Dipolar Condensates Research Articles

A variational approach to Bogoliubov excitations and dynamics of dipolar Bose–Einstein condensates

We investigate the stability properties and the dynamics of Bose–Einstein condensates with axial symmetry, especially with dipolar long-range interaction, using both simulations on grids and variational calculations. We present an extended variational ansatz which is applicable for axial symmetry and show that this ansatz can reproduce the lowest eigenfrequencies of the Bogoliubov spectrum, and also the corresponding eigenfunctions. Our variational ansatz is capable of describing the roton instability of pancake-shaped dipolar condensates for arbitrary angular momenta. After investigating the linear regime we apply the ansatz to determine the dynamics and show how the angular collapse is correctly described within the variational framework.

Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates

We investigate a Bose-Einstein condensate with additional long-range dipolar interaction in a cylindrically symmetric trap within a variational framework. Compared to the ground state of this system, little attention has as yet been payed to its unstable excited states. For thermal excitations, however, the latter is of great interest, because it forms the ``activated complex'' that mediates the collapse of the condensate. For a certain value of the $s$-wave scatting length our investigations reveal a bifurcation in the transition state, leading to the emergence of two additional and symmetry-breaking excited states. Because these are of lower energy than their symmetric counterpart, we predict the occurrence of a symmetry-breaking thermally induced collapse of dipolar condensates. We show that its occurrence crucially depends on the trap geometry and calculate the thermal decay rates of the system within leading-order transition state theory with the help of a uniform rate formula near the rank-2 saddle which allows the bifurcation to be smoothly passed.

Faraday patterns in coupled one-dimensional dipolar condensates

We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves differ substantially in two- and one-dimensional geometries, providing a clear example of the key role of confinement dimensionality in dipolar gases. Moreover, Faraday patterns constitute an excellent tool to study non-local effects in polar gases, as we illustrate for two parallel quasi-one-dimensional dipolar condensates. Non-local interactions between the condensates give rise to an excitation spectrum characterized by symmetric and anti-symmetric modes, even in the absence of hopping. We show that this feature, absent in non-dipolar gases, results in a critical driving frequency at which a marked transition occurs between correlated and anti-correlated Faraday patterns in the two condensates. Interestingly, at this critical frequency, the emergent Faraday pattern stems from a spontaneous symmetry breaking mechanism.

Dipolar-induced interplay between inter-level physics and macroscopic phase transitions in triple-well potentials

We propose a scheme to reveal the interplay between dipole–dipole interaction (DDI), inter-level coupling and macroscopic phase transitions in dipolar condensates. By considering a macroscopic sample of dipolar bosons in triple-well potentials, DDI-induced coupling between the inter-level physics and the macroscopic phase transitions is presented. When the DDI exceeds certain thresholds, the degeneracy of the two lowest energy levels and the excitation of new eigenstates occur, respectively. Interestingly, these thresholds give the boundaries of various quantum phase transitions. That is, the quantum phase transitions are the consequence of the levels' degeneracy and the new eigenstates' excitation. Furthermore, DDI-induced long-range macroscopic Josephson oscillations are observed and long-range coherent quantum transportation is achieved. Our results give clear proof of the interplay between the multi-level physics and quantum phase transitions, and also provide a way for designing the long-range coherent quantum transportation.

The inhomogeneous extended Bose‐Hubbard model: A mean‐field theory

AbstractWe develop an inhomogeneous mean‐field theory for the extended Bose‐Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean‐field theory yields the phase diagram of the homogeneous extended Bose‐Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott‐insulator (MI), density‐wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on‐site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest‐neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density‐wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold‐atom dipolar condensates in optical lattices in a confining potential.

The Anisotropy of Dipolar Condensate in One-Dimensional Optical Lattices

The anisotropy of dipole-dipole interaction is revealed by energy band, tunneling dynamics and stabilities of a dipolar condensate in one-dimensional optical lattices. It is demonstrated that the Bloch band structure, the tunneling rate between Bloch bands and the stabilities of Bloch states can be controlled by adjusting the effective aspect ratio of the condensate and the dipolar orientation.

Superfluid pairing in a mixture of a spin-polarized Fermi gas and a dipolar condensate

We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We show that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. We formulate, in the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory which allows us to estimate the critical temperature when the anisotropic Fock potential is taken into consideration and to determine the system parameters that optimize the critical temperature at which such a superfluid emerges before the system begins to phase separate.

