Generation of wave structures by a two-dimensional object (laser beam) moving in a two-dimensional two-component Bose-Einstein condensate with a velocity greater than both sound velocities of the mixture is studied by means of analytical methods and systematic simulations of the coupled Gross-Pitaevskii equations. The wave pattern features three regions separated by two Mach cones. Two branches of linear patterns similar to the so-called "ship waves" are located outside the corresponding Mach cones, and oblique dark solitons are found inside the wider cone. An analytical theory is developed for the linear patterns. A particular dark-soliton solution is also obtained, its stability is investigated, and two unstable modes of transverse perturbations are identified. It is shown that, for a sufficiently large flow velocity, this instability has a convective character in the reference frame attached to the moving body, which makes the dark soliton effectively stable. The analytical findings are corroborated by numerical simulations.
Stability of dark solitons generated by a supersonic flow of Bose-Einstein condensate past an obstacle is investigated. It is shown that in the reference frame attached to the obstacle a transition occurs at some critical value of the flow velocity from absolute instability of dark solitons to their convective instability. This leads to decay of disturbances of solitons at fixed distance from the obstacle and formation of effectively stable dark solitons. This phenomenon explains surprising stability of the flow picture that has been observed in numerical simulations.
Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.
We calculate the effect of quantum noise in supersonic transport of Bose-Einstein condensates. When an obstacle obstructs the flow of atoms, quantum fluctuations cause atoms to be scattered incoherently into random directions. This suppresses the propagation of Cherenkov radiation, creating quantum turbulence and a crescent of incoherent atoms around the obstacle. We observe similar dynamics if the BEC is stirred by a laser beam: crescents of incoherent atoms are emitted from the laser's turning-points. Finally, we investigate supersonic flow through a disordered potential, and find that the q…
We propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a hollow laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilise up to 9 vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we disc…
We investigate the effects of disorder on the propagation of one-dimensional polariton condensates in semiconductor microcavities. We observe a strong suppression of the backscattering produced by the imperfections of the structure when increasing the condensate density. This suppression occurs in the supersonic regime and is simultaneous to the onset of parametric instabilities which enable the "hopping" of the condensate through the disorder. Our results evidence a new mechanism for the frictionless flow of polaritons at high speeds.
We consider the motion of a quasi one dimensional beam of Bose-Einstein condensed particles in a disordered region of finite extent. Interaction effects lead to the appearance of two distinct regions of stationary flow. One is subsonic and corresponds to superfluid motion. The other one is supersonic, dissipative and shows Anderson localization. We compute analytically the interaction-dependent localization length. We also explain the disappearance of the supersonic stationary flow for large disordered samples.
We derive and analyze shock-wave solutions of hydrodynamic equations describing repulsively interacting one dimensional Bose gas. We also use the number-conserving Bogolubov approach to verify accuracy of the Gross-Pitaevskii equation in shock wave problems. We show that quantum corrections to dynamics of shocks (dark-shock-originated solitons) in a Bose-Einstein condensate are negligible (important) for a realistic set of system parameters. We point out possible signatures of a Bose-Einstein condensate -- Tonks crossover in shock dynamics. Our findings can be directly verified in different ex…
We present a statistical description of Bose-Einstein condensates with general higher order nonlinearities. In particular, we investigate the case of cubic-quintic nonlinearities, of particular interest for dilute condensates. The implication of decoherence for the stability properties of the condensate is discussed.
We study an ultracold Bose gas in the presence of 1D disorder for repulsive inter-atomic interactions varying from zero to the Thomas-Fermi regime. We show that for weak interactions the Bose gas populates a finite number of localized single-particle Lifshits states, while for strong interactions a delocalized disordered Bose-Einstein condensate is formed. We discuss the schematic quantum-state diagram and derive the equations of state for various regimes.
We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensate, the popular Gross-Pitaevskii theory and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensate, with the U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like…
We compare the collective modes for Bose-condensed systems with two degenerate components with and without spontaneous intercomponent coherence at finite temperature using the time-dependent Hartree-Fock approximation. We show that the interaction between the condensate and non-condensate in these two cases results in qualitatively different collective excitation spectra. We show that at zero temperature the single-particle excitations of the incoherent Bose condensate can be probed by intercomponent excitations.
We study the temperature dependence of single-particle and pair coherent condensate densities for a Bose liquid with a "depleted" single-particle Bose-Einstein condensate (BEC) at $T \neq 0$. Our investigations were based on the field-theoretical Green's functions. On the basis of the use of empirical data about the speeds of the first and second sounds is described superfluid state at $T \neq 0$. It is studied the structure of superfluid state taking into account appearance with the different from zero temperatures of normal component and taking into account the branch of the second sound, wh…
We observe the formation of momentum distributions indicative of spatial period-doubling of superfluid Bose-Einstein condensates in periodically translated optical lattices. The effect is attributed to dynamic instability of the condensate wavefunction caused by modulation-induced coupling of ground and excited bands.
We show that it is possible to observe matter wave interference patterns in the collision of bright solitons (Bose Einstein condensates) without free ballistic expansion for suitable choices of scattering length and time dependent trap.
