We determine the quantum ground state of dipolar bosons in a quasi-one-dimensional optical lattice and interacting via $s$-wave scattering. The Hamiltonian is an extended Bose-Hubbard model which includes hopping terms due to the interactions. We identify the parameter regime for which the coefficients of the interaction-induced hopping terms become negative. For these parameters we numerically determine the phase diagram for a canonical ensemble and by means of density matrix renormalization group. We show that at sufficiently large values of the dipolar strength there is a quantum interference between the tunneling due to single-particle effects and the one due to the interactions. Because of this phenomenon, incompressible phases appear at relatively large values of the single-particle tunneling rates. This quantum interference cuts the phase diagram into two different, disconnected superfluid phases. In particular, at vanishing kinetic energy, the phase is always superfluid with a staggered superfluid order parameter. These dynamics emerge from quantum interference phenomena between quantum fluctuations and interactions and shed light into their role in determining the thermodynamic properties of quantum matter.
We present a superfluid theory of a polarized dipolar Fermi gas. For two dipolar molecules each of which consists of two atoms with positive charge and negative charge, we derive an effective dipole-dipole pairing interaction. Using this pairing interaction, we show that the resulting BCS gap equation is not suffered from the well-known ultraviolet divergence, so that one can quantitatively predict superfluid properties of a dipolar Fermi gas. Using this cutoff-free superfluid theory, we examine the symmetry of the superfluid order parameter at T=0. We also discuss the deformation of the Fermi…
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.
A key manifestation of superfluidity in liquids and gases is a reduction of the moment of inertia under slow rotations. Non-classical rotational effects have been searched for a long time also for the elusive supersolid phase of matter, in which superfluidity coexists with a lattice structure. Here we show that the recently discovered supersolid phase in dipolar quantum gases features a reduced moment of inertia. We study a peculiar rotational oscillation mode in a harmonic potential, the scissors mode, already employed for superfluids. From the measured moment of inertia, we infer a superflui…
Weyl superconductivity or superfluidity, a fascinating topological state of matter, features novel phenomena such as emergent Weyl fermionic excitations and anomalies. Here we report that an anisotropic Weyl superfluid state can arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial ingredient of our model is a rotating external field that generates a direction-dependent two-body effective attraction. Experimental signatures are predicted for cold gases in radio-frequency spectroscopy. The finite temperature phase diagram of this system is studied and the transition tempe…
Experiments on dipolar Bose-Einstein condensates have recently reported the observation of supersolidity. Although quantized vortices constitute a key probe of superfluidity, their observability in dipolar supersolids is largely prevented by the strong density depletion caused by the formation of droplets. We present a novel approach to the nucleation of vortices and their observation, based on the quenching of the s-wave scattering length across the superfluid-supersolid transition. Starting from a slowly rotating, vortex-free, configuration in the superfluid phase, we predict vortex nucleati…
We develop a simple numerical method that allows us to calculate the Bardeen-Cooper-Schriefer (BCS) superfluid transition temperature (Tc) precisely for any interaction potential. We apply it to a polarised, ultracold Fermi gas with long-range, anisotropic, dipolar interactions and include the effects of anisotropic exchange interactions. We pay particular attention to the short-range behaviour of dipolar gasses and re-examine current renormalisation methods. In particular, we find that dimerisation of both atoms and molecules significantly hampers the formation of a superfluid. The end result…
We consider the ground state of a bilayer system of dipolar bosons, where dipoles are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix, and the superfluid response as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from a single-particle to a pair superfluid. The single-particle superfluid i…
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 …
We analyze the spin dynamics of an out-of-equilibrium large spin dipolar atomic Bose gas in an optical lattice. We observe a smooth crossover from a complex oscillatory behavior to an exponential behavior throughout the Mott to superfluid transition. While both of these regimes are well described by our theoretical models, we provide data in the intermediate regime where dipolar interactions, contact interactions, and super-exchange mechanisms compete. In this strongly correlated regime, spin dynamics and transport are coupled, which challenges theoretical models for quantum magnetism.
