We identify the quantum phases in a binary mixture of dipolar bosons in two-dimensional optical lattices. Our study is motivated by the recent experimental realization of binary dipolar condensate mixtures of Er-Dy [Phys. Rev. Lett. 121, 213601 (2018)]. We model the system by using the extended two-species Bose-Hubbard model and calculate the ground-state phase diagrams by using mean-field theory. For selected cases we also obtain analytical phase boundaries by using the site-decoupled mean-field theory. For comparison we also examine the phase diagram of two-species Bose-Hubbard model. Our results show that the quantum phases with the long-range intraspecies interaction phase separate with no phase ordering. The introduction of the long-range interspecies interaction modifies the quantum phases of the system. It leads to the emergence of phase-separated quantum phases with phase ordering. The transition from the phase-separated quantum phases without phase ordering to phase ordered ones breaks the inversion symmetry.
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 two-mode atomic Josephson junction realized with dilute dipolar bosons confined by a double-well. We employ the two-site extended Bose-Hubbard Hamiltonian and characterize the ground-state of this system by the Fisher information, coherence visibility, and entanglement entropy. These quantities are studied as functions of the interaction between bosons in different wells. The emergence of Schroedinger-cat like state with a loss of coherence is also commented.
We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping phenomena in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-in…
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-…
Combining two Bose-Einstein condensates (BECs) may result in a miscible or immiscible mixture, or even a violent implosion. We theoretically demonstrate that dipolar two-component BECs produce far richer physics than their nondipolar counterparts. Intriguingly, when both components have equivalent dipoles, the transition to immiscibility is largely unaffected by dipolar physics, yet the dipoles maximally affect stability. Conversely, antiparallel dipoles strongly affect miscibility but have little effect on stability. By performing three-dimensional calculations of the ground states and their …
We explore the groundstates of a few dipolar bosons in optical lattices with incommensurate filling. The competition of kinetic, potential, and interaction energies leads to the emergence of a variety of crystal state orders with characteristic one- and two-body densities. We probe the transitions between these orders and construct the emergent state diagram as a function of the dipolar interaction strength and the lattice depth. We show that the crystal state orders can be observed using the full distribution functions of the particle number extracted from simulated single-shot images.
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 investigate the occurence of Wigner-localization phenomena in bosonic dipolar ultracold few-body systems with Rashba-like spin-orbit coupling. We show that the latter strongly enhances the effects of the dipole-dipole interactions, allowing to reach the Wigner-localized regime for strengths of the dipole moment much smaller than those necessary in the spin-orbit-free case.
The main properties and methods of describing dipolar and spinor atomic systems, composed of bosonic atoms or molecules, are reviewed. The general approach for the correct treatment of Bose-condensed atomic systems with nonlocal interaction potentials is explained. The approach is applied to Bose-condensed systems with dipolar interaction potentials. The properties of systems with spinor interaction potentials are described. Trapped atoms and atoms in optical lattices are considered. Effective spin Hamiltonians for atoms in optical lattices are derived. The possibility of spintronics with cold…
Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases stabilized by anisotropic, long-range dipolar interaction. Moreover, the unprecedented control over the various physical properties of these systems, ranging from the quantum statistics of the particles, to the inter-particle interactions, allow one to engineer novel devices. In this paper, we consider dipolar bosons trapped in a stack of one-dimensional optical …
We show that multichannel interactions significantly alter the phase diagram of ultracold bosonic molecules in an optical lattice. Most prominently, an unusual fluid region intervenes between the conventional superfluid and the Mott insulator. In it, number fluctuations remain but phase coherence is suppressed by a significant factor. This factor can be made arbitrarily large, at least in a two-site configuration. We calculate the phase diagram using complementary methods, including Gutzwiller mean-field and density matrix renormalization group (DMRG) calculations. Although we focus on bosonic…
The dipolar collision between ultracold polar molecules is an important topic both by its own right from the fundamental point of view and for the successful exploration of many-body physics with strong and long-range dipolar interactions. Here, we report the investigation of collisions between ultracold ground-state sodium-rubidium molecules in electric fields with induced electric dipole moments as large as 0.7$\;$D. We observe a step-wise enhancement of losses due to the coupling between different partial waves induced by the increasingly stronger anisotropic dipolar interactions. Varying t…
We present a quantum Monte Carlo study of two-dimensional dipolar Bose gases in the limit of zero temperature. The analysis is mainly focused on the anisotropy effects induced in the homogeneous gas when the polarization angle with respect to the plane is changed. We restrict our study to the regime where the dipolar interaction is strictly repulsive, although the strength of the pair repulsion depends on the vector interparticle distance. Our results show that the effect of the anisotropy in the energy per particle scales with the gas parameter at low densities as expected, and that this scal…
In a combined experimental and theoretical effort, we demonstrate a novel type of dipolar system made of ultracold bosonic dipolar molecules with large magnetic dipole moments. Our dipolar molecules are formed in weakly bound Feshbach molecular states from a sample of strongly magnetic bosonic erbium atoms. We show that the ultracold magnetic molecules can carry very large dipole moments and we demonstrate how to create and characterize them, and how to change their orientation. Finally, we confirm that the relaxation rates of molecules in a quasi-two dimensional geometry can be reduced by usi…
Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected…
We study by first principle computer simulations the low temperature phase diagram of bosonic dipolar gases in a bilayer geometry, as a function of the two control parameters, i.e., the in-plane density and the interlayer distance. We observe four distinct phases, namely paired and decoupled superfluids, as well as a crystal of dimers and one consisting of two aligned crystalline layers. A direct quantum phase transition from a dimer crystal to two independent superfluids is observed in a relatively wide range of parameters. No supersolid phase is predicted for this system.
