We describe a method for studying the dynamics of a condensate in a weakly interacting, dilute Bose gas which is based on a finite-temperature extension of the Gross-Pitaevskii equation. We present a general finite-temperature linear response formalism for nonuniform systems and give explicit results for homogeneous ones, where we can link our treatment to well-known results. This treatment leads to a consistent ${V}^{2}$ calculation of the excitations for a weakly interacting Bose gas, including Landau and Beliaev damping as well as collisional lifetimes. We do not make use of the Popov approximation, but include pair and triplet anomalous averages to second order in the interaction potential and thus obtain a gapless theory for the excitations of a weakly interacting homogeneous gas. We also show how the formalism can be used to obtain self-consistent theories. We explicitly derive gapless equations for a weakly coupled finite-temperature condensate with a static thermal component and give a clear criterion of their validity in trapped systems.We describe a method for studying the dynamics of a condensate in a weakly interacting, dilute Bose gas which is based on a finite-temperature extension of the Gross-Pitaevskii equation. We present a general finite-temperature linear response formalism for nonuniform systems and give explicit results for homogeneous ones, where we can link our treatment to well-known results. This treatment leads to a consistent ${V}^{2}$ calculation of the excitations for a weakly interacting Bose gas, including Landau and Beliaev damping as well as collisional lifetimes. We do not make use of the Popov approximation, but include pair and triplet anomalous averages to second order in the interaction potential and thus obtain a gapless theory for the excitations of a weakly interacting homogeneous gas. We also show how the formalism can be used to obtain self-consistent theories. We explicitly derive gapless equations for a weakly coupled finite-temperature condensate with a static thermal component and give a clear criterion of their validity in trapped systems.

Physical Review AMay 1, 199925 citations

Elementary excitations of the trapped Bose-condensed gas

Patrik Öhberg, E.L. Surkov, Ilkka Juhani Tittonen +3 more

Jan 1, 19970 citations

Experimental Evidence for the Breakdown of a Hartree-Fock Approach in a Weakly Interacting Bose Gas

Jean-Baptiste Trebbia, Jérôme Estève, Christoph Ira Westbrook +1 more

We investigate the physics underlying the presence of a quasicondensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree-Fock (mean-field) approach fails to predict the existence of the quasicondensate in the center of the cloud: the quasicondensate is generated by interaction-induced correlations between atoms and not by a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the crossover density in agreement with experimental results.We investigate the physics underlying the presence of a quasicondensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree-Fock (mean-field) approach fails to predict the existence of the quasicondensate in the center of the cloud: the quasicondensate is generated by interaction-induced correlations between atoms and not by a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the crossover density in agreement with experimental results.

arXiv:quant-ph/0606247Physical Review LettersDec 22, 200644 citations

Adiabatic output coupling of a Bose gas at finite temperatures

Seok Jin Choi, Yonathan Japha, Keith R. Burnett

We develop a general theory of adiabatic output coupling from trapped, weakly interacting, atomic Bose-Einstein condensates at finite temperatures. For weak coupling, the output rate from the condensate and the excited levels in the trap settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state, where the population inside the trap is not appreciably depleted. We show how the composition of the output beam, containing the condensate and the thermal component, may be controlled by changing the frequency of the output coupling lasers. This composition determines the first- and second-order coherence of the output beam. We discuss the changes in the composition of the Bose gas left in the trap, and show how nonresonant output coupling can stimulate either the evaporation of the thermal excitations in the trap or the growth of the nonthermal excitations, when pairs of correlated atoms leave the condensate.We develop a general theory of adiabatic output coupling from trapped, weakly interacting, atomic Bose-Einstein condensates at finite temperatures. For weak coupling, the output rate from the condensate and the excited levels in the trap settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state, where the population inside the trap is not appreciably depleted. We show how the composition of the output beam, containing the condensate and the thermal component, may be controlled by changing the frequency of the output coupling lasers. This composition determines the first- and second-order coherence of the output beam. We discuss the changes in the composition of the Bose gas left in the trap, and show how nonresonant output coupling can stimulate either the evaporation of the thermal excitations in the trap or the growth of the nonthermal excitations, when pairs of correlated atoms leave the condensate.

arXiv:quant-ph/0001033Physical Review AMay 15, 200021 citations

DENSITY EXCITATIONS OF WEAKLY INTERACTING BOSE GAS

Jürgen Bosse, Thomas Schlieter

International Conference on Path IntegralsNov 1, 20080 citations

{V}^{2}

calculation of the excitations for a weakly interacting Bose gas, including Landau and Beliaev damping as well as collisional lifetimes. We do not make use of the Popov approximation, but include pair and triplet anomalous averages to second order in the interaction potential and thus obtain a gapless theory for the excitations of a weakly interacting homogeneous gas. We also show how the formalism can be used to obtain self-consistent theories. We explicitly derive gapless equations for a weakly coupled finite-temperature condensate with a static thermal component and give a clear criterion of their validity in trapped systems.