Dilute Atomic Bose-Einstein Condensates Research Articles

Quantum turbulence in atomic Bose-Einstein condensates

Weakly interacting, dilute atomic Bose-Einstein condensates (BECs) have proved to be an attractive context for the study of nonlinear dynamics and quantum effects at the macroscopic scale. Recently, weakly interacting, dilute atomic BECs have been used to investigate quantum turbulence both experimentally and theoretically, stimulated largely by the high degree of control which is available within these quantum gases. In this article we motivate the use of weakly interacting, dilute atomic BECs for the study of turbulence, discuss the characteristic regimes of turbulence which are accessible, and briefly review some selected investigations of quantum turbulence and recent results. We focus on three stages of turbulence – the generation of turbulence, its steady state and its decay – and highlight some fundamental questions regarding our understanding in each of these regimes.

Tuning the Mobility of a Driven Bose-Einstein Condensate via Diabatic Floquet Bands

We study the response of ultracold atoms to a weak force in the presence of a temporally strongly modulated optical lattice potential. It is experimentally demonstrated that the strong ac driving allows for a tailoring of the mobility of a dilute atomic Bose-Einstein condensate with the atoms moving ballistically either along or against the direction of the applied force. Our results are in agreement with a theoretical analysis of the Floquet spectrum of a model system, thus revealing the existence of diabatic Floquet bands in the atoms' band spectra and highlighting their role in the nonequilibrium transport of the atoms.

Weak localization with nonlinear bosonic matter waves

We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross–Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions.

Vortex Pump for Dilute Bose-Einstein Condensates

The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.

Dynamically stable multiply quantized vortices in dilute Bose-Einstein condensates

Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.

On stability of spatially periodic structures of an atomic Bose-Einstein condensate

The stability of spatially periodic structures, including vortex lattices, in a dilute atomic Bose-Einstein condensate is analyzed. By using the approximate solution of the nonlocal nonlinear Schrodinger equation (the generalized Gross-Pitaevskiĭ equation), it is shown that, in the limit of low concentrations, such structures are stable.

Stationary vortex clusters in nonrotating Bose-Einstein condensates

We investigate the recently found stationary vortex cluster states in dilute atomic Bose-Einstein condensates confined by a nonrotating trap, and also present a stationary three-vortex cluster. We find the stationary states by minimizing directly an error norm for the stationary Gross-Pitaevskii equation, and study the dynamic and energetic stability of the resulting states by solving the corresponding Bogoliubov equations for the elementary excitations. The results are verified by integrating the time-dependent Gross-Pitaevskii equation. Contrary to previously reported results, the stationary states were observed to be both energetically and dynamically unstable. The dynamical decay rate of the clusters is typically very slow, but it should be experimentally observable. The most promising circumstances to experimentally generate and observe these structures and their dynamics is in weakly dissipative condensate systems, using phase-imprinting techniques.

Adiabaticity criterion for moving vortices in dilute Bose-Einstein condensates.

Considering a moving vortex line in a dilute atomic Bose-Einstein condensate within time-dependent Hartree-Fock-Bogoliubov-Popov theory, we derive a criterion for the quasiparticle excitations to follow the vortex core rigidly. The assumption of adiabaticity, which is crucial for the validity of the stationary self-consistent theories in describing such time-dependent phenomena, is shown to imply a stringent criterion for the velocity of the vortex line. Furthermore, this condition is shown to be violated in the recent vortex precession experiments.

Ground state and quasiparticle spectrum of a two-component Bose-Einstein condensate

We consider a dilute atomic Bose-Einstein condensate with two non-degenerate internal energy levels. The presence of an external radiation field can result in new ground states for the condensate which result from the lowering of the condensate energy due to the interaction energy with the field. In this approach there are no instabilities in the quasiparticle spectrum as was previously found by Goldstein and Meystre (Phys. Rev. A \QTR{bf}{55}, 2935 (1997)).

Structure and stability of vortices in dilute Bose-Einstein condensates at ultralow temperatures.

We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing "classical" superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.

Feshbach resonances in atomic Bose–Einstein condensates

The low-energy Feshbach resonances recently observed in the inter-particle interactions of trapped ultra-cold atoms involve an intermediate quasi-bound molecule with a spin arrangement that differs from the trapped atom spins. Variations of the strength of an external magnetic field then alter the difference of the initial and intermediate state energies (i.e. the ‘detuning’). The effective scattering length that describes the low-energy binary collisions, similarly varies with the near-resonant magnetic field. Since the properties of the dilute atomic Bose–Einstein condensates (BECs) are extremely sensitive to the value of the scattering length, a ‘tunable’ scattering length suggests very interesting many-body studies. In this paper, we review the theory of the binary collision Feshbach resonances, and we discuss their effects on the many-body physics of the condensate. We point out that the Feshbach resonance physics in a condensate can be considerably richer than that of an altered scattering length: the Feshbach resonant atom–molecule coupling can create a second condensate component of molecules that coexists with the atomic condensate. Far off-resonance, a stationary condensate does behave as a single condensate with effective binary collision scattering length. However, even in the off-resonant limit, the dynamical response of the condensate mixture to a sudden change in the external magnetic field carries the signature of the molecular condensate's presence: experimentally observable oscillations of the number of atoms and molecules. We also discuss the stationary states of the near-resonant condensate system. We point out that the physics of a condensate that is adiabatically tuned through resonance depends on its history, i.e. whether the condensate starts out above or below resonance. Furthermore, we show that the density dependence of the many-body ground-state energy suggests the possibility of creating a dilute condensate system with the liquid-like property of a self-determined density.