1,721,021 research outputs found
The truncated Wigner method for Bose-condensed gases: limits of validity and applications
No full textWe study the truncated Wigner method applied to a weakly interacting spinless Bose-condensed gas which is perturbed away from thermal equilibrium by a time-dependent external potential. The principle of the method is to generate an ensemble of classical fields ?(r) which samples the Wigner quasi-distribution function of the initial thermal equilibrium density operator of the gas, and then to evolve each classical field with the Gross–Pitaevskii equation. In the first part of the paper we improve the sampling technique over our previous work (Sinatra et al2000 J. Mod. Opt. 47 2629–44) and we test its accuracy against the exactly solvable model of the ideal Bose gas. In the second part of the paper we investigate the conditions of validity of the truncated Wigner method. For short evolution times it is known that the time-dependent Bogoliubov approximation is valid for almost pure condensates. The requirement that the truncated Wigner method reproduces the Bogoliubov prediction leads to the constraint that the number of field modes in the Wigner simulation must be smaller than the number of particles in the gas. For longer evolution times the nonlinear dynamics of the noncondensed modes of the field plays an important role. To demonstrate this we analyse the case of a three-dimensional spatially homogeneous Bose-condensed gas and we test the ability of the truncated Wigner method to correctly reproduce the Beliaev–Landau damping of an excitation of the condensate. We have identified the mechanism which limits the validity of the truncated Wigner method: the initial ensemble of classical fields, driven by the time-dependent Gross–Pitaevskii equation, thermalizes to a classical field distribution at a temperature Tclass which is larger than the initial temperature T of the quantum gas. When Tclass significantly exceeds T a spurious damping is observed in the Wigner simulation. This leads to the second validity condition for the truncated Wigner method, Tclass ? T T, which requires that the maximum energy max of the Bogoliubov modes in the simulation does not exceed a few kB T. <br/
Classical-field method for time dependent Bose-Einstein condensed gases
Full text linkWe propose a method to study the time evolution of Bose-Einstein condensed gases perturbed from an initial thermal equilibrium, based on the Wigner representation of the N-body density operator. We show how to generate a collection of random classical fields sampling the initial Wigner distribution in the number conserving Bogoliubov approximation. The fields are then evolved with the time dependent Gross-Pitaevskii equation. We illustrate the method with the damping of a collective excitation of a one-dimensional Bose ga
A Monte Carlo formulation of the Bogolubov theory
No full textWe propose an efficient stochastic method to implement numerically the Bogolubov approach to study finite-temperature Bose-Einstein condensates. Our method is based on the Wigner representation of the density matrix describing the non-condensed modes and a Brownian motion simulation to sample the Wigner distribution at thermal equilibrium. Allowing it to sample any density operator Gaussian in the field variables, our method is very general and it applies both to the Bogolubov and to the Hartree-Fock Bogolubov approach, in the equilibrium case as well as in the time-dependent case. We think that our method can be useful to study trapped Bose-Einstein condensates in two or three spatial dimensions without rotational symmetry properties, as in the case of condensates with vortices, where the traditional Bogolubov approach is difficult to implement numerically due to the need to diagonalize very big matrices.<br/
Vortex lattice formation in Bose-Einstein condensates
No full textWe show that the formation of a vortex lattice in a weakly interacting Bose condensed gas can be modeled with the nonlinear Schrödinger equation for both T=0 and finite temperatures without the need for an explicit damping term. Applying a weak rotating anisotropic harmonic potential, we find numerically that the turbulent dynamics of the field produces an effective dissipation of the vortex motion and leads to the formation of a lattice. For T=0, this turbulent dynamics is triggered by a rotational dynamic instability of the condensate. For finite temperatures, noise is present at the start of the simulation and allows the formation of a vortex lattice at a lower rotation frequency, the Landau frequency. These two regimes have different vortex dynamics. We show that the multimode interpretation of the classical field is essentia
Comment on Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas
Full text linkWe present simple arguments suggesting that H. Biss et al [PRL 128, 100401 (2022)] did not measure with the required accuracy the low-wavenumber curvature of the acoustic excitation branch of the ground-state unitary Fermi gas. This difficult-to-calculate quantity is crucial for the relaxation dynamics of the gas at low temperature.Published version in English (2 pages) and extended version in French (2 pages