We systematically investigate the zero temperature phase diagram of bosons interacting via dipolar interactions in three dimensions in free space via path integral Monte Carlo simulations with few hundreds of particles and periodic boundary conditions based on the worm algorithm. Upon increasing the strength of the dipolar interaction and at sufficiently high densities we find a wide region where filaments are stabilized along the direction of the external field. Most interestingly by computing the superfluid fraction we conclude that superfluidity is anisotropic and is greatly suppressed alon…
We investigate the superfluid properties of a dipolar Bose-Einstein condensate (BEC) in a fully three-dimensional trap. Specifically, we calculate a superfluid critical velocity for this system by applying the Landau criterion to its discrete quasiparticle spectrum. We test this critical velocity by direct numerical simulation of condensate depletion as a blue-detuned laser moves through the condensate. In both cases, the presence of the roton in the spectrum serves to lower the critical velocity beyond a critical particle number. Since the shape of the dispersion, and hence the roton minimum,…
Crossed electric and magnetic fields influence dipolar neutral particles in the same way as the magnetic field influences charged particles. The effect of crossed fields is proportional to the dipole moment of the particle (inherent or induced). We show that this effect is quite spectacular in a multilayer system of polar molecules. In this system molecules may bind in chains. At low temperature the gas of chains becomes the superfluid one. The crossed fields then induce vortices in the superfluid gas of chains. The density of vortices is proportional to the number of particles in the chain. T…
We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional (q2D) geometry. In particular, we allow for the dipole polarization to have some non-zero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion for propagation of quasiparticles. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the prob…
Recent breakthrough experiments on dipolar condensates have reported the creation of supersolids, including two-dimensional arrays of quantum droplets. Droplet arrays are, however, not the only possible non-trivial density arrangement resulting from the interplay of mean-field instability and quantum stabilization. Several other possible density patterns may occur in trapped condensates at higher densities, including the so-called honeycomb supersolid, a phase that exists, as it is also the case of a triangular droplet supersolid, in the thermodynamic limit. We show that compared to droplet su…
The chiral p-wave (p_x \pm ip_y) superfluid has attracted significant attention in recent years, mainly because its vortex core supports a Majorana fermion which, due to its non-Abelian statistics, can be explored for implementing topological quantum computation. Mixing dipolar bosons with fermions in quasi-two-dimensional (2D) space offers the opportunity to use the roton minimum as a tool for engineering the phonon-induced attractive interaction between fermions. We study, within the Hartree-Fock-Bogoliubov approach, the p-wave superfluid pairings in a quasi-2D dipolar Bose-Fermi mixture. We…
We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave $(sl)$, extended s-wave $(se)$, d-wave $(d)$ or time-reversal-symmetry breaking $(sl + se \pm id)$-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that $(sl + se)$-wa…
We analyse the coexistence of superfluid and density wave (stripe) order in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. Remarkably, the anisotropic nature of the dipolar interaction allows for such a coexistence in a large region of the zero temperature phase diagram. In this region, the repulsive part of the interaction drives the stripe formation and the attractive part induces the pairing, resulting in a supersolid with $p$-wave Cooper pairs aligned along the stripes. From a momentum space perspective, the stability of the supersolid phase is due to the fac…
We study ultra-cold dipolar excitons confined in a 10$μ$m trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons at pure thermodynamic equilibrium. In this regime we show that, below a critical temperature of about $1$ Kelvin, a superfluid forms in the inner region of the trap at a local exciton density $n \sim 2-3 \, 10^{10} \text{cm}^{-2}$, encircled by a more dilute and normal component in the outer rim of the trap. Remarkably, this spatial arrangement correlates directly with the concentration of defects …
