Advances in creating stable dipolar Bose systems, and ingenious box traps have generated tremendous interest. Theory study of dipolar bosons at finite temperature (T) has been limited. Motivated by these, we study 2D dipolar bosons at arbitrary tilt angle, $θ$, using finite-T random phase approximation. We show that a comprehensive understanding of phases and instabilities at non-zero T can be obtained on concurrently considering dipole strength, density, temperature and $θ$. We find the system to be in a homogeneous non-condensed phase that undergoes a collapse transition at large $θ$, and a finite momentum instability, signaling a striped phase, at large dipolar strength; there are important differences with the T=0 case. At T = 0, BEC appears at critical dipolar strength, and at critical density. Our predictions for polar molecule system, $^{41}K^{87}Rb$, and $^{166}Er$ may provide tests of our results. Our approach may apply broadly to systems with long-range, anisotropic interactions.
Recent experimental advances in creating stable dipolar bosonic systems, including polar molecules with large electric dipole moments, have led to vigorous theoretical activities. Recent reporting of observation of roton feature in dipolar erbium has provided added impetus to theoretical and experimental work. Here we discuss our mean-field theory work on 2D and quasi-2D dipolar bosons with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane, i.e. for {\it non-zero tilt angles}. Using Bogoliubov-de Gennes equations, we present results on a number of T=0 proper…
We consider a $^{168}$Er-$^{164}$Dy dipolar mixture, trapped by a cigar shaped harmonic potential. We derive the quasi-1D inter-species effective potential exhibiting the tilting angles and show that it is a quite natural generalization of the situation of a single dipolar gas. By solving the coupled Gross-Pitaevskii equations, we observe a transition from miscible to immiscible mixture as the orientations of the magnetic moments are varied. The atom numbers are also shown to lead to noticeable effects on the mixture.
Motivated by recent experiments with ultracold magnetic atoms trapped in optical lattices where the orientation of atomic dipoles can be fully controlled by external fields, we study the ground state properties of dipolar bosons trapped in a two-dimensional lattice with density-induced hopping and where the dipoles are tilted along the $xz$ plane. We present ground state phase diagrams of the above system at different tilt angles. We find that, as the dipolar interaction increases, the superfluid phase at half filling factor is destroyed in favor of either a checkerboard or stripe solid phase …
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate-plane. The tilting angle constitutes an additional tuning parameter, which help us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without c…
We analyze the microscopic few-body properties of dipolar particles confined in two parallel quasi-one-dimensional harmonic traps. In particular, we show that an adiabatic rotation of the dipole orientation about the trap axes can drive an initially non-localized few-fermion state into a localized state with strong inter-trap pairing. For an instant, non-adiabatic rotation, however, localization is inhibited and a highly excited state is reached. This state may be interpreted as the few-body analog of a super-Tonks-Girardeau state, known from one-dimensional systems with contact interactions.
We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. We show that the Random Phase Approximation (RPA) for the density-density response function is never accurate for the dipolar gas. We incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sjolander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontane…
The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid at all tilt angl…
We point out the possibility of occurring instabilities in Laughlin liquids of rotating dipolar fermions with zero thickness. Previously such a system was predicted to be the Laughlin liquid for filling factors being greater and equal to 1/7. However, from intra-Landau-level excitations of the liquid in the single-mode approximation, the roton minima become negative and Laughlin liquids are unstable for filling factors being less and equal to 1/7. We then conclude that there are correlated Wigner crystals for filling factors being less and equal to 1/7.
