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.
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 study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by inter-species contact interaction in a trapped non-dipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164Dy droplet bound in a trapped non-dipolar 87Rb BEC with a variable number of 164Dy atoms and the inter-species scattering length. A trapped non-dipolar BEC of a fixed number of atoms can only bind a dipolar droplet containing atoms less than a critical number for the inter-species scattering length between two critical values. The shape and size (statics) as well a…
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.
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 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 investigated the ground state wave function and free expansion of a trapped dipolar condensate. We find that dipolar interaction may induce both biconcave and dumbbell density profiles in, respectively, the pancake- and cigar-shaped traps. On the parameter plane of the interaction strengths, the density oscillation occurs only when the interaction parameters fall into certain isolated areas. The relation between the positions of these areas and the trap geometry is explored. By studying the free expansion of the condensate with density oscillation, we show that the density oscillation is de…
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.
We study a harmonically trapped Bose-Einstein condensate with dipole-dipole interactions in a regime where a roton spectrum emerges. We show that the roton spectrum is clearly revealed in the static and dynamic structure factors which can be measured using Bragg spectroscopy. We develop and validate a theory based on the local density approximation for the dynamic structure factor.
Thanks to their immense purity and controllability, dipolar Bose-Einstein condensates are an exemplar for studying fundamental non-local nonlinear physics. Here we show that a family of fundamental nonlinear waves - the dark solitons - are supported in trapped quasi-one-dimensional dipolar condensates and within reach of current experiments. Remarkably, the oscillation frequency of the soliton is strongly dependent on the atomic interactions, in stark contrast to the non-dipolar case. The failure of a particle analogy, so successful for dark solitons in general, to account for this behaviour i…
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…
The collective excitations of a zero-temperature, spin-polarized, harmonically trapped, two-dimensional dipolar Fermi gas are examined within the Thomas-Fermi von Weizsäcker hydrodynamic theory. We focus on repulsive interactions, and investigate the dependence of the excitation frequencies on the strength of the dipolar interaction and particle number. We find that the mode spectrum can be classified according to bulk modes, whose frequencies are shifted upward as the interaction strength is increased, and an infinite ladder of surface modes, whose frequencies are {\em independent} of the int…
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…
We introduce a confocal shift-interferometer based on optical fibers. The presented spectroscopy allows measuring coherence maps of luminescent samples with a high spatial resolution even at cryogenic temperatures. We apply the spectroscopy onto electrostatically trapped, dipolar excitons in a semiconductor double quantum well. We find that the measured spatial coherence length of the excitonic emission coincides with the point spread function of the confocal setup. The results are consistent with a temporal coherence of the excitonic emission down to temperatures of 250 mK.
We consider the non-condensate density and density fluctuations of a trapped dipolar Bose-Einstein condensate, focusing on the regime where a roton-like excitation spectrum develops. Our results show that a characteristic peak in the non-condensate density occurs at trap center due to the rotons. In this regime we also find that the anomalous density becomes positive and peaked, giving rise to enhanced density fluctuations. We calculate the non-condensate density in momentum space and show that a small momentum halo is associated with the roton excitations.
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…
We consider the quasi-particle excitations of a trapped dipolar Bose-Einstein condensate. By mapping these excitations onto radial and angular momentum we show that the roton modes are clearly revealed as discrete fingers in parameter space, whereas the other modes form a smooth surface. We examine the properties of the roton modes and characterize how they change with the dipole interaction strength. We demonstrate how the application of a perturbing potential can be used to engineer angular rotons, i.e. allowing us to controllably select modes of non-zero angular momentum to become the lowes…
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 …
We calculate the stability diagram for a trapped normal Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry, temperature, and short-ranged interactions on the stability. We predict a robust double instability feature in oblate trapping geometries arising from the interplay of thermal gas saturation and the anisotropy of the interaction. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate.
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 develop a finite temperature Hartree theory for the trapped dipolar Bose gas. We use this theory to study thermal effects on the mechanical stability of the system and density oscillating condensate states. We present results for the stability phase diagram as a function of temperature and aspect ratio. In oblate traps above the critical temperature for condensation we find that the Hartree theory predicts significant stability enhancement over the semiclassical result. Below the critical temperature we find that thermal effects are well described by accounting for the thermal depletion of …
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…
From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in $d=3$ and $d=2$. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap the gases under harmonic potential in $d=1$. This result suggests the equivalence between Bose and Fermi gases which is a…
We calculate the stability diagram for a trapped normal Fermi or Bose gas with dipole-dipole interactions. Our study characterizes the roles of trap geometry and temperature on the stability using Hartree-Fock theory. We find that exchange appreciably reduces stability, and that, for bosons, the double instability feature in oblate trapping geometries predicted previously is still predicted by the Hartree-Fock theory. Our results are relevant to current experiments with polar molecules and will be useful in developing strategies to obtain a polar molecule Bose-Einstein condensate or degenerate…
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…
Using the time-dependent density matrix renormalization group method, we calculate transport properties of an interacting Fermi gas in an optical lattice with a confining trap after a sudden displacement of the trap center. In the regime of attractive interactions, the dipolar motion after the displacement can be classified into underdamped oscillations and overdamped relaxations, depending on the interaction strength. These numerical calculations are consistent with experimental results. In the regime of repulsive interactions, we predict a revival of the oscillations of the center of mass wh…
Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact Path Integral Ground State Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of interaction parameters leading to stable ground- state configurations of droplets in a crystalline arrangement. We find that this effect is entirely due to the interaction present in the Hamiltonian without resorting to additional stabilizing mechanisms or specific three-body forces. We analyze the number of droplets formed in terms of the Hamiltonian paramet…
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 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,…
We present a general method for obtaining the exact static solutions and collective excitation frequencies of a trapped Bose-Einstein condensate (BEC) with dipolar atomic interactions in the Thomas-Fermi regime. The method incorporates analytic expressions for the dipolar potential of an arbitrary polynomial density profile, thereby reducing the problem of handling non-local dipolar interactions to the solution of algebraic equations. We comprehensively map out the static solutions and excitation modes, including non-cylindrically symmetric traps, and also the case of negative scattering lengt…
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…
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 hi…
We perform collective spin measurements to study the buildup of two-body correlations between $\approx10^4$ spin $s=3$ chromium atoms pinned in a 3D optical lattice. The spins interact via long range and anisotropic dipolar interactions. From the fluctuations of total magnetization, measured at the standard quantum limit, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. The quantum nature of the correlations is assessed by comparisons with short and long time expansions, and numerical simulations. Our work shows that measuring fluctuations …
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…
We develop a meanfield treatment of a polarized trapped Fermi gas with dipole-dipole interactions. Our approach is based on self-consistent semiclassical Hartree-Fock theory that accounts for direct and exchange interactions. We discuss our procedure for numerically implementing the calculation. We study the thermodynamic and the first and second order correlation properties of the system. We find that the system entropy depends on the trap geometry, allowing the system to be cooled as the trap aspect ratio is increased, and that exchange interactions cause the correlation functions to be anis…
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: …
