Using a combination of results from exact mappings and from mean-field theory we explore the phase diagram of quasi-one-dimensional systems of identical fermions with attractive dipolar interactions. We demonstrate that at low density these systems provide a realization of a single-component one-dimensional Fermi gas with a generalized contact interaction. Using an exact duality between one-dimensional Fermi and Bose gases, we show that when the dipole moment is strong enough, bound many-body states exist, and we calculate the critical coupling strength for the emergence of these states. At higher densities, the Hartree-Fock approximation is accurate, and by combining the two approaches we determine the structure of the phase diagram. The many-body bound states should be accessible in future experiments with ultracold polar molecules.
We study the scissors modes of dipolar boson and fermion gases trapped in a spherically symmetric potential. We use the harmonic oscillator states to solve the time-dependent Gross-Pitaevskii equation for bosons and the time-dependent Hartree-Fock equation for fermions. It is pointed out that the scissors modes of bosons and fermions can be of quite different nature.
We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed by a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are considered all to be perpendicular to the plane, turning the dipolar potential in a purely repulsive and isotropic model. Our analysis is carried out by using the diffusion Monte Carlo method which allows for an exact solution to the many-body problem within some statistical noise. Our results show that the miscibility between the two specie…
The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the Schrödinger equation. In the present study we employ different Monte Carlo methods, that are stochastic techniques that allow to find numerical solutions to it.
This article reviews the recent theoretical and experimental advances in the study of ultracold gases made of bosonic particles interacting via the long-range, anisotropic dipole-dipole interaction, in addition to the short-range and isotropic contact interaction usually at work in ultracold gases. The specific properties emerging from the dipolar interaction are emphasized, from the mean-field regime valid for dilute Bose-Einstein condensates, to the strongly correlated regimes reached for dipolar bosons in optical lattices.
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.
We consider two separated pancake-shaped trapped gases interacting with a dipolar (either magnetic or electric) force. We study how the center of mass motion propagates from one cloud to the other as a consequence of the long-range nature of the interaction. The corresponding dynamics is fixed by the frequency difference between the in-phase and the out-of-phase center of mass modes of the two clouds, whose dependence on the dipolar interaction strength and the cloud separation is explicitly investigated. We discuss Fermi gases in the degenerate as well as in the classical limit and comment on…
We study the propagation of sound in a homogeneous dipolar gas at zero temperature, known as zero sound. We find that undamped sound propagation is possible only in a range of solid angles around the direction of polarization of the dipoles. Above a critical dipole moment, we find an unstable mode, by which the gas collapses locally perpendicular to the dipoles' direction.
We investigate the phase diagrams of two-dimensional lattice dipole systems with variable geometry. For bipartite square and triangular lattices with tunable vertical sublattice separation, we find rich phase diagrams featuring a sequence of easy-plane magnetically ordered phases separated by incommensurate spin-wave states.
We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born approximation and assuming purely dipolar interactions, we find that the second-order virial coefficient for both bosons and fermions depends quadratically on the dipole length and is negative at high temperature, indicating that to lowest order in the dipole-dipole interactions the dipolar single-component quantum gases are repulsive. If the $s$-wave scatter…
We develop a practical Hartree-Fock theory for trapped Bose and Fermi gases that interact with dipole-dipole interactions. This theory is applicable at zero and finite temperature. Our approach is based on the introduction of local momentum distortion fields that characterize the exchange effects in terms of a local effective potential. We validate our theory against existing theories, finding excellent agreement with full Hartree-Fock calculations.