We analyze the nature of quantum phase transition to a superfluid state of flexible chains in a gas of polar bosonic molecules confined in a stack of $N$ identical 1d ("cigar" type) optical lattice layers and polarized perpendicularly to the layers. Monte Carlo simulations within the $J$-current model show that, in the absence of the inter-tube tunneling, the transition to the $N$-layered superfluid is in the Berezinskii-Kosterlitz-Thouless universality class in the one-particle density matrix channel. The inter-layer tunneling changes it to the $q=N$ 2d Potts universality. The low energy fiel…
In this paper, we study phase diagrams of dipolar hard-core boson gases on the honeycomb lattice. The system is described by the Haldane-Bose-Hubbard model with complex hopping amplitudes and the nearest neighbor repulsion. By using the slave-particle representation of the hard-core bosons and also the path-integral quantum Monte-Carlo simulations, we investigate the system and to show that the systems have a rich phase diagram. There are Mott, superfluid, chiral superfluid, and sublattice chiral superfluid phases as well as the density-wave phase. We also found that there exists a coexisting …
Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；L. D. Landau Institute for Theoretical Physics（列夫·朗道理论物理研究所）；Laboratory for Condensed Matter Physics, HSE University（高等经济大学凝聚态物理实验室）；Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；Van der Waals–Zeeman Institute, Institute of Physics, University of Amsterdam（阿姆斯特丹大学范德瓦尔斯-泽曼凝聚态物理研究所）
We use the Bogoliubov theory of Bose-Einstein condensation to study the properties of dipolar particles (atoms or molecules) confined in a uniform two-dimensional geometry at zero temperature. We find equilibrium solutions to the dipolar Gross-Pitaevskii equation and the Bogoliubov-de Gennes equations. Using these solutions we study the effects of quantum fluctuations in the system, particularly focussing on the instability point, where the roton feature in the excitation spectrum touches zero. Specifically, we look at the behaviour of the noncondensate density, the phase fluctuations, and the…
We investigate a system of two- and three-body constrained dipolar bosons in a pair of one-dimensional optical lattices coupled to each other by the non-local dipole-dipole interactions. Assuming attractive dipole-dipole interactions, we obtain the ground state phase diagram of the system by employing the cluster mean-field theory. The competition between the repulsive on-site and attractive nearest-neighbor interactions between the chains yields three kinds of superfluids; namely the trimer superfluid, pair superfluid and the usual single particle superfluid along with the insulating Mott pha…
Dynamical signatures of superfluidity and shear rigidity in different phases of a dipolar Bose-Einstein condensate
Indian Institute of Technology Gandhinagar（印度理工学院甘地纳加尔分校）；Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）；Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道）
We study the superfluid properties of a system of fully polarized dipolar bosons moving in the $xy$ plane. We focus on the general case where the polarization field forms an arbitrary angle $α$ with respect to the $z$ axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite large-distance asymptotic value in the $s$-wave component of the one-bo…
We construct a fully self-consistent Hartree-Fock-Bogoliubov theory that describes a spinless Fermi gas with long-range interaction. We apply this theory to a system of uniform dipolar fermionic polar molecules, which has attracted much attention recently, due to rapid experimental progress in achieving such systems. By calculating the anisotropic superfluid order parameter, and the critical temperature $T_{c}$, we show that, "hign $T_c$" superfluid can be achieved with a quite modest value of interaction strength for polar molecules. In addition, we also show that the presence of the Fock exc…
We investigate topological supersolidity of dipolar Fermi gases in a spin-dependent 2D optical lattice. Numerical results show that the topological supersolid states can be synthesized via the combination of topological superfluid states with the stripe order, where the topological superfluid states generated with dipolar interaction possess the $Δ_{x}+iΔ_{y}$ order, and it is of D class topological classification. By adjusting the ratio between hopping amplitude $t_{x}/t_{y}$ and interaction strength $U$ with dipole orientation $ϕ\approx \fracπ{4}$, the system will undergo phase transitions a…
We examine density ordered and superfluid phases of fermionic dipoles in a two-dimensional square lattice at non-zero temperature. The critical temperature of the density ordered phases is determined and is shown to be proportional to the coupling strength for strong coupling. We calculate the superfluid fraction and demonstrate that the Berezinskii-Kosterlitz-Thouless transition temperature of the superfluid phase is proportional to the hopping matrix element in the strong coupling limit. We finally analyze the effects of an external harmonic trapping potential.
