We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.
We produce Bose-Einstein condensates of 6Li2 molecules in a low power (22 W) crossed optical dipole trap. Fermionic 6Li atoms are collected in a magneto-optical trap from a Zeeman slowed atomic beam, then loaded into the optical dipole trap where they are evaporatively cooled to quantum degeneracy. Our simplified system offers a high degree of flexibility in trapping geometry for studying ultracold Fermi and Bose gases.
The lowest-lying collective modes of a trapped Bose gas in an optical lattice are studied in the Bose-Hubbard model. An exact diagonalization of the Hamiltonian is performed in a one-dimensional five-particle system in order to find the lowest few eigenstates. Dipole and breathing character of the eigenstates is confirmed in the limit where the tunneling dominates the dynamics, but under Mott-like conditions the excitations do not correspond to oscillatory modes.
We calculate the critical rotation frequency at which a vortex state becomes energetically favorable over the vortex-free ground state in a harmonically trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as well as the usual s-wave contact interactions. In the Thomas-Fermi (hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with the dipoles aligned along the axis of symmetry of the trap) tend to have lower critical rotation frequencies than their purely s-wave contact interaction counterparts. The converse is true for dipolar condensates in prolate…
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 point out the possibility of having a roton-type excitation spectrum in a quasi-1D Bose-Einstein condensate with dipole-dipole interactions. Normally such a system is quite unstable due to the attractive portion of the dipolar interaction. However, by reversing the sign of the dipolar interaction using either a rotating magnetic field or a laser with circular polarization, a stable cigar-shaped configuration can be achieved whose spectrum contains a `roton' minimum analogous to that found in helium II. Dipolar gases also offer the exciting prospect to tune the depth of this `roton' minimum …
We calculate the ground states and ground state phase diagrams of Bose-Einstein condensates of spin-3 atoms under the assumption of conserved magnetization. We especially concentrate on the ground states of a chromium condensate. In chromium the magnetic dipole-dipole interaction enables magnetization changing collisions, but in a strong magnetic field these are suppressed. In the calculation of the phase diagrams we neglect the contribution from the dipole-dipole interaction, but discuss its effects at the end of the paper. We show that the ground state of a chromium condensate does not seem …
Starting from one-dimensional Mott Insulators, we use a bichromatic optical lattice to add controlled disorder to an ideal optical crystal where bosonic atoms are pinned by repulsive interactions. Increasing disorder, we observe a broadening of the Mott Insulator resonances and the transition to an insulating state with a flat density of excitations, suggesting the formation of a Bose-Glass.
Magnetic dipole-dipole interaction dominated Bose-Einstein condensates are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from large spin limit to obtain an effective minimal Hamiltonian; a version extended from a non-linear sigma model. By solving the Gross-Pitaevskii equation we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.
We have measured the relative strength $ε_dd$ of the magnetic dipole-dipole interaction compared to the contact interaction in a chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of a dipolar chromium BEC with different orientations of the atomic magnetic dipole moments. By comparing them with numerical solutions of the hydrodynamic equations for dipolar condensates, we are able to determine $ε_dd = 0.159\pm0.034$ with high accuracy. Since the absolute strength of the dipole-dipole interaction is known exactly, the relative strength of the dipoledipole intera…
We consider quasi-two-dimensional atomic/molecular Bose-Einstein condensates with both contact and dipole-dipole interactions. It is shown that, as a consequence of the dimensional reduction, and within mean-field theory, the condensates do not develop unstable excitation spectra, even when the dipole-dipole interaction completely dominates the contact interaction.
Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole moments polarized \emph{perpendicular} to the confinement direction. Unlike isotropic solitons predicted for the moments aligned with the confinement axis [Phys. Rev. Lett. \textbf{95}, 200404 (2005)], no sign reversal of the dipole-dipole interaction is necessary to support the solitons. Direct 3D simulations confirm their stability.
Expansion of a Bose-Einstein condensate (BEC) is studied, in the presence of a random potential. The expansion is controlled by a single parameter, $(μτ_{eff} /\hbar)$, where $μ$ is the chemical potential, prior to the release of the BEC from the trap, and $τ_{eff}$ is a transport relaxation time which characterizes the strength of the disorder. Repulsive interactions (nonlinearity) facilitate transport and can lead to diffusive spreading of the condensate which, in the absence of interactions, would have remained localized in the vicinity of its initial location.
We examine bosonic atoms that are confined in a toroidal, quasi-one-dimensional trap, subjected to a random potential. The resulting inhomogeneous atomic density is smoothened for sufficiently strong, repulsive interatomic interactions. Statistical analysis of our simulations show that the gas supports persistent currents, which become more fragile due to the disorder.
We theoretically study the dipole oscillations of an ideal Fermi gas in a disordered trap. We show that even weak disorder induces strong damping of the oscillations and we identify a metal-insulator crossover. For very weak disorder, we show that damping results from a dephasing effect related to weak random perturbations of the energy spectrum. For increasing disorder, we show that the Fermi gas crosses over to an insulating regime characterized by strong-damping due to the proliferation of localized states.
In this letter we investigate the effects of dipole-dipole interactions on the vortex lattices in fast rotating Bose-Einstein condensates. For single planar condensate, we show that the triangular lattice structure will be unfavorable when the s-wave interaction is attractive and exceeds a critical value. It will first change to a square lattice, and then become more and more flat with the increase of s-wave attraction, until the collapse of the condensate. For an array of coupled planar condensates, we discuss how the dipole-dipole interactions between neighboring condensates compete with the…
We consider the thermodynamics of a homogeneous superfluid dilute Bose gas in the presence of weak quenched disorder. Following the zero-temperature approach of Huang and Meng, we diagonalize the Hamiltonian of a dilute Bose gas in an external random delta-correlated potential by means of a Bogoliubov transformation. We extend this approach to finite temperature by combining the Popov and the many-body T-matrix approximations. This approach permits us to include the quasi-particle interactions within this temperature range. We derive the disorder-induced shifts of the Bose-Einstein critical te…
We suggest a method to create turbulence in a trapped atomic Bose-Einstein condensate (BEC). By replacing in the upper half part of our box the wave function, Psi, with its complex conjugate, Psi^{*}, new negative vortices are introduced into the system. The simulations are performed by solving the two-dimensional Gross-Pitaevskii equation (2D GPE). We study the successive dynamics of the wave function by monitoring the evolution of density and phase profile.
