We examine the superfluid and collapse instabilities of a quasi two-dimensional gas of dipolar fermions aligned by an orientable external field. It is shown that the interplay between the anisotropy of the dipolar interaction, the geometry of the system, and the p-wave symmetry of the superfluid order parameter means that the effective interaction for pairing can be made very large without the system collapsing. This leads to a broad region in the phase diagram where the system forms a stable superfluid. Analyzing the superfluid transition at finite temperatures, we calculate the Berezinskii--Kosterlitz--Thouless temperature as a function of the dipole angle.
We present a concise review of the physics of ultra-cold dipolar gases, based mainly on the theoretical developments in our own group. First, we discuss shortly weakly interacting ultra-cold trapped dipolar gases. Dipolar Bose-Einstein condensates exhibit non-standard instabilities and the physics of both Bose and Fermi dipolar gases depends on the trap geometry. We focus then the second part of the paper on strongly correlated dipolar gases and discuss ultra-cold dipolar gases in optical lattices. Such gases exhibit a spectacular richness of quantum phases and metastable states, which may per…
We analyze the physics of cold dipolar gases in quasi one-dimensional geometries, showing that the confinement-induced scattering resonances produced by the transversal trapping are crucially affected by the dipole-dipole interaction. As a consequence, the dipolar interaction may drastically change the properties of quasi-1D dipolar condensates, even for situations in which the dipolar interaction would be completely overwhelmed by the short-range interactions in a 3D environment.
We investigate the stability and the free expansion of a trapped dipolar Fermi gas. We show that stabilizing the system relying on tuning the trap geometry is generally inefficient. We further show that the expanded density profile always gets stretched along the attractive direction of dipolar interaction. We also point out that by switching off the dipolar interaction simultaneously with the trapping potential, the deformation of momentum distribution can be directly observed.
We investigate dynamical properties of a one-component Fermi gas with dipole-dipole interaction between particles. Using a variational function based on the Thomas-Fermi density distribution in phase space representation, the total energy is described by a function of deformation parameters in both real and momentum space. Various thermodynamic quantities of a uniform dipolar Fermi gas are derived, and then instability of this system is discussed. For a trapped dipolar Fermi gas, the collective oscillation frequencies are derived with the energy-weighted sum rule method. The frequencies for th…
We consider a system of quantum degenerate spin polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the Fermi gas in phase space and use it to examine the stability of the system. We emphasize the important roles played by the Fock exchange term of the dipolar interaction which results in a non-spherical Fermi surface.
We report on experiments exploring the physics of dipolar quantum gases using a Chromium Bose-Einstein condensate (BEC). By means of a Feshbach resonance, it is possible to reduce the effects of short range interactions and reach a regime where the physics is governed by the long-range, anisotropic dipole-dipole interaction between the large ($6 μ_{\rm B}$) magnetic moments of Chromium atoms. Several dramatic effects of the dipolar interaction are observed: the usual inversion of ellipticity of the condensate during time-of flight is inhibited, the stability of the dipolar gas depends strongly…
We study the equilibrium properties of dipolar Bose and Fermi gases at finite temperatures. We recently developed a variational ansatz for the phase-space distribution function of a dipolar Fermi gas at finite temperatures. We extend the variational formalism to a Bose gas and discuss the effect of dipolar interactions with different statistics on the thermal equilibrium, with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio and the dipole moment. In addition, we discuss how deformation in both real a…
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 report on the experimental observation of the dipolar collapse of a quantum gas which sets in when we reduce the contact interaction below some critical value using a Feshbach resonance. Due to the anisotropy of the dipole-dipole interaction, the stability of a dipolar Bose-Einstein condensate depends not only on the strength of the contact interaction, but also on the trapping geometry. We investigate the stability diagram and find good agreement with a universal stability threshold arising from a simple theoretical model. Using a pancake-shaped trap with the dipoles oriented along the sho…
Possible signatures of a super-Tonks-Girardeau gas in bosonic systems of trapped quasi-one-dimensional dipoles are discussed at zero temperature. We provide estimation of the frequency of the lowest compressional mode and compare it to analytical results derived using harmonic approach in the high density regime. We construct an exact mapping of the ground-state wave function of one-dimensional dipolar system of bosons, fermions and Bose-Fermi mixture and conclude that local properties and energy are the same at zero temperature. A question of to which extent the dipolar potential can be treat…
