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 the monopole and quadrupole modes are calculated, and softening against collapse is shown as the dipolar strength approaches the critical value. Finally, we investigate the effects of the dipolar interaction on the expansion dynamics of the Fermi gas and show how the dipolar effects manifest in an expanded cloud.
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.
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 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 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…
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 analyze the Mott-insulator phases of dipolar bosonic gases placed in neighboring but unconnected 1D traps. Whereas for short-range interactions the 1D systems are independent, the non-local dipole-dipole interaction induces a direct Mott-insulator to pair-superfluid transition which significantly modifies the boundaries of the lowest Mott-insulator phases. The lowest boundary of the lowest Mott regions becomes progressively constant as a function of the hopping rate, eventually inverting its slope, leading to a re-entrant configuration which is retained in 2D. We discuss the consequences of…
We evaluate the dipolar oscillations of a harmonically trapped fermion gas containing thermal bosonic impurities as a function of the anisotropy of the trap, from the numerical solution of the Vlasov-Landau equations for the one-body phase-space distribution functions. Starting from a situation in which the two components of the gaseous mixture perform almost independent oscillations inside a spherical trap, we demonstrate that different collision behaviors arise for oscillations in different directions as the trap is deformed into an elongated cigar-like shape. An increase in the anisotropy o…
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 present a detailed study of the BCS pairing transition in a trapped polarized dipolar Fermi gas. In the case of a shallow nearly spherical trap, we find the decrease of the transition temperature as a function of the trap aspect ratio and predict the existence of the optimal trap geometry. The latter corresponds to the highest critical temperature of the BCS transition for a given number of particles. We also derive the phase diagram for an ultracold trapped dipolar Fermi gases in the situation, where the trap frequencies can be of the order of the critical temperature of the BCS transition…
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.
Ultra-cold atomic systems provide a new setting where to investigate the role of long-range interactions. In this paper we will review the basics features of those physical systems, in particular focusing on the case of Chromium atoms. On the experimental side, we report on the observation of dipolar effects in the expansion dynamics of a Chromium Bose-Einstein condensate. By using a Feshbach resonance, the scattering length characterising the contact interaction can be strongly reduced, thus increasing the relative effect of the dipole-dipole interaction. Such experiments make Chromium atoms …
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 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 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…
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 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…
We study the ground state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits novel transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the…
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 determine the excitation spectrum of a bosonic dipolar quantum gas in a one-dimensional geometry, from the dynamical density-density correlation functions simulated by means of Reptation Quantum Monte Carlo techniques. The excitation energy is always vanishing at the first vector of the reciprocal lattice in the whole crossover from the liquid-like at low density to the quasi-ordered state at high density, demonstrating the absence of a roton minimum. Gaps at higher reciprocal lattice vectors are seen to progressively close with increasing density, while the quantum state evolves into a qua…
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.
Particles with repulsive power-law interactions undergo a transition from a single to a double chain (zigzag) by decreasing the confinement in the transverse direction. We theoretically characterize this transition when the particles are classical dipoles, polarized perpendicularly to the plane in which the motion occurs, and argue that this transition is of first order, even though weakly. The nature of the transition is determined by the coupling between transverse and axial modes of the chain and contrasts with the behaviour found in Coulomb systems, where the linear-zigzag transition is co…
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…
By combining theory and experiments, we demonstrate that dipolar quantum gases of both $^{166}$Er and $^{164}$Dy support a state with supersolid properties, where a spontaneous density modulation and a global phase coherence coexist. This paradoxical state occurs in a well defined parameter range, separating the phases of a regular Bose-Einstein condensate and of an insulating droplet array, and is rooted in the roton mode softening, on the one side, and in the stabilization driven by quantum fluctuations, on the other side. Here, we identify the parameter regime for each of the three phases. …
The concept of a roton, a special kind of elementary excitation, forming a minimum of energy at finite momentum, has been essential to understand the properties of superfluid $^4$He. In quantum liquids, rotons arise from the strong interparticle interactions, whose microscopic description remains debated. In the realm of highly-controllable quantum gases, a roton mode has been predicted to emerge due to magnetic dipole-dipole interactions despite of their weakly-interacting character. This prospect has raised considerable interest; yet roton modes in dipolar quantum gases have remained elusive…
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.
