In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $\ensuremath{\pi}{\mathrm{na}}^{3}.$ There are two types of excitations, molecular excitations and atomic excitations. Atomic excitations are gapless, consistent with the traditional theory of a dilute Bose gas. The molecular excitation energy is finite in the long-wavelength limit as observed in recent experiments on ${}^{85}\mathrm{Rb}.$ In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on ${}^{23}\mathrm{Na}.$ In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $\ensuremath{\pi}{\mathrm{na}}^{3}.$ There are two types of excitations, molecular excitations and atomic excitations. Atomic excitations are gapless, consistent with the traditional theory of a dilute Bose gas. The molecular excitation energy is finite in the long-wavelength limit as observed in recent experiments on ${}^{85}\mathrm{Rb}.$ In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on ${}^{23}\mathrm{Na}.$

arXiv:cond-mat/0304548Physical Review ASep 19, 20038 citations

Temperature-Dependent Damping and Frequency Shifts in Collective Excitations of a Dilute Bose-Einstein Condensate

D. S. Jin, M. R. Matthews, J. R. Ensher +2 more

We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of ${}^{87}\mathrm{Rb}$ . Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations.We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of ${}^{87}\mathrm{Rb}$. Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations.

Physical Review LettersFeb 3, 1997372 citations

Mean-field theory for excitations of trapped Bose condensates at finite temperatures

M. Rusch, Keith R. Burnett

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

{}^{85}\mathrm{Rb}.

In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on

{}^{23}\mathrm{Na}.

We extend to finite temperature the study of collective excitations of a Bose-Einstein condensate in a dilute gas of

{}^{87}\mathrm{Rb}

. Measurements of two modes with different angular momenta show unexpected temperature-dependent frequency shifts, with very different behavior for the two symmetries; in addition there is a sharp feature in the temperature dependence of one mode. The damping of these excitations exhibits dramatic temperature dependence, with condensate modes at temperatures near the transition damping even faster than analogous noncondensate oscillations.

{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.