Trapped degenerate dipolar Bose and Fermi gases of cylindrical symmetry with the polarization vector along the symmetry axis are only stable for the strength of dipolar interaction below a critical value. In the case of bosons, the stability of such a dipolar Bose-Einstein condensate (BEC) is investigated for different strengths of contact and dipolar interactions using variational approximation and numerical solution of a mean-field model. In the disk shape, with the polarization vector perpendicular to the plane of the disk, the atoms experience an overall dipolar repulsion and this fact sho…
We develop a non-perturbative theoretical framework to treat collisions with generic anisotropic interactions in quasi-one-dimensional geometries. Our method avoids the limitations of pseudopotential theory allowing to include accurately long-range anisotropic interactions. Analyzing ultracold dipolar collisions in a harmonic waveguide we predict dipolar confinement-induced resonances (DCIRs) which are attributed to different angular momentum states. The analytically derived resonance condition reveals in detail the interplay of the confinement with the anisotropic nature of the dipole-dipole …
We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction $D/r^3$ favors an equilateral triangular arrangement of the molecules, which competes against the square symmetry of the underlying optical lattice with lattice constant $b$ and amplitude $V$. We find the minimal-energy states at the commensurate density $n = 1/b^2$ and establish the complete square-to-triangular transformation pathway of the lattice with decreasing $V$ involving period-doubled, solitonic, and distorted-triangular conf…
We propose an effective Ising spin chain constructed with dipolar quantum gases confined in a one-dimensional optical superlattice. Mapping the motional degrees of freedom of a single particle in the lattice onto a pseudo-spin results in effective transverse and longitudinal magnetic fields. This effective Ising spin chain exhibits a quantum phase transition from a paramagnetic to a single-kink phase as the dipolar interaction increases. Particularly in the single-kink phase,a magnetic kink arises in the effective spin chain and behaves as a quasi-particle in a pinning potential exerted by the…
Stabilized by quantum fluctuations, dipolar Bose-Einstein condensates can form self-bound liquidlike droplets in the mean-field unstable regime. However in the Bogoliubov theory, some phonon energies are imaginary in the long-wavelength limit, implying dynamical instability of this system. A similar instability appears in the Bogoliubov theory of a binary quantum droplet, and is removed due to higher-order quantum fluctuations as shown recently [1]. In this work, we study the phonon energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations can enhance the…
The properties of ultracold quantum gases of bosons with dipole-dipole interaction is investigated at finite temperature in the frame of the representative ensembles theory. Self-consistent coupled equations of motion are derived for the condensate and the non-condensate components. Corrections due to the dipolar interaction to the condensate depletion, the anomalous density and thermodynamic quantities such as the ground state energy, the equation of state, the compressibility and the presure are calculated in the homogeneous case at both zero and finite temperatures. Effects of interaction a…
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-…
We study the collapse of ultracold fermionic gases into inhomogeneous states due to strong dipolar interaction in both 2D and 3D. Depending on the dimensionality, we find that two different types of inhomogeneous states are stabilized once the dipole moment reaches a critical value $d>d_c$: the {\it stripe phase} and {\it phase separation} between high and low densities. In 2D, we prove that the stripe phase is always favored for $d\gtrsim d_c$, regardless of the microscopic details of the system. In 3D, the one-loop perturbative calculation suggests that the same type of instability leads to …
In this letter we consider dipolar quantum gases in a quasi-one-dimensional tube with dipole moment perpendicular to the tube direction. We deduce the effective one-dimensional interaction potential and show that this potential is not purely repulsive, but rather has an attractive part due to high-order scattering processes through transverse excited states. The attractive part can induce bound state and cause scattering resonances. This represents the dipole induced resonance in low-dimension. We work out an unconventional behavior of low-energy phase shift for this effective potential and sh…
We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole-dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find tha…
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 study phase transitions in homogeneous spin-1 Bose gases in the presence of long-range magnetic dipole-dipole interactions (DDI). We concentrate on three-dimensional geometries and employ momentum shell renormalization group to study the possible instabilities caused by the dipole-dipole interaction. At the zero-temperature limit where quantum fluctuations prevail, we find the phase diagram to be unaffected by the dipole-dipole interaction. When the thermal fluctuations dominate, polar and ferromagnetic condensates with DDI become unstable and we discuss this crossover in detail. On the oth…