We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gas-like state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.
We study the emergence of several magnetic phases in dipolar bosonic gases subject to three-body loss mechanism employing numerical simulations based on the density matrix renormalization group(DMRG) algorithm. After mapping the original Hamiltonian in spin language, we find a strong parallelism between the bosonic theory and the spin-1 Heisenberg model with single ion anisotropy and long-range interactions. A rich phase diagram, including ferromagnetic, antiferromagnetic and non-local ordered phases, emerges in the half-filled one-dimensional case, and is preserved even in presence of a trapp…
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…
Probing the radial collective oscillation of a trapped quantum system is an accurate experimental tool to investigate interactions and dimensionality effects. We consider a fully polarized quasi-one dimensional dipolar quantum gas of bosonic dysprosium atoms in a parabolic trap at zero temperature. We model the dipolar gas with an effective quasi-one dimensional Hamiltonian in the single-mode approximation, and derive the equation of state using a variational approximation based on the Lieb-Liniger gas Bethe Ansatz wavefunction or perturbation theory. We calculate the breathing mode frequencie…
We demonstrate the realization of topological band structures by exploiting the intrinsic spin-orbit coupling of dipolar interactions in combination with broken time-reversal symmetry. The system is based on polar molecules trapped in a deep optical lattice, where the dynamics of rotational excitations follows a hopping Hamiltonian which is determined by the dipolar exchange interactions. We find topological bands with Chern number $C=2$ on the square lattice, while a very rich structure of different topological bands appears on the honeycomb lattice. We show that the system is robust against …
As dipolar gases become more readily accessible in experiment there is a need to develop a comprehensive theoretical framework of the few-body physics of these systems. Here, we extend the coupled-pair approach developed for the unitary two-component Fermi gas to a few-body system of dipolar bosons in a spherical harmonic trap. The long range and anisotropy of the dipole-dipole interaction is handled by a flexible and efficient correlated gaussian basis with stochastically variational optimisation. We calculate the eigenenergy spectrum and structural properties of two and three trapped bosonic…
We consider $N$ interacting dipolar bosonic atoms at zero temperature in a double-well potential. This system is described by the two-space-mode extended Bose-Hubbard (EBH) Hamiltonian which includes (in addition to the familiar BH terms) the nearest-neighbor interaction, correlated hopping and bosonic-pair hopping. For systems with $N=2$ and $N=3$ particles we calculate analytically both the ground state and the Fisher information, the coherence visibility, and the entanglement entropy that characterize the correlations of the lowest energy state. The structure of the ground state crucially d…
We study a gas of bosonic dipolar atoms in the presence of a transverse harmonic trapping potential by using an improved variational Bethe ansatz, which includes the transverse width of the atomic cloud as a variational parameter. Our calculations show that the system behavior evolves from quasi-one dimensional to a strictly one-dimensional one by changing the atom-atom interaction, or the axial density, or the frequency of the transverse confinement. Quite remarkably, in the droplet phase induced by the attractive dipolar interaction the system becomes sub-one dimensional when the transverse …
We discuss a possible link between the recently observed macroscopic ordering of ultra cold dipolar excitons (MOES) and the phenomenon of supersolidity. In the dilute limit we predict a stable supersolid state for a quasi-one-dimensional system of bosonic dipoles characterized by two- and three-body contact repulsion. We phenomenologically extend our theory to the strongly-correlated regime and find a critical value of the contact interaction parameter at which the supersolid exhibits a quantum phase transition to a fragmented state. The wavelength of the fragmented-condensate solid is defined…
We theoretically investigate the droplets formation in a tightly trapped one-dimensional dipolar gas of bosonic atoms. When the strength of the dipolar interaction becomes sufficiently attractive compared to the contact one, we show how a solitonic-like density profile evolves into a liquid-like droplet on increasing the number of particles in the trap. The incipient gas-liquid transition is also signalled by a steep increase of the breathing mode and a change in sign of the chemical potential. Upon a sudden release of the trap, varying the number of trapped atoms and the scattering length, th…
