Mean-Field Theory of Feshbach-Resonant Interactions in 85Rb Condensates

Recent Feshbach-resonance experiments with 85Rb Bose-Einstein condensates have led to a host of unexplained results: dramatic losses of condensate atoms for an across-resonance sweep of the magnetic field, a collapsing condensate with a burst of atoms emanating from the remnant condensate, increased losses for decreasing interaction times-- until short times are reached, and seemingly coherent oscillations between remnant and burst atoms. Using a simple yet realistic mean-field model, we find that rogue dissociation, molecular dissociation to noncondensate atom pairs, is strongly implicated as the physical mechanism responsible for these observations.Comment: v2: numbers changed, not conclusions; 5 pages, 3 figures, submitted to PR

Mean-field stationary state of a Bose gas at a Feshbach resonance

We study the steady state of a zero-temperature Bose gas near a Feshbach or photoassociation resonance using a two-channel mean-field model that incorporates atomic and molecular condensates, as well as correlated atom pairs originating from dissociation of molecules into pairs of atoms. We start from a many-body Hamiltonian for atom-molecule conversion, and derive the time dependent version of the mean-field theory. The stationary solution of the time dependent model is rendered unique with an approximation that entails that all noncondensate atoms are correlated, as if emerging from dissociation of molecules. The steady state is solved numerically, but limiting cases are also found analytically. The system has a phase transition in which the atomic condensate emerges in a nonanalytic fashion. We quantify the scaling of the observable quantities, such as fractions of atomic and molecular condensates, with the detuning and the atom-molecule conversion strength. Qualitatively, the dependence on detuning rounds out with increasing coupling strength. A study of the thermodynamics shows that the pressure of the atom-molecule system is negative, even on the molecule side of the resonance. This indicates the possibility of mechanical instability

Directional `superradiant' collisions: bosonic amplification of atom pairs emitted from an elongated Bose-Einstein condensate

We study spontaneous directionality in the bosonic amplification of atom pairs emitted from an elongated Bose-Einstein condensate (BEC), an effect analogous to `superradiant' emission of atom-photon pairs. Using a simplified model, we make analytic predictions regarding directional effects for both atom-atom and atom-photon emission. These are confirmed by numerical mean-field simulations, demonstrating the the feasibility of nearly perfect directional emission along the condensate axis. The dependence of the emission angle on the pump strength for atom-atom pairs is significantly different than for atom-photon pairs

Dynamic splitting of a Bose-Einstein Condensate

We study the dynamic process of splitting a condensate by raising a potential barrier in the center of a harmonic trap. We use a two-mode model to describe the phase coherence between the two halves of the condensate. Furthermore, we explicitly consider the spatial dependence of the mode funtions, which varies depending on the potential barrier. This allows to get the tunneling coupling between the two wells and the on-site energy as a function of the barrier height. Moreover we can get some insight on the collective modes which are excited by raising the barrier. We describe the internal and external degrees of freedom by variational ansatz. We distinguish the possible regimes as a function of the characteristic parameters of the problem and identify the adiabaticity conditions.Comment: 17 pages, 8 figure

Optimal measurement precision of a nonlinear interferometer

We study the best attainable measurement precision when a double-well trap with bosons inside acts as an interferometer to measure the energy difference of the atoms on the two sides of the trap. We introduce time independent perturbation theory as the main tool in both analytical arguments and numerical computations. Nonlinearity from atom-atom interactions will not indirectly allow the interferometer to beat the Heisenberg limit, but in many regimes of the operation the Heisenberg limit scaling of measurement precision is preserved in spite of added tunneling of the atoms and atom-atom interactions, often even with the optimal prefactor.Comment: very close to published versio

Optical linewidth of a low density Fermi-Dirac gas

We study propagation of light in a Fermi-Dirac gas at zero temperature. We analytically obtain the leading density correction to the optical linewidth. This correction is a direct consequence of the quantum statistical correlations of atomic positions that modify the optical interactions between the atoms at small interatomic separations. The gas exhibits a dramatic line narrowing already at very low densities.Comment: 4 pages, 2 figure

Momentum Analysis in Strong-field Double Ionization

We provide a basis for the laser intensity dependence of the momentum distributions of electrons and ions arising from strong-field non-sequential double ionization (NSDI) at intensities in the range $I=1-6.5 \times 10^{14} W/cm^2$. To do this we use a completely classical method introduced previously \cite{ho-etal05}. Our calculated results reproduce the features of experimental observations at different laser intensities and depend on just two distinct categories of electon trajectories.Comment: 5 pages, 7 figure

Comment on ``Phase and Phase Diffusion of a Split Bose-Einstein Condensate''

Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have analysed an experiment in which an interacting Bose condensate, after being allowed to form in a single potential well, is "cut" by splitting the well adiabatically with a very high potential barrier, and estimate the rate at which, following the cut, the two halves of the condensate lose the "memory" of their relative phase. We argue that, by neglecting the effect of interactions in the initial state before the separation, they have overestimated the rate of phase randomization by a numerical factor which grows with the interaction strength and with the slowness of the separation process.Comment: 2 pages, no figures, to appear in Phys. Rev. Let

Phase resolution limit in macroscopic interference between Bose-Einstein condensates

We study the competition between phase definition and quantum phase fluctuations in interference experiments between independently formed Bose condensates. While phase-sensitive detection of atoms makes the phase progressively better defined, interactions tend to randomize it faster as the uncertainty in the relative particle number grows. A steady state is reached when the two effects cancel each other. Then the phase resolution saturates to a value that grows with the ratio between the interaction strength and the atom detection rate, and the average phase and number begin to fluctuate classically. We discuss how our study applies to both recently performed and possible future experiments.Comment: 4 pages, 5 figure