We analyze the ground state of a system of dipolar bosons moving in the $XY$ plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle $α$ with respect to the $Z$ axis. We use the Path Integral Ground State method to analyze the static properties of the system as both $α$ and the density $n$ vary over a wide range were the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them…
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…
We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a non-perpendicular polarization with respect to the system plane. For sufficiently high density an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting…
We investigate the quench dynamics of the dipolar bosons in two dimensional optical lattice of square geometry using the time dependent Gutzwiller method. The system exhibits different density orders like the checkerboard and the striped pattern, depending upon the polarization angle of the dipoles. We quench the hopping parameter across the striped density wave (SDW) to striped supersolid (SSS) phase transition, and obtain the scaling laws for the correlation length and topological vortex density, as function of the quench rate. The results are reminiscent of the Kibble-Zurek mechanism (KZM).…
We have employed the theory of harmonically trapped dipolar Bose-Einstein condensates to examine the influence of a uniform magnetic field that rotates at an arbitrary angle to its own orientation. This is achieved by semi-analytically solving the dipolar superfluid hydrodynamics of this system within the Thomas-Fermi approximation and by allowing the body frame of the condensate's density profile to be tilted with respect to the symmetry axes of the nonrotating harmonic trap. This additional degree of freedom manifests itself in the presence of previously unknown stationary solution branches …
We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle $θ$ of the dipolar bosons. At low tilt angles $0^{\circ}\leqslantθ\apprle25^{\circ}$, the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles $55^{\circ}\apprgeθ\apprge35^{\circ}$, phases with striped order of super…
We study the stability, form and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a non-local Gross Pitaevskii equation, and characterized as a function of the key experimental parameters, namely the ratio of the dipolar atomic interactions to the van der Waals interactions, the polarization angle and the condensate width. The solutions and their integrals of motion are strongly affected by the phonon and roton instabilities of the system. Dipolar matter…
We study fingering instabilities and pattern formation at the interface of an oppositely polarized two-component Bose-Einstein condensate with strong dipole-dipole interactions in three dimensions. It is shown that the rotational symmetry is spontaneously broken by fingering instability when the dipole-dipole interactions are strengthened. Frog-shaped and mushroom-shaped patterns emerge during the dynamics due to the dipolar interactions. We also demonstrate the spontaneous density modulation and domain growth of a two-component dipolar BEC in the dynamics. Bogoliubov analyses in the two-dimen…
We consider a trapped quasi2D dipolar Bose Einstein condensate (q2D DBEC) with a polariza- tion tilted into the plane of motion. We show that by tilting the polarization axis, the coherence properties are anisotropic. Such a system will have density fluctuations whose amplitude strongly depend on their trap location relative to the polarization axis. Additionally, interference contrast will also be anisotropic despite an isotropic density profile. The anisotropy is related to a roton like mode that becomes unstable and supports local collapse along the polarization axis.
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 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…
We present vortex solutions for the homogeneous two-dimensional Bose-Einstein condensate featuring dipolar atomic interactions, mapped out as a function of the dipolar interaction strength (relative to the contact interactions) and polarization direction. Stable vortex solutions arise in the regimes where the fully homogeneous system is stable to the phonon or roton instabilities. Close to these instabilities, the vortex profile differs significantly from that of a vortex in a nondipolar quantum gas, developing, for example, density ripples and an anisotropic core. Meanwhile, the vortex itself…
We consider the density wave instability of fermionic dipoles aligned by an external field, and moving in equidistant layers at zero temperature. Using a conserving Hartree-Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase fo…
We present a Quantum Monte Carlo study of the ground state properties of a two dimensional system of Bose particle with dipole moment in a harmonic trap. The direction of the dipoles is assumed to be fixed by an external field. We study how the system behaves when the direction of the dipole moments is changed. Our analysis is made using Path Integral Monte Carlo simulations in the Grand Canonical ensemble, using the Worm Algorithm. We study systems of increasing size, focusing on the spatial distribution of the atoms inside the trap and on the superfluid fraction of the sample. We find that v…