We study stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time …
We study the dipole collective oscillations in the bose-fermi mixture using a dynamical time-dependent approach, which are formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. We find big difference in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the random-phase approximation and the sum-rule approach. While the bose gas oscillates monotonously, the fermion oscillation shows a beat and a damping. When the amplitude is not minimal, the dipole oscillation of the fermi gas cannot be described with a simple cent…
The extended Bose-Hubbard model captures the essential properties of a wide variety of physical systems including ultracold atoms and molecules in optical lattices, Josephson junction arrays, and certain narrow band superconductors. It exhibits a rich phase diagram including a supersolid phase where a lattice solid coexists with a superfluid. We use quantum Monte Carlo to study the supersolid part of the phase diagram of the extended Bose-Hubbard model on the simple cubic lattice. We add disorder to the extended Bose-Hubbard model and find that the maximum critical temperature for the supersol…
Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this article the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found.
We study the conservative dynamics and stationary configurations of a vortex-antivortex pair in a harmonically trapped two-dimensional Bose-Einstein condensate. We establish the conceptual framework for understanding the stationary states and the topological defect trajectories, through considerations of different mechanisms of vortex motion and the bifurcation of soliton-like stationary solutions. Our insights are based on Lagrangian-based variational calculations, numerical solutions of both the time-dependent and time-independent Gross-Pitaevskii equations, and exact solutions for the non-i…
We establish the full groundstate phase diagram of disordered Bose-Hubbard model in two-dimensions at unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid--insulator transition of the pure system, we observe an unexpectedly weak---almost not resolvable---sensitivity of the critical interaction to the strength of (weak…
We observe large density modulations in time-of-flight images of elongated Bose-Einstein condensates, initially confined in a harmonic trap and in the presence of weak disorder. The development of these modulations during the time-of-flight and their dependence with the disorder are investigated. We render an account of this effect using numerical and analytical calculations. We conclude that the observed large density modulations originate from the weak initial density modulations induced by the disorder, and not from initial phase fluctuations (thermal or quantum).
The influence of a weak random potential on the collective modes of a trapped interacting Bose-Einstein condensate at zero temperature is calculated in the limit when the correlation length of the disorder is smaller than the healing length of the superfluid. The problem is solved in the Thomas-Fermi limit by generalizing the superfluid hydrodynamic equations to allow for the presence of weak disorder. We find that the disorder-induced frequency-shifts of the low-energy excitations can be of the same order of magnitude as the beyond mean-field corrections in the normal interaction recently obs…
We consider the propagation of a dark soliton in a quasi 1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.
We study the zero temperature phase diagram of the disordered spin-1 Bose-Hubbard model in a 2-dimensional square lattice. To this aim, we use a mean field Gutzwiller ansatz and a probabilistic mean field perturbation theory. The spin interaction induces two different regimes corresponding to a ferromagnetic and antiferromagnetic order. In the ferromagnetic case, the introduction of disorder reproduces analogous features of the disordered scalar Bose-Hubbard model, consisting in the formation of a Bose glass phase between Mott insulator lobes. In the antiferromagnetic regime the phase diagram …
We investigate the effect of diagonal disorder on bosons in an optical lattice described by an Anderson-Hubbard model at zero temperature. It is known that within Gutzwiller mean-field theory spatially resolved calculations suffer particularly from finite system sizes in the disordered case, while arithmetic averaging of the order parameter cannot describe the Bose glass phase for finite hopping $J>0$. Here we present and apply a new \emph{stochastic} mean-field theory which captures localization due to disorder, includes non-trivial dimensional effects beyond the mean-field scaling level and …
We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {\it theorem of inclusions} which states that for any transition in a disordered system one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for…
We predict solitary vortices in quasi-planar condensates of dipolar atoms, polarized parallel to the confinement direction, with the effective sign of the dipole-dipole interaction inverted by means of a rapidly rotating field. Energy minima corresponding to vortex solitons with topological charges ${% \ell}=1$ and 2 are predicted for moderately strong dipole-dipole interaction, using an axisymmetric Gaussian ansatz. The stability of the solitons with $\ell =1$ is confirmed by full 3D simulations, whereas their counterparts with $\ell =2$ are found to be unstable against splitting into a set o…
We propose and analyze a general mechanism of disorder-induced order in two-component Bose-Einstein condensates, analogous to corresponding effects established for XY spin models. We show that a random Raman coupling induces a relative phase of pi/2 between two BECs and that the effect is robust. We demonstrate it in 1D, 2D and 3D at T=0 and present evidence that it persists at small T>0. Applications to phase control in ultracold spinor condensates are discussed.
We show that the Calogero-Sutherland (C-S) gas, a famous exact soluble one-dimensional system with an inverse square long range interaction, can be realized by dimension reduction in a cold Bose atom system with a dipole-dipole interaction. Depending on the orientation of the dipoles, the effective interaction is either attractive or repulsive. The low-lying effective theory may be a Luttinger liquid when the exclusion statistics parameter $λ$ may be well-defined. We hope that the C-S gas can be realized experimentally and the Luttinger liquid character can be observed.