Effects of fermion flavor on exciton condensation in double-layer systems

We use fermionic path integral quantum Monte Carlo to study the effects of fermion flavor on the physical properties of dipolar exciton condensates in double layer systems. We find that by including spin in the system weakens the effective interlayer interaction strength, yet this has very little effect on the Kosterlitz-Thouless transition temperature. We further find that, to obtain the correct description of screening, it is necessary to account for correlation in both the interlayer and intralayer interactions. We show that while the excitonic binding cannot completely surpress screening by additional fermion flavors, their screening effectiveness is reduced leading to a much higher transition temperatures than predicted with large-N analysis.

Anisotropic sound and shock waves in dipolar Bose–Einstein condensate

We study the propagation of anisotropic sound and shock waves in dipolar Bose–Einstein condensate in three dimensions (3D) as well as in quasi-two (2D, disk shape) and quasi-one (1D, cigar shape) dimensions using the mean-field approach. In 3D, the propagation of sound and shock waves are distinct in directions parallel and perpendicular to dipole axis with the appearance of instability above a critical value corresponding to attraction. Similar instability appears in 1D and not in 2D. The numerical anisotropic Mach angle agrees with theoretical prediction. The numerical sound velocity in all cases agrees with that calculated from Bogoliubov theory. A movie of the anisotropic wave propagation in a dipolar condensate is made available as supplementary material.

Phase slippage and self-trapping in a self-induced bosonic Josephson junction

A dipolar condensate confined in a toroidal trap constitutes a self-induced Josephson junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the $s$-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that, in this system, the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and antivortex are spontaneously nucleated in the low-density regions before a minimum of the population imbalance is reached and then cross the toroidal section in opposite directions through the junctions. This vortex dynamics yields a phase slip between the two weakly linked condensates causing an inversion of the particle flux.

Singlet and triplet superfluid competition in a mixture of two-component Fermi and one-component dipolar Bose gases

We consider a mixture of two-component Fermi and (one-component) dipolar Bose gases in which both dipolar interaction and s-wave scattering between fermions of opposite spins are tunable. We show that in the long wavelength limit, the anisotropy in the Fermi-Fermi interaction induced by phonons of the dipolar condensate can strongly enhance the scattering in the triplet channel. We investigate in detail the conditions for achieving optimal critical temperature at which the triplet superfluid begins to compete with the singlet superfluid.

Bright soliton in an expulsive potential in a dipolar condensate

We study the stability of matter-wave bright solitons for a dipolar Bose–Einstein condensate in a harmonic potential which is transversely attractive and longitudinally expulsive. We map the regimes of stability as a function of dipole–dipole interaction strength using sech-based variational ansatz. The critical points for collapse and explosion are presented.

Spatial Landau-Zener-Stückelberg interference in spinor Bose-Einstein condensates

We investigate the St\"{u}ckelberg oscillations of a spin-1 Bose-Einstein condensate subject to a spatially inhomogeneous transverse magnetic field and a periodic longitudinal field. We show that the time-domain St\"{u}ckelberg oscillations result in interference fringes in the density profiles of all spin components due to the spatial inhomogeneity of the transverse field. This phenomenon represents the Landau-Zener-St\"{u}ckelberg interference in the space-domain. Since the magnetic dipole-dipole interaction between spin-1 atoms induces an inhomogeneous effective magnetic field, interference fringes also appear if a dipolar spinor condensate is driven periodically. We also point out some potential applications of this spatial Landau-Zener-St\"{u}kelberg interference.

Spatial density oscillations in trapped dipolar condensates

We investigated the ground state wave function and free expansion of a trapped dipolar condensate. We find that dipolar interaction may induce both biconcave and dumbbell density profiles in, respectively, the pancake- and cigar-shaped traps. On the parameter plane of the interaction strengths, the density oscillation occurs only when the interaction parameters fall into certain isolated areas. The relation between the positions of these areas and the trap geometry is explored. By studying the free expansion of the condensate with density oscillation, we show that the density oscillation is detectable from the time-of-flight image.

Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. II. Applications

Bose-Einstein condensates with an attractive 1/r interaction and with dipole-dipole interaction are investigated in the framework of the Gaussian variational ansatz introduced by S. Rau, J. Main, and G. Wunner [Phys. Rev. A, submitted]. We demonstrate that the method of coupled Gaussian wave packets is a full-fledged alternative to direct numerical solutions of the Gross-Pitaevskii equation, or even superior in that coupled Gaussians are capable of producing both, stable and unstable states of the Gross-Pitaevskii equation, and thus of giving access to yet unexplored regions of the space of solutions of the Gross-Pitaevskii equation. As an alternative to numerical solutions of the Bogoliubov-de Gennes equations, the stability of the stationary condensate wave functions is investigated by analyzing the stability properties of the dynamical equations of motion for the Gaussian variational parameters in the local vicinity of the stationary fixed points. For blood-cell-shaped dipolar condensates it is shown that on the route to collapse the condensate passes through a pitchfork bifurcation, where the ground state itself turns unstable, before it finally vanishes in a tangent bifurcation.

Coherent matter waves of a dipolar condensate in two-dimensional optical lattices

The coherent matter waves of a dipolar condensate in deep two-dimensional (2D) tilted and nontilted optical lattices are studied both analytically and numerically. It is shown that, in tilted lattices, by properly designing the sign and the magnitude of the contact interaction and the dipolar interaction, it is possible to control the decoherence of Bloch oscillations. Contrary to the usual short-range interacting Bose system, long-lived Bloch oscillations of the dipolar condensate are achieved when the dipolar interaction, the contact interaction, and the lattice dimension satisfy an analytical condition. Furthermore, we predict that, in untilted lattices, stable coherent 2D moving soliton and breather states of the dipolar condensate exist. This fact is very different from the purely short-range interacting Bose system (where the moving soliton cannot be stabilized in high-dimensional lattices). The dipolar interaction can lead to some novel phenomena that can not appear in short-range interacting BEC system.

Pitchfork bifurcations in blood-cell-shaped dipolar Bose-Einstein condensates

We demonstrate that the method of coupled Gaussian wave packets is a full-fledged alternative to direct numerical solutions of the Gross-Pitaevskii equation of condensates with electromagnetically induced attractive $1/r$ interaction or with dipole-dipole interaction. Moreover, Gaussian wave packets are superior in that they are capable of producing both stable and unstable stationary solutions and thus of giving access to yet unexplored regions of the space of solutions of the Gross-Pitaevskii equation. We apply the method to clarify the theoretical nature of the collapse mechanism of blood-cell-shaped dipolar condensates: On the route to collapse the condensate passes through a pitchfork bifurcation, where the ground state itself turns unstable, before it finally vanishes in a tangent bifurcation.

Magneto-optical control of atomic spin mixing in dipolar spinor Bose-Einstein condensates

We study the role in an external photoassociation light field in the spin mixing dynamics of a spin-one Bose condensate with long-range magnetic dipole-dipole interaction. The mean-field energy functional of the system is found to be formally identical to that of two coupled nonrigid pendulums, manifesting either constructive or destructive interferences. The interplay between photoassociation and the magnetic dipole-dipole interaction provides a novel route to the magneto-optical quantum control of atomic spin mixing in dipolar spinor condensates.

Phonon instability and self-organized structures in multilayer stacks of confined dipolar Bose-Einstein condensates in optical lattices

In calculations to date [1,2] of multi-layer stacks of dipolar condensates, created in one-dimensional optical lattices, the condensates have been assumed to be two-dimensional. In a real experiment, however, the condensates do not extend to infinity in the oblate direction, but have to be confined by a trap potential, too. By three-dimensional numerical simulations of this realistic experimental situation we find a crucial dependence of the phonon instability boundary on the number of layers. Moreover, near the boundary of the phonon instability, a variety of structured ground-state wave functions emerges, which may indicate the onset of a roton instability [3,4].

Exact solutions and stability of rotating dipolar Bose-Einstein condensates in the Thomas-Fermi limit

We present a theoretical analysis of dilute gas Bose-Einstein condensates with dipolar atomic interactions under rotation in elliptical traps. Working in the Thomas-Fermi limit, we employ the classical hydrodynamic equations to first derive the rotating condensate solutions and then consider their response to perturbations. We thereby map out the regimes of stability and instability for rotating dipolar Bose-Einstein condensates and, in the latter case, discuss the possibility of vortex lattice formation. We employ our results to propose several routes to induce vortex lattice formation in a dipolar condensate.