Dynamics of Fluctuating Bose-Einstein Condensates

We present a generalized Gross-Pitaevskii equation that describes also the dissipative dynamics of a trapped partially Bose condensed gas. It takes the form of a complex nonlinear Schr\"odinger equation with noise. We consider an approximation to this Langevin field equation that preserves the correct equilibrium for both the condensed and the noncondensed parts of the gas. We then use this formalism to describe the reversible formation of a one-dimensional Bose condensate, and compare with recent experiments. In addition, we determine the frequencies and the damping of collective modes in this case.Comment: 4 pages of REVTeX, including 4 figure

A strongly interacting Bose gas: Nozi\`eres and Schmitt-Rink theory and beyond

We calculate the critical temperature for Bose-Einstein condensation in a gas of bosonic atoms across a Feshbach resonance, and show how medium effects at negative scattering lengths give rise to pairs reminiscent of the ones responsible for fermionic superfluidity. We find that the formation of pairs leads to a large suppression of the critical temperature. Within the formalism developed by Nozieres and Schmitt-Rink the gas appears mechanically stable throughout the entire crossover region, but when interactions between pairs are taken into account we show that the gas becomes unstable close to the critical temperature. We discuss prospects of observing these effects in a gas of ultracold Cs133 atoms where recent measurements indicate that the gas may be sufficiently long-lived to explore the many-body physics around a Feshbach resonance.Comment: 8 pages, 8 figures, RevTeX. Significantly expanded to include effects beyond NS

Resummation of infrared divergencies in the theory of atomic Bose gases

We present a general strong-coupling approach for the description of an atomic Bose gas beyond the Bogoliubov approximation, when infrared divergences start to occur that need to be resummed exactly. We consider the determination of several important physical properties of the Bose gas, namely the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. It is shown how the approach can be systematically improved with renormalization-group methods and how it reduces to the Bogoliubov theory in the weak-coupling limit

Quantum rotor model for a Bose-Einstein condensate of dipolar molecules

We show that a Bose-Einstein condensate of heteronuclear molecules in the regime of small and static electric fields is described by a quantum rotor model for the macroscopic electric dipole moment of the molecular gas cloud. We solve this model exactly and find the symmetric, i.e., rotationally invariant, and dipolar phases expected from the single-molecule problem, but also an axial and planar nematic phase due to many-body effects. Investigation of the wavefunction of the macroscopic dipole moment also reveals squeezing of the probability distribution for the angular momentum of the molecules

Vortex-line solitons in a periodically modulated Bose gas

We study the nonlinear excitations of a vortex-line in a Bose-Einstein condensate trapped in a one-dimensional optical lattice. We find that the classical Euler dynamics of the vortex results in a description of the vortex line in terms of a (discrete) one-dimensional Gross-Pitaevskii equation, which allows for both bright and gray soliton solutions. We discuss these solutions in detail and predict that it is possible to create vortex-line solitons with current experimental capabilities.Comment: minor changes, updated/corrected references, 4 pages, 3 figure

Hydrodynamic modes of partially condensed Bose mixtures

We generalize the Landau-Khalatnikov hydrodynamic theory for superfluid helium to two-component (binary) Bose mixtures at arbitrary temperatures. In particular, we include the spin-drag terms that correspond to viscous coupling between the clouds. Therefore, our theory not only describes the usual collective modes of the individual components, e.g., first and second sound, but also results in new collective modes, where both constituents participate. We study these modes in detail and present their dispersions using thermodynamic quantities obtained within the Popov approximation

Dressed Feshbach molecules in the BEC-BCS crossover

We present the RPA theory of the BEC-BCS crossover in an atomic Fermi gas near a Feshbach resonance that includes the relevant two-body atomic physics exactly. This allows us to determine the probability $Z$ for the dressed molecules in the Bose-Einstein condensate to be in the closed channel of the Feshbach resonance and to compare with the recent experiments of Partridge {\it et al.} [cond-mat/0505353] with $^{6}$Li. We determine for this extremely broad resonance also the condensate density of the dressed molecules throughout the BEC-BCS crossover.Comment: 4 pages, 3 figure

Phase fluctuations in atomic Bose gases

We improve on the Popov theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. As a result, the theory becomes valid in arbitrary dimensions and is able to describe the low-temperature crossover between three, two and one-dimensional Bose gases, which is currently being explored experimentally. We consider both homogeneous and trapped Bose gases.Comment: 4 pages. Title changed Major changes involve extension of theory to include trapped Bose gases. Deletion of reference to and comparison with hydrogen experiment. Due to these changes, second author added. Modified manuscript accepted for PR