We examine the magnetostrictive position and momentum space distortions that occur in harmonically confined dipolar Bose and Fermi gases. Direct interactions give rise to position space magnetostriction and exchange interactions give rise to momentum space magnetostriction. While the position space magnetostriction is similar in Bose and Fermi systems, the momentum space magnetostriction is markedly different: the Bose gas momentum distribution distorts in the opposite sense to that of the Fermi gas. By relating exchange effects to short range correlations between the particles we discuss the …
Recently, a seminal STIRAP experiment allowed the creation of 40K-87Rb molecules in the rovibrational ground state [K.-K. Ni et al., Science 322, 231 (2008)]. In order to describe such a polarized dipolar Fermi gas in the hydrodynamic regime, we work out a variational time-dependent Hartree-Fock approach. With this we calculate dynamical properties of such a system as, for instance, the frequencies of the low-lying excitations and the time-of-flight expansion. We find that the dipole-dipole interaction induces anisotropic breathing oscillations in momentum space. In addition, after release fro…
We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the fea…
By means of the Boltzmann-Vlasov kinetic equation we investigate dynamical properties of a trapped, one-component Fermi gas at zero temperature, featuring the anisotropic and long-range dipole-dipole interaction. To this end, we determine an approximate solution by rescaling both space and momentum variables of the equilibrium distribution, thereby obtaining coupled ordinary differential equations for the corresponding scaling parameters. Based on previous results on how the Fermi sphere is deformed in the hydrodynamic regime of a dipolar Fermi gas, we are able to implement the relaxation-time…
Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts. There is growing evidence that quantum liquid crystals play a central role in many electron systems including high temperature superconductors, but a quantitative understanding is lacking due to disorder and other complications. Here, we analyse the quantum phase diagram of a two-dimensional dipolar gas, which exhibits stripe, nematic and supersolid phases.…
We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov-de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximati…
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 consider dipolar bosons in two tubes of one-dimensional lattices, where the dipoles are aligned to be maximally repulsive and the particle filling fraction is the same in each tube. In the classical limit of zero inter-site hopping, the particles arrange themselves into an ordered crystal for any rational filling fraction, forming a complete devil's staircase like in the single tube case. Turning on hopping within each tube then gives rise to a competition between the crystalline Mott phases and a liquid of defects or solitons. However, for the two-tube case, we find that solitons from diff…
Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: …
We investigate fast rotating quasi-two-dimensional dipolar Fermi gases in the quantum Hall regime. By tuning the direction of the dipole moments with respect to the z-axis, the dipole-dipole interaction becomes anisotropic in the $x$-$y$ plane. For a soft confining potential we find that, as we tilt the angle of the dipole moments, the system evolves from a $ν= 1/3$ Laughlin state with dipoles being polarized along the z axis to a series of ground states characterized by distinct mean total angular momentum, and finally to an anisotropic integer quantum Hall state. During the transition from t…
We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the condensate and the excited particles. This allows to obtain the Bogoliubov spectrum analytically in the limit of large particle numbers. After discussing the condensate depletion and the ground-state energy correction, we derive quantum corrected equations of motion for harmonically trapped dipolar Bose gases by using superfluid hydrodynamics. These equations are…
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 investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalised Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction and approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\hbar$, reflecting the redu…
We present a hydrodynamic model of ultracold, but not yet quantum condensed, dipolar Bosonic gases. Such systems present both $s$-wave and dipolar scattering, the latter of which results in anisotropic transport tensors of thermal conductivity and viscosity. This work presents an analytic derivation of the viscosity tensor coefficients, utilizing the methods established in [Wang et al., arXiv:2205.10465], where the thermal conductivities were derived. Taken together, these transport tensors then permit a comprehensive description of hydrodynamics that is now embellished with dipolar anisotropy…
We consider plane wave modes in ultracold, but not quantum degenerate, dipolar Fermi gases in the hydrodynamic limit. Longitudinal waves present anisotropies in both the speed of sound and their damping, and experience a small, undulatory effect in their flow velocity. Two distinct types of shear waves appear, a ``familiar" one, and another that is accompanied by nontrivial density and temperature modulations. We propose these shear modes as an experimental means to measure the viscosity coefficients, including their anisotropies.
