Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements.
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.
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…
The collective dynamics of a dipolar fermionic quantum gas confined in a one-dimensional double-well superlattice is explored. The fermionic gas resides in a paramagnetic-like ground state in the weak interaction regime, upon which a new type of collective dynamics is found when applying a local perturbation. This dynamics is composed of the local tunneling of fermions in separate supercells, and is a pure quantum effect, with no classical counterpart. Due to the presence of the dipolar interactions the local tunneling transports through the entire superlattice, giving rise to a collective dyn…
We perform a theoretical study into how dipole-dipole interactions modify the properties of superfluid vortices within the context of a two-dimensional atomic Bose gas of co-oriented dipoles. The reduced density at a vortex acts like a giant anti-dipole, changing the density profile and generating an effective dipolar potential centred at the vortex core whose most slowly decaying terms go as $1/ρ^2$ and $\ln(ρ)/ρ^3$. These effects modify the vortex-vortex interaction which, in particular, becomes anisotropic for dipoles polarized in the plane. Striking modifications to vortex-vortex dynamics …
We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves differ substantially in two- and one-dimensional geometries, providing a clear example of the key role of confinement dimensionality in dipolar gases. Moreover, Faraday patterns constitute an excellent tool to study non-local effects in polar gases, as we illustrate for two parallel quasi-one-dimensional dipolar condensates. Non-local interactions between the c…
We report on the anisotropic expansion of ultracold bosonic dysprosium gases at temperatures above quantum degeneracy and develop a quantitative theory to describe this behavior. The theory expresses the post-expansion aspect ratio in terms of temperature and microscopic collisional properties by incorporating Hartree-Fock mean-field interactions, hydrodynamic effects, and Bose-enhancement factors. Our results extend the utility of expansion imaging by providing accurate thermometry for dipolar thermal Bose gases, reducing error in expansion thermometry from tens of percent to only a few perce…
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…
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…
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.
We study a quasi-two dimensional gas of bosonic dipoles, calculating the beyond mean field corrections to the ground state energy and chemical potential neglecting the transverse mode structure. We show that the corrections are sensitive to the high momentum part of the interaction and cannot be expressed solely in terms of the scattering length and the dipole strength. While nonuniversal, the correction is found to be negative, which provides an additional attractive term in the extended Gross-Pitaevskii equation, enhancing the roton instability.
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.
Roton excitations constitute a key feature of dipolar gases, connecting these gases with superfluid helium. We show that the density dependence of the roton minimum results in a spatial roton confinement, particularly relevant in pancake dipolar condensates with large aspect ratios. We show that roton confinement plays a crucial role in the dynamics after roton instability, and that arresting the instability may create a trapped roton gas revealed by confined density modulations. We discuss the local susceptibility against density perturbations, which we illustrate for the case of vortices. Ro…
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.
Point defects in self-assembled crystals, such as vacancies and interstitials, attract each other and form stable clusters. This leads to a phase separation between perfect crystalline structures and defect conglomerates at low temperatures. We propose a method that allows one to tune the effective interactions between point defects from attractive to repulsive by means of external periodic fields. In the quantum regime, this allows one to engineer strongly-correlated many-body phases. We exemplify the microscopic mechanism by considering dipolar quantum gases of ground state polar molecules a…
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…
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 consider dipolar interactions between heteronuclear molecules in a low-dimensional setup consisting of two one-dimensional tubes. We demonstrate that attraction between molecules in different tubes can overcome intratube repulsion and complexes with several molecules in the same tube are stable. In situ detection schemes of the few-body complexes are proposed. We discuss extensions to the case of many tubes and layers, and outline the implications of our results on many-body physics.
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.
A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an additional anisotropic dipole-dipole interaction. The interplay of a model but realistic short-range Born-Oppenheimer potential and the dipole-dipole interaction for two confined particles is investigated. A variation of the strength of the dipole-dipole interaction leads to diverse resonance phenomena. In a harmonic confinement potential some resonances show similar…
Finite fermion systems are known to exhibit shell structure in the weakly-interacting regime, as well known from atoms, nuclei, metallic clusters or even quantum dots in two dimensions. All these systems have in common that the particle interactions between electrons or nucleons are spatially isotropic. Dipolar quantum systems as they have been realized with ultra-cold gases, however, are governed by an intrinsic anisotropy of the two-body interaction that depends on the orientation of the dipoles relative to each other. Here we investigate how this interaction anisotropy modifies the shell st…
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 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…
The Berezinskii-Kosterlitz-Thouless transition in 2D dipolar systems has been studied recently by path integral Monte Carlo (PIMC) simulations [A. Filinov et al., PRL 105, 070401 (2010)]. Here, we complement this analysis and study temperature-coupling strength dependence of the density (particle-hole) and single-particle (SP) excitation spectra both in superfluid and normal phases. The dynamic structure factor, S(q,omega), of the longitudinal excitations is rigorously reconstructed with full information on damping. The SP spectral function, A(q,omega), is worked out from the one-particle Mats…
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 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…
Inter-site interactions play a crucial role in polar gases in optical lattices even in the absence of hopping. We show that due to these long-range interactions a destabilized stack of quasi-one dimensional Bose-Einstein condensates develops a correlated modulational instability in the non-overlapping sites. Interestingly, this density pattern may evolve spontaneously into soliton filaments or a crystal of solitons that can be so created for the first time in ultra-cold gases. These self-assembled structures may be observed under realistic conditions within current experimental feasibilities.
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.
Motivated by recent experimental advances in creating polar molecular gases in the laboratory, we theoretically investigate the many body effects of two-dimensional dipolar systems with the anisotropic and $1/r^3$ dipole-dipole interactions. We calculate collective modes of 2D dipolar systems, and also consider spatially separated bilayer and multilayer superlattice dipolar systems. We obtain the characteristic features of collective modes in quantum dipolar gases. We quantitatively compare the modes of these dipolar systems with the modes of the extensively studied usual two-dimensional elect…
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.
Site-selective preparation of two-dimensional dipolar quantum gases in an optical beat-note lattice
Institut für Quantenoptik und Quanteninformation (IQOQI), Österreichische Akademie der Wissenschaften（奥地利科学院量子光学与量子信息研究所）；Institut für Experimentalphysik, Universität Innsbruck（因斯布鲁克大学实验物理系）
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…
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…
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 study dipolar relaxation in both ultra-cold thermal and Bose-condensed chromium atom gases. We show three different ways to control dipolar relaxation, making use of either a static magnetic field, an oscillatory magnetic field, or an optical lattice to reduce the dimensionality of the gas from 3D to 2D. Although dipolar relaxation generally increases as a function of a static magnetic field intensity, we find a range of non-zero magnetic field intensities where dipolar relaxation is strongly reduced. We use this resonant reduction to accurately determine the S=6 scattering length of chromi…
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…
