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Imaging the phase of an evolving bose-einstein condensate wave function

We demonstrate a spatially resolved autocorrelation measurement with a Bose-Einstein condensate and measure the evolution of the spatial profile of its quantum mechanical phase. Upon release of the condensate from the magnetic trap, its phase develops a form that we measure to be quadratic in the spatial coordinate. Our experiments also reveal the effects of the repulsive interaction between two overlapping condensate wave packets and we measure the small momentum they impart to each other.

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Vortex precession in Bose-Einstein condensates: observations with filled and empty cores.

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of 87Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value of the healing length. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of 2.

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Manifestation of superfluidity in an evolving Bose-Einstein condensed gas.

We study the generation of excitations due to an "impurity" (static perturbation) placed into an oscillating Bose-Einstein condensed gas in the time-dependent trapping field. It is shown that there are two regions for the position of the local perturbation. In the first region the condensate flows around the impurity without generation of excitations demonstrating superfluid properties. In the second region the creation of excitations occurs, at least within a limited time interval, revealing destruction of superfluidity. The phenomenon can be studied by measuring the damping of condensate oscillations at different positions of the impurity.

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Nonequilibrium field theory description of the Bose-Einstein condensate.

We study the detailed out-of-equilibrium time evolution of a homogeneous Bose-Einstein condensate (BEC). We consider a nonrelativistic quantum theory for a self-interacting complex scalar field, immersed in a thermal bath, as an effective microscopic model for the description of the BEC. The interaction between fluctuations proves to be crucial in the mechanism of instability generation. We show the existence of two regimes in k space, with a crossover for k(2)/2m approximately 2 lambda|phi(0)|(2), where lambda is the coupling constant and |phi(0)|(2) is the condensate density. We deduce and solve a set of coupled equations that completely determines the nonequilibrium dynamics of the condensate density.

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Suppression and enhancement of impurity scattering in a Bose-Einstein condensate.

Impurity atoms propagating at variable velocities through a trapped Bose-Einstein condensate were produced using a stimulated Raman transition. The redistribution of momentum by collisions between the impurity atoms and the stationary condensate was observed in a time-of-flight analysis. The collisional cross section was dramatically reduced when the impurity velocity was reduced below the condensate speed of sound, in agreement with the Landau criterion for superfluidity. For large numbers of impurity atoms, we observed an enhancement of atomic collisions due to bosonic stimulation. This enhancement is analogous to optical super-radiance.

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Watching dark solitons decay into vortex rings in a Bose-Einstein condensate.

We have created spatial dark solitons in two-component Bose-Einstein condensates in which the soliton exists in one of the condensate components and the soliton nodal plane is filled with the second component. The filled solitons are stable for hundreds of milliseconds. The filling can be selectively removed, making the soliton more susceptible to dynamical instabilities. For a condensate in a spherically symmetric potential, these instabilities cause the dark soliton to decay into stable vortex rings. We have imaged the resulting vortex rings.

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Quantum superchemistry: dynamical quantum effects in coupled atomic and molecular Bose-Einstein condensates.

We show that in certain parameter regimes there is a macroscopic dynamical breakdown of the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive- P representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The full quantum theory includes the spontaneous processes which will become significant when the atomic population is low. The experimental signature of the quantum effects will be the time scale of the revival of the atomic population after a near total conversion to the molecular condensate.

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Bose-Einstein condensation of metastable helium.

We have observed a Bose-Einstein condensate in a dilute gas of 4He in the (3)2S(1) metastable state. We find a critical temperature of (4.7+/-0.5) microK and a typical number of atoms at the threshold of 8 x 10(6). The maximum number of atoms in our condensate is about 5 x 10(5). An approximate value for the scattering length a = (16+/-8) nm is measured. The mean elastic collision rate at threshold is then estimated to be about 2 x 10(4) s(-1), indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is 2 s, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.

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Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation.

Using a focused laser beam we stir a 87Rb Bose-Einstein condensate confined in a magnetic trap. We observe that the steady states of the condensate correspond to an elliptic cloud, stationary in the rotating frame. These steady states depend nonlinearly on the stirring parameters (amplitude and frequency), and various solutions can be reached experimentally depending on the path followed in this parameter space. These states can be dynamically unstable and we observe that such instabilities lead to vortex nucleation in the condensate.

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Superfluid and dissipative dynamics of a Bose-Einstein condensate in a periodic optical potential.