We study the equilibrium properties of a dipolar Fermi gas at finite temperatures. We introduce a variational ansatz for the phase-space distribution function that can describe the deformation in both real and momentum space. The effect of dipole--dipole interactions on the thermal equilibrium is discussed with particular emphasis on the deformation in momentum space. We examine the stability of the system by varying the temperature, trap aspect ratio, and the dipole moment. In addition, we discuss how the deformation in both real and momentum space can be observed in the high-temperature regi…
We use a simple model to describe the nonlinear dynamics of a dense two dimensional dipolar exciton gas. The model predicts an initial fast expansion due to dipole-dipole pressure, followed by a much slower diffusion. The model is in very good agreement with recent experimental results. We show that the dipole pressure induced expansion strongly constrains the time available for achieving and observing Bose-Einstein quantum statistical effects, indicating a need for spatial exciton traps. We also suggest that nonlinear ballistic exciton transport due to the strong internal dipole pressure is r…
Using an ansatz wave function for the ground state of rotating two-dimensional dipolar fermions, which occupy only partially the lowest Landau level, we study the correlation energy and elastic properties of the Wigner crystal of rotating dipolar Fermi gases. From a simple Hartree-Fock approach, we show that the correlation energy of a particle crystal is lower and higher than the correlation energy of a hole crystal for filling factors v<1/2 and v>1/2, respectively. Furthermore we find that the shear moduli of these dipolar crystals have a nonmonotonic behavior as a function of the filling fa…
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 the framework of the semiclassical theory, we investigate the equilibrium-state properties of a spin polarized dipolar Fermi gas through full numerical calculation. We show that the Fermi surfaces in both real and momentum spaces are stretched along the attractive direction of dipolar interaction. We further verify that the deformed Fermi surfaces can be well approximated by ellipsoids. In addition, the deformation parameters slightly depend on the local real- and momentum-space densities. We also study the interaction strength dependence of the energy and real- and momentum-space densit…
Ultracold dipolar Fermi gases represent relatively unexplored, strongly correlated systems arising from long-range and anisotropic interactions. We demonstrate the possibility of a spontaneous symmetry breaking biaxial phase in these systems, which may be realized in, e.g., gases of ultracold polar molecules or strongly magnetic atoms. This biaxial nematic phase is manifest in a spontaneous distortion of the Fermi surface perpendicular to the axis of polarization. We describe these dipolar interaction induced phases using Landau Fermi liquid theory.
We calculate the ground-state properties of fermionic dipolar atoms or molecules in a one-dimensional double-tube potential by using the Luttinger liquid theory and the density matrix renormalization-group calculation. When the external field is applied near a magic angle with respect to the double-tube plane, the long-ranged dipolar interaction can generate a spontaneous correlation between fermions in different tubes, even when the bare intertube tunneling rate is negligibly small. Such interaction-induced correlation strongly enhances the contrast of the interference fringes and therefore c…
We calculate the excitation modes of a 1D dipolar quantum gas confined in a harmonic trap with frequency $ω_0$ and predict how the frequency of the breathing n=2 mode characterizes the interaction strength evolving from the Tonks-Girardeau value $ω_2=2ω_0$ to the quasi-ordered, super-strongly interacting value $ω_2=\sqrt{5}ω_0$. Our predictions are obtained within a hydrodynamic Luttinger-Liquid theory after applying the Local Density Approximation to the equation of state for the homogeneous dipolar gas, which are in turn determined from Reptation Quantum Monte Carlo simulations. They are sho…
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 investigate the physics of dipolar bosons in a two dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical lattice presents novel quantum phases, like checkerboard and supersolid phases. In this paper, we consider the properties of the system beyond its ground state, finding that it is characterised by a multitude of almost degenerate metastable states, often competing with the ground state. This makes dipolar bosons in a lattice similar to a disordered system and open…
We describe a simple model of fermions in quasi-one dimension that features interaction induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on …
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.
It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realisation of this soft quantum matter physics in an ultra-cold gas. It uses optical lattices and dipolar interactions to realise a particularly simple model. Our analysis reveals a rich phase diagram featuring a meta-nematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes); and a crystalline, `checkerboard' phase.
The ground state and structure of a one-dimensional Bose gas with dipolar repulsions is investigated at zero temperature by a combined Reptation Quantum Monte Carlo (RQMC) and bosonization approach. A non trivial Luttinger-liquid behavior emerges in a wide range of intermediate densities, evolving into a Tonks-Girardeau gas at low density and into a classical quasi-ordered state at high density. The density dependence of the Luttinger exponent is extracted from the numerical data, providing analytical predictions for observable quantities, such as the structure factor and the momentum distribu…
