localization of matter waves is now the subject of a great interest, as undesirable decoherence and interactions can be made negligible in these systems. It was proposed that a static disordered potential can be realized by trapping atoms of a given species in randomly chosen sites of a deep 3D optical lattice with no multiple occupation. We analyze in detail the prospects of this scheme for observing localized states in 3D for a matter wave of a different atomic species that interacts with the trapped particles and that is sufficiently far detuned from the optical lattice to be insensitive to it. We demonstrate that at low energy a large number of 3D strongly localized states can be produced for the matter wave, if the effective scattering length describing the interaction of the matter wave with a trapped atom is of the order of the mean distance between the trapped particles. Such high values of the effective scattering length can be obtained by using a Feshbach resonance to adjust the free space inter-species scattering length and by taking advantage of confinement-induced resonances induced by the trapping of the scatterers in the lattice.

cond-mat.dis-nn↗

arXiv2006

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.

cond-mat.other↗

arXiv2005

Seeing zeros of random polynomials: quantized vortices in the ideal Bose gas

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.

cond-mat.other↗