We create Bose-Einstein condensates of 87Rb in a static magnetic trap with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic trap center we are able to control the condensate evolution. We observe a change in the frequency of the center-of-mass oscillation in the harmonic trapping potential, in analogy with an increase in effective mass. For fluid velocities greater than a local speed of sound, we observe the onset of dissipative processes up to full removal of the superfluid component. A parallel simulation study visualizes the dynamics of the Bose-Einstein condensate and accounts for the main features of the observed behavior.

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Uniting Bose-Einstein condensates in optical resonators.

The relative phase of two initially independent Bose-Einstein condensates can be laser cooled to unite the two condensates by putting them into a ring cavity and coupling them with an internal Josephson junction. First, we show that this phase cooling process already appears within a semiclassical model. We calculate the stationary states, find regions of bistable behavior, and suggest a Ramsey-type experiment to measure the buildup of phase coherence between the condensates. We also study quantum effects and imperfections of the system.

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Anomalous modes drive vortex dynamics in confined Bose-Einstein condensates.

The dynamics of vortices in trapped Bose-Einstein condensates are investigated both analytically and numerically. In axially symmetric traps, the critical rotation frequency for metastability of an isolated vortex coincides with the largest vortex precession frequency (or anomalous mode) in the Bogoliubov excitation spectrum. The number of anomalous modes increases for an elongated condensate. The largest mode frequency exceeds the thermodynamic critical frequency and the nucleation frequency at which vortices are created dynamically. Thus, anomalous modes describe both vortex precession and the critical rotation frequency for creation of the first vortex in an elongated condensate.

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Phase-fluctuating 3D Bose-Einstein condensates in elongated traps.

We find that in very elongated 3D trapped Bose gases, even at temperatures far below the BEC transition temperature T(c), the equilibrium state will be a 3D condensate with fluctuating phase (quasicondensate). At sufficiently low temperatures the phase fluctuations are suppressed and the quasicondensate turns into a true condensate. The presence of the phase fluctuations allows for extending thermometry of Bose-condensed gases well below those established in current experiments.

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Quasipure Bose-Einstein condensate immersed in a Fermi sea.

We report the observation of coexisting Bose-Einstein condensate (BEC) and Fermi gas in a magnetic trap. With a very small fraction of thermal atoms, the 7Li condensate is quasipure and in thermal contact with a 6Li Fermi gas. The lowest common temperature is 0.28 microK approximately 0.2(1)T(C) = 0.2(1)T(F) where T(C) is the BEC critical temperature and T(F) the Fermi temperature. The 7Li condensate has a one-dimensional character.

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Finite-temperature simulations of the scissors mode in Bose-Einstein condensed gases.

The dynamics of a trapped Bose-condensed gas at finite temperatures is described by a generalized Gross-Pitaevskii equation for the condensate order parameter and a semiclassical kinetic equation for the thermal cloud, solved using N-body simulations. The two components are coupled by mean fields as well as collisional processes that transfer atoms between the two. We use this scheme to investigate scissors modes in anisotropic traps as a function of temperature. Frequency shifts and damping rates of the condensate mode are extracted, and are found to be in good agreement with recent experiments.

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Realization of Bose-Einstein condensates in lower dimensions.

Bose-Einstein condensates of sodium atoms have been prepared in optical and magnetic traps in which the energy-level spacing in one or two dimensions exceeds the interaction energy between atoms, realizing condensates of lower dimensionality. The crossover into two-dimensional and one-dimensional condensates was observed by a change in aspect ratio and by the release energy converging to a nonzero value when the number of trapped atoms was reduced.

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Domain wall solitons in binary mixtures of Bose-Einstein condensates.

The structure and dynamics of the domain walls separating segregated condensates in trapped mixtures of repulsive Bose-Einstein condensates are studied. Our work reveals that, under fairly general conditions, these domain walls behave as independent dynamical entities, which allows us to identify them as constituting a novel class of multicomponent solitons in Bose-Einstein condensates.

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Vortex nucleation in a stirred Bose-Einstein condensate.

We studied the nucleation of vortices in a Bose-Einstein condensate stirred by a laser beam. The vortex cores were observed using time-of-flight absorption imaging. Depending on the stirrer size, either discrete resonances or a broad response was visible as the stir frequency was varied. Stirring beams small compared to the condensate size generated vortices below the critical rotation frequency for the nucleation of surface modes, suggesting a local mechanism of generation. In addition, we observed the centrifugal distortion of the condensate due to the rotating vortex lattice and found evidence for bent vortices.

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