We present transport measurements on a dipolar superfluid using a Bose-Einstein condensate of Dy-162 with strong magnetic dipole-dipole interactions. By moving an attractive laser beam through the condensate we observe an anisotropy in superfluid flow. This observation is compatible with an anisotropic critical velocity for the breakdown of dissipationless flow, which, in the spirit of the Landau criterion, can directly be connected to the anisotropy of the underlying dipolar excitation spectrum. In addition, the heating rate above this critical velocity reflects the same anisotropy. Our obser…
We consider dipolar fermions in a two-dimensional square lattice and a harmonic trapping potential. The anisotropy of the dipolar interaction combined with the lattice leads to transitions between phases with density order of different symmetries. We show that the attractive part of the dipolar interaction results in a superfluid phase which is suppressed by density order. The trapping potential is demonstrated to make the different phases co-exist, forming ring and island structures. The phases with density and superfluid order can overlap forming regions with supersolid order.
Low temperature properties of harmonically confined two-dimensional assemblies of dipolar bosons are systematically investigated by Monte Carlo simulations. Calculations carried out for different numbers of particles and strengths of the confining potential yield evidence of a quantum phase transition from a superfluid to a crystal-like phase, consistently with what is observed in the ho- mogeneous system. It is found that the crystal phase nucleates in the center of the trap, as the density increases. Bose-Einstein condensation vanishes at T = 0 upon entering the crystalline phase, concurrent…
We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero soun…
We present results of computer simulations at low temperature of a two-dimensional system of dipolar bosons, with dipole moments aligned at an arbitrary angle with respect to the direction perpendicular to the plane. The phase diagram includes a homogeneous superfluid phase, as well as triangular and striped crystalline phases, as the particle density and the tilt angle are varied. In the striped solid, no phase coherence among stripes and consequently no ``supersolid" phase is found, in disagreement with recent theoretical predictions.
We investigate the rotational properties of a dipolar Bose-Einstein condensate trapped in a toroidal geometry. Studying the ground states in the rotating frame and at fixed angular momenta, we observe that the condensate acts in distinctly different ways depending on whether it is in the superfluid or in the supersolid phase. We find that intriguingly, the toroidal dipolar condensate can support a supersolid persistent current which occurs at a local minimum in the ground state energy as a function of angular momentum, where the state has a vortex solution in the superfluid component of the co…
We discuss a model of dipolar bosons trapped in a weakly coupled planar array of one-dimensional tubes. We consider the situation where the dipolar moments are aligned by an external field, and find a rich phase diagram as a function of the angle of this field exhibiting quantum phase transitions between solid, superfluid and supersolid phases. In the low energy limit, the model turns out to be identical to one describing quasi-one-dimensional superconductivity in condensed matter systems. This opens the possibility of using bosons as a quantum analogue simulator of electronic systems, a scena…
In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseduospins in the presence of an AC electric field. When trapped in a 2D optical lattice, such a dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid st…
We study by first principle computer simulations the low temperature phase diagram of bosonic dipolar gases in a bilayer geometry, as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We observe four distinct phases, namely paired and decoupled superfluids, as well as a crystal of dimers and one consisting of two aligned crystalline layers. A direct quantum phase transition from a dimer crystal to two independent superfluids is observed in a relatively wide range of parameters. No supersolid phase is predicted for this system.
Supersolid phases as a result of a coexistence of superfluid and density ordered checkerboard phases are predicted to appear in ultracold Fermi molecules confined in a bilayer array of two-dimensional square optical lattices. We demonstrate the existence of these phases within the inhomogeneous mean-field approach. In particular, we show that tuning the interlayer separation distance at a fixed value of the chemical potential produces different fractions of superfluid, density ordered, and supersolid phases.