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 study the family of static and moving dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates, exploring their modified form and interactions. The density dip of the soliton acts as a giant anti-dipole which adds a non-local contribution to the conventional local soliton-soliton interaction. We map out the stability diagram as a function of the strength and polarization direction of the atomic dipoles, identifying both roton and phonon instabilities. Away from these instabilities, the solitons collide elastically. Varying the polarization direction relative to the condensat…
By means of quantum Monte Carlo simulations we study phase diagrams of dipolar bosons in a square optical lattice. The dipoles in the system are parallel to each other and their orientation can be fixed in any direction of the three-dimensional space. Starting from experimentally tunable parameters like scattering length and dipolar interaction strength, we derive the parameters entering the effective Hamiltonian. Depending on the direction of the dipoles, various types of supersolids (e.g. checkerboard, stripe) and solids (checkerboard, stripe, diagonal stripe, and an incompressible phase) ca…
We present a detailed functional renormalization group analysis of spin-1/2 dipolar Heisenberg model on square lattice. This model is similar to the well known $J_1$-$J_2$ model and describes the pseudospin degrees of freedom of polar molecules confined in deep optical lattice with long-range anisotropic dipole-dipole interactions. Previous study of this model based on tensor network ansatz indicates a paramagnetic ground state for certain dipole tilting angles which can be tuned in experiments to control the exchange couplings. The tensor ansatz formulated on a small cluster unit cell is inad…
We discuss complete theory of point-like particles in fully polarized BECs describing difference in behaviour of electrically- and magnetically polarized BECs. Next we present generalization of this theory on finite size particles to include contribution of size of real molecules on dynamical properties of dipolar BECs. As an application of obtained equation we calculate spectrum of linear collective excitations getting generalization of the Bogoliubov's spectrum. We show absence of roton instability due to positivity of polarization contribution in the excitation spectrum. We found that new t…
We investigate Bose-Einstein condensates in bubble trap potentials in the presence of a small gravity. In particular, we focus on thin shells and study both contact and dipolar interacting condensates. We first analyze the effects of the anisotropic nature of the dipolar interactions, which already appear in the absence of gravity and are enhanced when the polarization axis of the dipoles and the gravity are slightly misaligned. Then, in the small gravity context, we investigate the dynamics of small oscillations of these thin, shell-shaped condensates triggered either by an instantaneous tilt…
Quantized vortices are the prototypical feature of superfluidity. Pervasive in all natural systems, vortices are yet to be observed in dipolar quantum gases. Here, we exploit the anisotropic nature of the dipole-dipole interaction of a dysprosium Bose-Einstein condensate to induce angular symmetry breaking in an otherwise cylindrically symmetric pancake-shaped trap. Tilting the magnetic field towards the radial plane deforms the cloud into an ellipsoid through magnetostriction, which is then set into rotation. At stirring frequencies approaching the radial trap frequency, we observe the genera…
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 study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multi-layer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF). The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multi-layer systems and the unstable wave-vector is indicated. In all cases, the in-plane density wave instability is foun…
We investigate the phase diagram of dipolar fermions with aligned dipole moments in a two-dimensional (2D) bilayer. Using a version of the Singwi-Tosi-Land-Sjolander scheme recently adapted to dipolar fermions in a single layer [M. M. Parish and F. M. Marchetti, Phys. Rev. Lett. 108, 145304 (2012)], we determine the density-wave instabilities of the bilayer system within linear response theory. We find that the bilayer geometry can stabilize the collapse of the 2D dipolar Fermi gas with intralayer attraction to form a new density wave phase that has an orientation perpendicular to the density …
The behaviour of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilise linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gr…
We investigate the behavior of identical dipolar fermions with aligned dipole moments in two-dimensional multilayers at zero temperature. We consider density instabilities that are driven by the attractive part of the dipolar interaction and, for the case of bilayers, we elucidate the properties of the stripe phase recently predicted to exist in this interaction regime. When the number of layers is increased, we find that this "attractive" stripe phase exists for an increasingly larger range of dipole angles, and if the interlayer distance is sufficiently small, the stripe phase eventually spa…
