We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the non-adiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyse the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.
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 study the Hartree ground state of a dipolar condensate of atoms or molecules in an three-dimensional anisotropic geometry and at T=0. We determine the stability of the condensate as a function of the aspect ratios of the trap frequencies and of the dipolar strength. We find numerically a rich phase space structure characterized by various structures of the ground-state density profile.
Faraday patterns can be induced in Bose-Einstein condensates by a periodic modulation of the system nonlinearity. We show that these patterns are remarkably different in dipolar gases with a roton-maxon excitation spectrum. Whereas for non-dipolar gases the pattern size decreases monotonously with the driving frequency, patterns in dipolar gases present, even for shallow roton minima, a highly non trivial frequency dependence characterized by abrupt pattern size transitions, which are especially pronounced when the dipolar interaction is modulated. Faraday patterns constitute hence an optimal …
We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously-identified "roton-like" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.
We calculate the hydrodynamic solutions for a dilute Bose-Einstein condensate with long-range dipolar interactions in a rotating, elliptical harmonic trap, and analyse their dynamical stability. The static solutions and their regimes of instability vary non-trivially on the strength of the dipolar interactions. We comprehensively map out this behaviour, and in particular examine the experimental routes towards unstable dynamics, which, in analogy to conventional condensates, may lead to vortex lattice formation. Furthermore, we analyse the centre of mass and breathing modes of a rotating dipol…
We have mapped out a detailed phase diagram that shows the ground state structure of a spin-1 condensate with magnetic dipole-dipole interactions. We show that the interplay between the dipolar and the spin-exchange interactions induces a rich variety of quantum phases that exhibit spontaneous magnetic ordering in the form of intricate spin textures.
We investigate the properties of single vortices and of vortex lattice in a rotating dipolar condensate. We show that vortices in this system possess many novel features induced by the long-range anisotropic dipolar interaction between particles. For example, when the dipoles are polarized along the rotation axis, vortices may display a crater-like structure; when dipoles are polarized orthogonal to the rotation axis, vortex cores takes an elliptical shape and the vortex lattice no longer possesses hexagonal symmetry.
Our recent measurements on the expansion of a chromium dipolar condensate after release from an optical trapping potential are in good agreement with an exact solution of the hydrodynamic equations for dipolar Bose gases. We report here the theoretical method used to interpret the measurement data as well as more details of the experiment and its analysis. The theory reported here is a tool for the investigation of different dynamical situations in time-dependent harmonic traps.
We propose a scheme for the measurement of the s-wave scattering length $a$ of an atom or molecule with significant dipole-dipole interaction with an accuracy at the percent level. The frequencies of the collective oscillations of a Bose-Einstein condensate are shifted by the magnetic dipole interaction. The shift is polarization dependent and proportional to the ratio $ε_{dd}$ of dipolar and s-wave coupling constants. Measuring the differences in the frequencies for different polarization we can extract the value of $ε_{dd}$ and thus measure $a$. We calculate the frequency shifts for a large …
The dynamical stability of dark solitons in dipolar Bose-Einstein condensates is studied. For standard short-range interacting condensates dark solitons are unstable against transverse excitations in two and three dimensions. On the contrary, due to its non local character, the dipolar interaction allows for stable 3D stationary dark solitons, opening a qualitatively novel scenario in nonlinear atom optics. We discuss in detail the conditions to achieve this stability, which demand the use of an additional optical lattice, and the stability regimes.
The physics of vortex lines in dipolar condensates is studied. Due to the nonlocality of the dipolar interaction, the 3D character of the vortex plays a more important role in dipolar gases than in typical short-range interacting ones. In particular, the dipolar interaction significantly affects the stability of the transverse modes of the vortex line. Remarkably, in the presence of a periodic potential along the vortex line, a roton minimum may develop in the spectrum of transverse modes. We discuss the appropriate conditions at which this roton minimum may eventually lead to an instability o…
Weak dipolar effects in atomic Bose-Einstein condensates (BECs) have recently been predicted to develop spin textures. However, observation of these effects requires magnetic field as low as $\sim 10 μ$G for spin-1 alkali BECs, so that they are not washed out by the Zeeman effect. We present a scheme to observe the magnetic dipole-dipole interaction in alkali BECs under a realistic magnetic field of $\sim 100$ mG. Our scheme enables us to extract genuine dipolar effects and should apply also to $^{52}$Cr BECs.
We investigate the quantum phases of polarized dipolar Bosons loaded into a two-dimensional square and three-dimensional cubic optical lattices. We show that the long-range and anisotropic nature of the dipole-dipole interaction induces a rich variety of quantum phases, including the supersolid and striped supersolid phases in 2D lattices, and the layered supersolid phase in 3D lattices.