A stationary wave pattern occurring in a flow of a two-component Bose-Einstein condensate past an obstacle is studied. We consider the general case of unequal velocities of two superfluid components. The Landau criterium applied to the two-component system determines a certain region in the velocity space in which superfluidity may take place. Stationary waves arise out of this region, but under the additional condition that the relative velocity of the components does not exceed some critical value. Under increase of the relative velocity the spectrum of the excitations becomes complex valued…
I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi condensate is derived.
How does a rapidly rotating condensed Bose gas carry extreme amounts of angular momentum? The energetically favored state of a not-too-rapidly rotating Bose condensed gas is, as observed, a triangular lattice of singly quantized vortices. This paper describes the fates of the vortex lattice in both harmonic and anharmonic traps when condensates are rotated extremely rapidly.
The general properties of the order parameter for a dipolar spinor Bose-Einstein condensate are discussed based on symmetries of interactions. An initially spin-polarized dipolar condensate is shown to dynamically generate a non-singular vortex via spin-orbit interactions -- a phenomenon reminiscent of the Einstein--de Haas effect in ferromagnets.
We investigate the dynamics of doubly charged vortices generated in dilute Bose-Einstein condensates by using the topological phase imprinting technique. We find splitting times of such vortices and show that thermal atoms are responsible for their decay.
Under a unified theory we investigate the formation of various types of vector-solitons in two-species Bose-Einstein condensates with arbitrary scattering lengths. We then show that by tuning the interaction parameter via Feshbach resonance, transformation between different types of vector solitons is possible. Our results open up new ways in the quantum control of multi-species Bose-Einstein condensates.
We argue that the main mechanism for condensate collapse in an attractive Bose-Einstein condensate is the loss of coherence between atoms a finite distance apart, rather than the growth of the occupation number in noncondensate modes. Since the former mechanism is faster than the latter by a factor of approximately 3/2, this helps to dispel the apparent failure of field theoretical models in predicting the collapse time of the condensate.
Bose-Einstein condensates of $^{87}$Rb atoms are transferred into radio-frequency (RF) induced adiabatic potentials and the properties of the corresponding dressed states are explored. We report on measurements of the spin composition of dressed condensates. We also show that adiabatic potentials can be used to trap atom gases in novel geometries, including suspending a cigar-shaped cloud above a curved sheet of atoms.
We study the ground state properties of a trapped Bose condensate with a neutral impurity. By varying the strength of the attractive atom-impurity interactions the degree of localization of the impurity at the trap center can be controlled. As the impurity becomes more strongly localized the peak condensate density, which can be monitored experimentally, grows markedly. For strong enough attraction, the impurity can make the condensate unstable by strongly deforming the atom density in the neighborhood of the impurity. This "collapse" can possibly be investigated in bosenova-type experiments.
We derive the dynamic and thermodynamic stability conditions for dilute multicomponent Bose-Einstein condensates (BECs). These stability conditions, generalized for $n$-component BECs, are found to be equivalent and are shown to be consistent with the phase diagrams of two- and three-component condensates that are derived from energetic arguments.
In this paper, we present a theoretical study of a Bose-Einstein condensate of interacting bosons in a quartic trap in one, two, and three dimensions. Using Thomas-Fermi approximation, suitably complemented by numerical solutions of the Gross-Pitaevskii equation, we study the ground sate condensate density profiles, the chemical potential, the effects of cross-terms in the quartic potential, temporal evolution of various energy components of the condensate, and width oscillations of the condensate. Results obtained are compared with corresponding results for a bose condensate in a harmonic con…
A neutral impurity atom immersed in a dilute Bose-Einstein condensate (BEC) can have a bound ground state in which the impurity is self-localized. In this small polaron-like state, the impurity distorts the density of the surrounding BEC, thereby creating the self-trapping potential minimum. We describe the self-localization in a strong coupling approach.
We experimentally investigate the collapse dynamics of dipolar Bose- Einstein condensates of chromium atoms in different harmonic trap geometries, from prolate to oblate. The evolutions of the condensates in the unstable regime are compared to three-dimensional simulations of the Gross-Pitaevskii equation including three-body losses. In order to probe the phase coherence of collapsed condensates, we induce the collapse in several condensates simultaneously and let them interfere.
We note the similarity between BEC (Bose-Einstein Condensates) formed of atoms between which we have long-range attraction (and shorter-range repulsions) and the field theoretic "Q balls". This allows us in particular to address the stability of various putative particle physics Q balls made of non-relativistic bosons using variational methods of many-body physics.
We propose that a charged two-condensate Bose system possesses point-like topological defects which can be interpreted as magnetic monopoles. By making use of the $ϕ$-mapping theory, the topological charges of these magnetic monopoles can be expressed in terms of the Hopf indices and Brouwer degree of the $ϕ$-mapping.
Using methods developed in Quantum Field Theory in curved space we can estimate the effects of the inhomogeneities and of a non vanishing velocity on the depletion of a Bose Einstein condensate within the hydrodynamical approximation.
We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.