We theoretically investigate a polarized dipolar Fermi gas in free expansion. The inter-particle dipolar interaction deforms phase-space distribution in trap and also in the expansion. We exactly predict the minimal quadrupole deformation in the expansion for the high-temperature Maxwell-Boltzmann and zero-temperature Thomas-Fermi gases in the Hartree-Fock and Landau-Vlasov approaches. In conclusion, we provide a proper approach to develop the time-of-flight method for the weakly-interacting dipolar Fermi gas and also reveal a scaling law associated with the Liouville's theorem in the long-tim…
We present a method for calculating the dynamics of a bosonic mixture, the multi-component correlated basis function (CBF) method. For single components, CBF results for the excitation energies agree quite well with experimental results, even for highly correlated systems like $^4$He, and recent systematic improvements of CBF achieve perfect agreement. We give a full derivation of multi-component CBF, and apply the method to a dipolar Bose gas cut into two-dimensional layers by a deep optical lattice, with coupling between layers due to the long-ranged dipole-dipole interaction. We consider th…
The stability of an unpolarized two-component dipolar Fermi gas is studied within mean-field theory. Besides the known instability towards spontaneous magnetization with Fermi sphere deformation, another instability towards spontaneous formation of a spin-orbit coupled phase with a Rashba-like spin texture is found. A phase diagram is presented and consequences are briefly discussed.
This tutorial is a theoretical work, in which we study the physics of ultra-cold dipolar bosonic gases in optical lattices. Such gases consist of bosonic atoms or molecules that interact via dipolar forces, and that are cooled below the quantum degeneracy temperature, typically in the nK range. When such a degenerate quantum gas is loaded into an optical lattice produced by standing waves of laser light, new kinds of physical phenomena occur. These systems realize then extended Hubbard-type models, and can be brought to a strongly correlated regime. The physical properties of such gases, domin…
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 compute the ground state of dipoles in a quasi-one-dimensional ring trap using few-body techniques combined with analytic arguments. The effective interaction between two dipoles depends on their center-of-mass coordinate and can be tuned by varying the angle between dipoles and the plane of the ring. For weak enough interactions, the state resembles a weakly interacting Fermi gas or an (inhomogeneous) Lieb-Liniger gas. A mapping between the Lieb-Liniger and the dipolar-gas parameters in and beyond the Born approximation is established, and we discuss the effect of inhomogeneities based on …
Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the p-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly, and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-pa…
Research on quantum magnetism with ultra-cold gases in optical lattices is expected to open fascinating perspectives for the understanding of fundamental problems in condensed-matter physics. Here we report on the first realization of quantum magnetism using a degenerate dipolar gas in an optical lattice. In contrast to their non-dipolar counterparts, dipolar lattice gases allow for inter-site spin-spin interactions without relying on super-exchange energies, which constitutes a great advantage for the study of spin lattice models. In this paper we show that a chromium gas in a 3D lattice real…
By using two-fluid model the effect of impurities on the transition temperature of a dipolar trapped Bose gas is investigated. By treating Gaussian spatial correlation for impurities from the interaction modified spectra of the system, the formula for the shift of transition temperature is derived. The shift of the transition temperature contains essentially three contributions due to contact, dipole-dipole and impurity interactions. Applying our results to Dipolar Bose gases show that the shift of the transition temperature due to impurities could be measured for isotropic trap (dipole-dipole…
In the presence of dipolar interactions the excitation spectrum of a Bose gas can acquire a local minimum. The corresponding quasiparticles are known as rotons. They are gaped and do not decay at zero temperature. Here we study the decay of rotons in one-dimensional Bose gases at low temperatures. It predominantly occurs due to the backscattering of thermal phonons on rotons. The resulting rate scales with the third power of temperature and is inversely proportional to the sixth power of the roton gap near the solidification phase transition. The hydrodynamic approach used here enables us to f…
Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms.
Analytic expressions for the differential cross sections of ultracold atoms and molecules that scatter primarily due to dipolar interactions are derived within the first Born approximation, and are shown to agree with the partial wave expansion. These cross sections are applied to the problem of cross-dimensional rethermalization. Strikingly, the rate of rethermalization can vary by as much as a factor of two, depending on the orientation of polarization of the dipoles. Thus the anisotropic dipole-dipole interaction can have a profound effect even on the behavior of a nondegenerate ultracold g…
A microscopic description of the zero energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole--dipole interaction, on the energy per particle, comparing the results with mean field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to…
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…