We study a dipolar boson-fermion mixture in a pancake geometry at absolute zero temperature, generalizing our previous work on the stability of polar condensates and the formation of a density-wave state in cylindrical traps. After examining the dependence of the polar condensate stability on the strength of the fermion-induced interaction, we determine the transition point from a ground-state Gaussian to a hexagonal density-wave state. We use a variational principle to analyze the stability properties of those density-wave state.
We analyze the physics of bright solitons in two-dimensional dipolar Bose-Einstein condensates. These solitons are not possible in short-range interacting gases. In particular, we discuss the necessary conditions for the existence of stable 2D bright solitary waves. The stability of the solutions is studied by means of the analysis of lowest-lying excitations. Additionally, we study the scattering of solitary waves, which contrary to the contact-interacting case, is inelastic, and could lead to fusion of solitary waves. Finally, the experimental possibilities for observability are discussed.
We theoretically propose and numerically realize spin echo in a spinor Bose--Einstein condensate (BEC). We investigate the influence on the spin echo of phase separation of the condensate. The equation of motion of the spin density exhibits two relaxation times. We use two methods to separate the relaxation times and hence demonstrate a technique to reveal magnetic dipole--dipole interactions in spinor BECs.
We consider a spinor condensate of $^{87}$Rb atoms in F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in $m_F=0$ component we find that the system evolves towards a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin mixing contact potential. Our results show that because of a dynamical separation of magnetic components the spin mixing dynamics in $^{87}$Rb condensate is governed by dipolar interaction which pla…
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.
Under many circumstances, the only important two-body interaction between atoms in ultracold dilute atomic vapors is the short-ranged isotropic s-wave collision. Recent studies have shown, however, that situations may arise where the dipolar interaction between atomic magnetic or electric dipole moments can play a significant role. The long-range anisotropic nature of the dipolar interaction greatly enriches the static and dynamic properties of ultracold atoms. In the case of dipolar spinor condensates, the interplay between the dipolar interaction and the spin exchange interaction may lead to…
We investigate the collapse dynamics of a dipolar condensate of 52Cr atoms when the s-wave scattering length characterizing the contact interaction is reduced below a critical value. A complex dynamics, involving an anisotropic, d-wave symmetric explosion of the condensate, is observed. The atom number decreases abruptly during the collapse. We find good agreement between our experimental results and those of a numerical simulation of the three-dimensional Gross-Pitaevskii equation, including contact and dipolar interactions as well as three-body losses. The simulation indicates that the colla…
The non-local non-linearity introduced by the dipole-dipole interaction plays a crucial role in the physics of dipolar Bose-Einstein condensates. In particular, it may distort significantly the stability of straight vortex lines due to the rotonization of the Kelvin-wave spectrum. In this paper we analyze this instability showing that it leads to a second-order-like phase transition from a straight vortex-line into novel helical or snake-like configurations, depending on the dipole orientation.
We report new results for the Thomas-Fermi groundstate and the quadrupolar modes of density oscillations of a spin- polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field is not orientated parallel to a principal axis of a harmonic anisotropic trap.
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 study superfluidity of supersolid phases of dipolar Bose gases in two-dimensional optical lattices. We perform linear stability analyses for the corresponding dipolar Bose-Hubbard model in the hardcore boson limit to show that a supersolid can have stable superflow until the flow velocity reaches a certain critical value. The critical velocity for the supersolid is found to be significantly smaller than that for a conventional superfluid phase. We propose that the critical velocity can be used as a signature to identify the superfluidity of the supersolid phase in experiment.
We analyze theoretically the collective mode dispersion in multi-layer stacks of two dimensional dipolar condensates and find a strong enhancement of the roton instability. We discuss the interplay between the dynamical instability and roton softening for moving condensates. We use our results to analyze the decoherence rate of Bloch oscillations for systems in which the s-wave scattering length is tuned close to zero using Feshbach resonance. Our results are in qualitative agreement with recent experiments of Fattori {\it et al.} on $^{39}$K atoms.
We investigate the time taken for global collapse by a dipolar Bose-Einstein condensate. Two semi-analytical approaches and exact numerical integration of the mean-field dynamics are considered. The semi-analytical approaches are based on a Gaussian ansatz and a Thomas-Fermi solution for the shape of the condensate. The regimes of validity for these two approaches are determined, and their predictions for the collapse time revealed and compared with numerical simulations. The dipolar interactions introduce anisotropy into the collapse dynamics and predominantly lead to collapse in the plane pe…
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 func…
We derive the criteria for the Thomas-Fermi regime of a dipolar Bose-Einstein condensate in cigar, pancake and spherical geometries. This also naturally gives the criteria for the mean-field one- and two-dimensional regimes. Our predictions, including the Thomas-Fermi density profiles, are shown to be in excellent agreement with numerical solutions. Importantly, the anisotropy of the interactions has a profound effect on the Thomas-Fermi/low-dimensional criteria.