Vortices are expected to exist in a supersolid but experimentally their detection can be difficult because the vortex cores are localized at positions where the local density is very low. We address here this problem by performing numerical simulations of a dipolar Bose-Einstein Condensate (BEC) in a pancake confinement at $T=0$ K and study the effect of quantized vorticity on the phases that can be realized depending upon the ratio between dipolar and short-range interaction. By increasing this ratio the system undergoes a spontaneous density modulation in the form of an ordered arrangement o…
We study the zero temperature phase diagram of an imbalanced bilayer of dipolar fermions. We consider perpendicularly aligned identical dipoles in two layers and investigate the effect of population imbalance on the ground state phase at different layer spacings and average densities. The attractive part of the interlayer interaction could lead to the BEC-BCS crossover and the Fermi surface mismatch between two layers results in interesting uniform and nonuniform superfluid phases, which we have investigated here using the BCS mean-field theory together with the superfluid-mass density criteri…
We investigate the properties of a three-dimensional homogeneous dipolar Bose gas in a weak random potential with a Gaussian correlation function at finite temperature. Using the Bogoliubov theory (beyond the mean field), we calculate the superfluid and the condensate fractions in terms of the interaction strength on the one hand and in terms of the width and the strength of the disorder on the other. The influence of the disordered potential on the second order correlation function, the ground state energy and the chemical potential is also analyzed. We find that for fixed strength and correl…
We show that the He-McKellar-Wilkens effect can induce a persistent flow in a Bose-Einstein condensate of polar molecules confined in a toroidal trap, with the dipolar interaction mediated via an electric dipole moment. For Bose-Einstein condensates of atoms with a magnetic dipole moment, we show that although it is theoretically possible to induce persistent flow via the Aharonov-Casher effect, the strength of electric field required is prohibitive. We also outline an experimental geometry tailored specifically for observing the He-McKellar-Wilkens effect in toroidally-trapped condensates.
Ultracold gases offer an unprecedented opportunity to engineer disorder and interactions in a controlled manner. In an effort to understand the interplay between disorder, dipolar interaction and quantum degeneracy, we study two-dimensional hard-core dipolar lattice bosons in the presence of on-site bound disorder. Our results are based on large-scale path-integral quantum Monte Carlo simulations by the Worm algorithm. We study the ground state phase diagram at fixed half-integer filling factor for which the clean system is either a superfluid at lower dipolar interaction strength or a checker…
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.
Distintictive features of supersolids show up in their rotational properties. We calculate the moment of inertia of a harmonically trapped dipolar Bose-Einstein condensed gas as a function of the tunable scattering length parameter, providing the transition from the (fully) superfluid to the supersolid phase and eventually to an incoherent crystal of self-bound droplets. The transition from the superfluid to the supersolid phase is characterized by a jump in the moment on inertia, revealing its first order nature. In the case of elongated trapping in the plane of rotation we show that the the …
We rigorously analyze the low-temperature properties of homogeneous three-dimensional two-component Bose mixture with dipole-dipole interaction. For such a system the effective hydrodynamic action that governs the behavior of low-energy excitations is derived. The infrared structure of the exact single-particle Green's functions is obtained in terms of macroscopic parameters, namely the inverse compressibility and the superfluid density matrices. Within one-loop approximation we calculate the anisotropic superfluid and condensate densities and give the beyond mean-field stability condition for…
We study the superfluidity of single component dipolar Fermi gases in three dimensions within a pairing fluctuation theory. The transition temperature $T_{c}$ for the dominant $p_z$ wave superfluidity exhibits a remarkable re-entrant behavior as a function of the pairing strength induced by the dipole-dipole interaction (DDI), which leads to an anisotropic pair dispersion. The anisotropy and the long range nature of the DDI cause $T_c$ to vanish for a narrow range of intermediate interaction strengths, where a pair density wave state emerges as the ground state. The superfluid density and ther…
In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological $p_{x}+ip_{y}$ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a 2D square optical lattice with this attractive interaction at low temperatures. The $p_{x}+ip_{y}$ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. In the weak-coupling limit, the p-wave superflui…
