Strong 1D lattices usually lead to unconnected two-dimensional gases. The long-range character of the dipole-dipole interactions leads to a novel scenario where non-overlapping gases at different sites may interact significantly. We show that the excitations of non-overlapping condensates in 1D optical lattices acquire a band-like character, being collectively shared by different sites. In particular, the hybridization of the modes significantly enhances the rotonization of the excitations, and may induce roton-instability. We discuss the observability of this effect in on-going 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.
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…
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 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.
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…
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 …
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 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 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.
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 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…
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…
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.
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.
We report on a study of the spin-1 ferromagnetic Bose-Einstein condensate with magnetic dipole-dipole interactions. By solving the non-local Gross-Pitaevskii equations for this system, we find three ground-state phases. Moreover, we show that a substantial orbital angular momentum accompanied by chiral symmetry breaking emerges spontaneously in a certain parameter regime. We predict that all these phases can be observed in the spin-1 $^{87}$Rb condensate by changing the number of atoms or the trap frequency.
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…
The partially attractive character of the dipole-dipole interaction leads to phonon instability in dipolar condensates, which is followed by collapse in three-dimensional geometries. We show that the nature of this instability is fundamentally different in two-dimensional condensates, due to the dipole-induced stabilization of two-dimensional bright solitons. As a consequence, a transient gas of attractive solitons is formed, and collapse may be avoided. In the presence of an harmonic confinement, the instability leads to transient pattern formation followed by the creation of stable two-dimen…
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.
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…
It is shown that the interface in a two-component Bose-Einstein condensate (BEC) in which one component exhibits a dipole-dipole interaction spontaneously forms patterns similar to those formed in a magnetic liquid subject to a magnetic field. A hexagonal pattern, hysteretic behavior, and soliton-like structure are numerically demonstrated. A phenomenon similar to the labyrinthine instability is also found. These phenomena may be realized using a 52Cr BEC. The periodic density modulation in the superfluid ground state offers evidence of supersolidity.
We study the stability of singly- and doubly-quantized vortex states of harmonically trapped dipolar Bose-Einstein Condensates (BECs) by calculating the low-lying excitations of these condensates. We map the dynamical stability of these vortices as functions of the dipole-dipole interaction strength and trap geometry by finding where their excitations have purely real energy eigenvalues. In contrast to BECs with purely contact interactions, we find that dipolar BECs in singly-quantized vortex states go unstable to modes with an increasing number of angular and radial nodes for more oblate trap…
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.
The quantum self-trapping phenomenon of a Bose-Einstein condensate (BEC) represents a remarkable nonlinear effect of wide interest. By considering a purely dipolar BEC in a double-well potential, we study how the dipole orientation affects the ground state structure and the transition between self-trapping and Josephson oscillation in dynamics. Three-dimensional numerical results and an effective two-mode model demonstrate that the onset of self-trapping of a dipolar BEC can be radically modified by the dipole orientation. We also analyze the failure of the two-mode model in predicting the rat…
We study the semiclassical dynamics of a spinor condensate with the magnetic dipole-dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depends greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin exchange and dipole-dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and Macroscopic Quantum Self Trapping. Simple estimate demonstrates that these effects are acces…
We study the macroscopic quantum tunneling of magnetization of the F=1 spinor condensate interacting through dipole-dipole interaction with an external magnetic field applied along the longitudinal or transverse direction. We show that the ground state energy and the effective magnetic moment of the system exhibit an interesting macroscopic quantum oscillation phenomenon originating from the oscillating dependence of thermodynamic properties of the system on the vacuum angle. Tunneling between two degenerate minima are analyzed by means of an effective potential method and the periodic instant…
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 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 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 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 to the create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can b…
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.