Two study of collective properties in quantum systems : nuclear spin squeezing in helium-3 via quantum non-demolition measurement and phonons damping in a 2D superfluid
No full textDans une première partie, nous étudions la possibilité d'obtenir des états comprimés de spin nucléaire dans un gaz d'hélium 3 à température ambiante en cellule par mesure quantique non destructive en continu. Comme les atomes dans l'état fondamental interagissent très peu avec l'environnement, nous les couplons à une faible fraction d'atomes dans l'état métastable par des collisions d'échange de métastabilité, ces derniers pouvant interagir avec un champ électromagnétique en cavité. Nous avons considéré deux configurations dans lesquelles on mesure un nombre de photons ou une quadrature du champ en sortie de la cavité. Nous prédisons qu'une compression significative du spin nucléaire de très longue durée de vie pourrait être ainsi obtenue avec des valeurs des paramètres à la portée d'une expérience. Dans une seconde partie, nous étudions, à température non nulle, l'amortissement des modes de phonons dans un superfluide bidimensionnel d'atomes froids bosoniques ou d'hélium 4 liquide. À cette fin, nous utilisons un hamiltonien effectif de basse énergie, celui de l'hydrodynamique quantique de Landau et Khalatnikov qui vaut même dans le régime d'interactions fortes pour peu que l'on connaisse l'équation d'état du système dans son état fondamental. Par des simulations de champ classique très précises, à notre connaissance jamais effectuées pour ce type d'hamiltonien, nous mettons en évidence des écarts significatifs à la décroissance exponentielle prédite par la règle d'or de Fermi, contrairement à ce qui se passe dans le cas tridimensionnel. Ces résultats sont confirmés par la méthode diagrammatique des fonctions de Green à N corps (dans son domaine de validité que nous précisons) et nous semblent accessibles à une vérification expérimentale.In a first part, we study the possibility of obtaining nuclear spin squeezing in a room temperature helium-3 gas in a cell by continuous quantum non-demolition measurement. As atoms in the ground state interact very little with the environment, we couple them to a small fraction of atoms in the metastable state by metastability exchange collisions, the latter being able to interact with an electromagnetic field in an optical cavity. We have considered two configurations in which either a photon number or a quadrature of the field at the cavity output is measured. We predict that a significant very long-lived squeezing of the nuclear spin could be obtained in this way with experimentally feasible parameter values. In a second part, we study, at non-zero temperature, the damping of phonon modes in a two-dimensional superfluid of cold bosonic atoms or liquid helium-4. For this purpose, we use an effective low-energy Hamiltonian, the Landau-Khalatnikov quantum hydrodynamics Hamiltonian, which holds even in the strong interaction regime as long as the equation of state of the system in its ground state is known. By means of very precise classical field simulations, to our knowledge never carried out for this type of Hamiltonian, we highlight significant deviations from the exponential decay predicted by Fermi's golden rule, contrary to what happens in the three-dimensional case. These results are confirmed by the diagrammatic method of many-body Green's functions (in its domain of validity that we specify) and seem accessible to experimental verification
Bose Einstein condensates in atomic gases; simple theoretical results
No full text1 - Introduction2 - The ideal Bose gas in a trap3 - A model for the atomic interactions4 - Interacting bose gas in the Hartree-Fock5 - Properties of the condensate wavefunction6 - What we learn from a linearization of the Gross-Pitaevskii equation7 - Bogoliubov approach and thermodynamical stability8 - Phase conherence properties of Bose-Einstein condensates9 - Symmetry breaking description of condensatesEinstein's prediction for the ideal Bose gas. Experimental proof. (146 pages)
Full text linkWe review some unresolved theoretical issues in three-dimensional two-component Fermi gases, drawing on recent experiments on cold atoms in immaterial traps close to a magnetic Feshbach resonance. We distinguish successively (i) the open questions arising in the few-body problem with Wigner–Bethe–Peierls contact interactions—essentially the stability of the gas with respect to the Efimov effect and the calculation of the cluster (or virial) coefficients, (ii) those arising in the effective low-energy theory of Landau and Khalatnikov quantum hydrodynamics—essentially the damping of phonon modes and the coherence time of the condensate of pairs, and finally (iii) questions requiring a complete, microscopic solution of the many-body problem, such as the specific properties of the acoustic excitation branch (Goldstone) of the condensate of pairs, or its collective excitation branch (Higgs) in the broken-pair continuum
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