Full counting statistics of heteronuclear molecules from Feshbach-assisted photo association

We study the effects of quantum statistics on the counting statistics of ultracold heteronuclear molecules formed by Feshbach-assisted photoassociation [Phys. Rev. Lett. {\bf 93}, 140405 (2004)]. Exploiting the formal similarities with sum frequency generation and using quantum optics methods we consider the cases where the molecules are formed from atoms out of two Bose-Einstein condensates, out of a Bose-Einstein condensate and a gas of degenerate fermions, and out of two degenerate Fermi gases with and without superfluidity. Bosons are treated in a single mode approximation and fermions in a degenerate model. In these approximations we can numerically solve the master equations describing the system's dynamics and thus we find the full counting statistics of the molecular modes. The full quantum dynamics calculations are complemented by mean field calculations and short time perturbative expansions. While the molecule production rates are very similar in all three cases at this level of approximation, differences show up in the counting statistics of the molecular fields. The intermediate field of closed-channel molecules is for short times second-order coherent if the molecules are formed from two Bose-Einstein condensates or a Bose-Fermi mixture. They show counting statistics similar to a thermal field if formed from two normal Fermi gases. The coherence properties of molecule formation in two superfluid Fermi gases are intermediate between the two previous cases. In all cases the final field of deeply-bound molecules is found to be twice as noisy as that of the intermediate state. This is a consequence of its coupling to the lossy optical cavity in our model, which acts as an input port for quantum noise, much like the situation in an optical beam splitter.Comment: replacement of earlier manuscript cond-mat/0508080 ''Feshbach-assisted photoassociation of ultracold heteronuclear molecules'' with minor revision

Superfluidity of the BEC at finite temperature

We use the classical fields approximation to study a translational flow of the condensate with respect to the thermal cloud in a weakly interacting Bose gas. We study both, subcritical and supercritical relative velocity cases and analyze in detail a state of stationary flow which is reached in the dynamics. This state corresponds to the thermal equilibrium, which is characterized by the relative velocity of the condensate and the thermal cloud. The superfluidity manifests itself in the existence of many thermal equilibria varying in (the value of this velocity) the relative velocity between the condensate and the thermal cloud. We pay a particular attention to excitation spectra in a phonon as well as in a particle regime. Finally, we introduce a measure of the amount of the superfluid fraction in a weakly interacting Bose gas, allowing for the precise distinction between the superfluid and the condensed fractions in a single and consistent framework.Comment: 8 pages, 5 figure

Depletion of a Bose-Einstein condensate by laser-iduced dipole-dipole interactions

We study a gaseous Bose-Einstein condensate with laser-induced dipole-dipole interactions using the Hartree-Fock-Bogoliubov theory within the Popov approximation. The dipolar interactions introduce long-range atom-atom correlations, which manifest themselves as increased depletion at momenta similar to that of the laser wavelength, as well as a "roton" dip in the excitation spectrum. Surprisingly, the roton dip and the corresponding peak in the depletion are enhanced by raising the temperature above absolute zero.Comment: 10 pages, 6 figure

Collisional relaxation of Feshbach molecules and three-body recombination in 87Rb Bose-Einstein condensates

We predict the resonance enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}$Rb Bose-Einstein condensate (BEC) close to 1007 G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.Comment: 4 pages, 3 eps figures (updated references

Role of Particle Interactions in the Feshbach Conversion of Fermion Atoms to Bosonic Molecules

We investigate the Feshbach conversion of fermion atomic pairs to condensed boson molecules with a microscopic model that accounts the repulsive interactions among all the particles involved. We find that the conversion efficiency is enhanced by the interaction between boson molecules while suppressed by the interactions between fermion atoms and between atom and molecule. In certain cases, the combined effect of these interactions leads to a ceiling of less than 100% on the conversion efficiency even in the adiabatic limit. Our model predicts a non-monotonic dependence of the efficiency on mean atomic density. Our theory agrees well with recent experiments on $^6$Li and $^{40}$K.Comment: 5 pages, 4 figure

"Supersolid" self-bound Bose condensates via laser-induced interatomic forces

We show that the dipole-dipole interatomic forces induced by a single off-resonant running laser beam can lead to a self-bound pencil-shaped Bose condensate, even if the laser beam is a plane-wave. For an appropriate laser intensity the ground state has a quasi-one dimensional density modulation --- a Bose "supersolid".Comment: 4 pages, 3 eps figure

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.Comment: 19 page

Strong dipolar effects in a quantum ferrofluid

We report on the realization of a Chromium Bose-Einstein condensate (BEC) with strong dipolar interaction. By using a Feshbach resonance, we reduce the usual isotropic contact interaction, such that the anisotropic magnetic dipole-dipole interaction between 52Cr atoms becomes comparable in strength. This induces a change of the aspect ratio of the cloud, and, for strong dipolar interaction, the inversion of ellipticity during expansion - the usual "smoking gun" evidence for BEC - can even be suppressed. These effects are accounted for by taking into account the dipolar interaction in the superfluid hydrodynamic equations governing the dynamics of the gas, in the same way as classical ferrofluids can be described by including dipolar terms in the classical hydrodynamic equations. Our results are a first step in the exploration of the unique properties of quantum ferrofluids.Comment: Final, published versio

Quantum phases of dipolar bosons in optical lattices

The ground state of dipolar bosons placed in an optical lattice is analyzed. We show that the modification of experimentally accessible parameters can lead to the realization and control of different quantum phases, including superfluid, supersolid, Mott insulator, checkerboard, and collapse phases.Comment: 4 pages, 4 eps figures, final versio

Bose-Einstein condensation with magnetic dipole-dipole forces

Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of the Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of e.g. chromium and a typical value of the scattering length all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region the ground state wavefunctions show internal structures not seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.Comment: final version, 4 pages, 4 figure