We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to wide layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of…
Ultracold dipolar droplets have been realized in a series of ground-breaking experiments, where the stability of the droplet state is attributed to beyond-mean-field effects in the form of the celebrated Lee-Huang-Yang (LHY) correction. We scrutinize the dipolar droplet states in a one-dimensional context using a combination of analytical and numerical approaches, and identify experimentally viable parameters for accessing our findings for future experiments. In particular we identify regimes of stability in the restricted geometry, finding multiple roton instabilities as well as regions suppo…
A few-body cluster is a building block of a many-body system in a gas phase provided the temperature at most is of the order of the binding energy of this cluster. Here we illustrate this statement by considering a system of tubes filled with dipolar distinguishable particles. We calculate the partition function, which determines the probability to find a few-body cluster at a given temperature. The input for our calculations -- the energies of few-body clusters -- is estimated using the harmonic approximation. We first describe and demonstrate the validity of our numerical procedure. Then we …
A two-dimensional quantum system of dipoles, with a polarization angle not perpendicular to the plane, shows a transition from a gas to a stripe phase. We have studied the thermal properties of these two phases using the path integral Monte Carlo (PIMC) method. By simulating the thermal density matrix, PIMC provides exact results for magnitudes of interest such as the superfluid fraction and the one-body density matrix. As it is well known, in two dimensions the superfluid-to-normal phase transition follows the Berezinskii-Kosterlitz-Thouless (BKT) scenario. Our results show that both the anis…
The impact of the short-range interaction on the resonances occurrence in the anisotropic dipolar scattering in a plane was numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We revealed the strong dependence of the cross section of the 2D dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We defined the critical (magic) tilt angle of one of the dipoles, depending on the direction of the seco…
We show that fermionic dipoles in a two-layer geometry form Cooper pairs with both singlet and triplet components, when they are tilted with respect to the normal of the planes. The mixed parity pairing arises because the interaction between dipoles in the two different layers is not inversion symmetric. We use an efficient eigenvalue approach to calculate the zero temperature phase diagram of the system as a function of the dipole orientation and the layer distance. The phase diagram contains purely triplet as well as mixed singlet and triplet superfluid phases. We show in detail how the pair…
Motivated by the experimental realization of quantum spin models of polar molecule KRb in optical lattices, we analyze the spin 1/2 dipolar Heisenberg model with competing anisotropic, long-range exchange interactions. We show that, by tilting the orientation of dipoles using an external electric field, the dipolar spin system on square lattice comes close to a maximally frustrated region similar, but not identical, to that of the $J_1$-$J_2$ model. This provides a simple yet powerful route to potentially realize a quantum spin liquid without the need for a triangular or kagome lattice. The gr…
We study zero sound in a weakly interacting 2D gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes i…
Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x-y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complimentary methods, the Hatree-Fock mean field theory and the linear response analysis of compressibility. Both give consistent results. In addition to the staggered ($π$, $π$) density wave, over a finite range of densities and hopping parameters, the ground state of the system f…
We study correlation effects and excitations in a dipolar Bose gas bilayer which is modeled by a one-dimensional double well trap that determines the width of an individual layer, the distance between the two layers, and the height of the barrier between them. For the ground state calculations we use the hypernetted--chain Euler Lagrange method and for the calculation of the excitations we use the correlated basis function method. We observe instabilities both for wide, well-separated layers dominated by \emph{intra-layer} attraction of the dipoles, and for narrow layers that are close to each…
Antiferromagnetic Heisenberg model on the triangular lattice is perhaps the best known example of frustrated magnets, but it orders at low temperatures. Recent density matrix renormalization group (DMRG) calculations find that next nearest neighbor interaction $J_2$ enhances the frustration and leads to a spin liquid for $J_2/J_1\in (0.08,0.15)$. In addition, DMRG study of a dipolar Heisenberg model with longer range interactions gives evidence for a spin liquid at small dipole titling angle $θ\in[0,10^\circ)$. In both cases, the putative spin liquid region appears to be small. Here, we show t…