We analyze the nature of quantum phase transition to a superfluid state of flexible chains in a gas of polar bosonic molecules confined in a stack of $N$ identical 1d ("cigar" type) optical lattice layers and polarized perpendicularly to the layers. Monte Carlo simulations within the $J$-current model show that, in the absence of the inter-tube tunneling, the transition to the $N$-layered superfluid is in the Berezinskii-Kosterlitz-Thouless universality class in the one-particle density matrix channel. The inter-layer tunneling changes it to the $q=N$ 2d Potts universality. The low energy fiel…
In this article we develop the framework to describe Bose-Fermi mixtures of magnetic atoms, focusing on the interaction of bosonic self-bound dipolar quantum droplets with a small number of fermions. We find an attractive interaction potential due to the dipolar interaction with several bound states, which can be occupied by one fermion each, resulting in a very weak back-action on the bosons. We conclude, that these impurities might act as unique probes giving access to inherent properties of dipolar quantum droplets.
In a joint experimental and theoretical effort, we report on the formation of a macro-droplet state in an ultracold bosonic gas of erbium atoms with strong dipolar interactions. By precise tuning of the s-wave scattering length below the so-called dipolar length, we observe a smooth crossover of the ground state from a dilute Bose-Einstein condensate (BEC) to a dense macro-droplet state of more than $10^4$ atoms. Based on the study of collective excitations and loss features, we quantitative prove that quantum fluctuations stabilize the ultracold gas far beyond the instability threshold impose…
We study fermions and hardcore bosons with long range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors \cite{Neupert2011}. We consider the case that the dipoles are aligned in the perpendicular direction by an external field without the complication of anisotropic interaction. Using exact diagonalization, we find clear signatures of fractional quantum Hall (FQH) states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in the lowest Chern band with a robust spectrum gap at moderate di…
We show that ultradilute quantum liquids can be formed with ultracold bosonic dipolar atoms in a bilayer geometry. Contrary to previous realizations of ultradilute liquids, there is no need for stabilizing the system with an additional repulsive short-range potential. The advantage of the proposed system is that dipolar interactions on their own are sufficient for creation of a self-bound state and no additional short-range potential is needed for the stabilization. We perform quantum Monte Carlo simulations and find a rich ground-state phase diagram that contains quantum phase transitions bet…
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.
A dipolar condensate confined in a toroidal trap constitutes a self-induced Josepshon junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the s-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that in this system the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and an…
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 the equilibrium properties of a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex-antivortex superposed state (VAVSS) using a quantum-hydrodynamic model. We show that, depending on the choice of parameters, the DBFM with a VAVSS can exhibit rich phase structures. For repulsive boson-fermion (BF) interaction, the Bose-Einstein condensate (BEC) may constitute a petal-shaped "core" inside the honeycomb-like fermionic component, or a ring-shaped joint "shell" around the onion-like fermionic cloud, or multiple segregated "islands" embedded in the dis…
We study the ground-state properties of a two-dimensional spin-polarized fluid of dipolar fermions within the Euler-Lagrange Fermi-hypernetted-chain approximation. Our method is based on the solution of a scattering Schrödinger equation for the "pair amplitude" $\sqrt{g(r)}$, where $g(r)$ is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow-Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree-Fock limit at weak coupling. Very good a…
We consider two-dimensional bosonic dipoles oriented perpendicularly to the plane. On top of the usual two-body contact and long-range dipolar interactions we add a contact three-body repulsion as expected, in particular, for dipoles in the bilayer geometry with tunneling. The three-body repulsion is crucial for stabilizing the system, and we show that our model allows for stable continuous space supersolid states in the dilute regime and calculate the zero-temperature phase diagram.
We report on the creation of bosonic NaCs molecules in their absolute rovibrational ground state via stimulated Raman adiabatic passage. We create ultracold gases with up to 22,000 dipolar NaCs molecules at a temperature of 300(50) nK and a peak density of $1.0(4) \times 10^{12}$ cm$^{-3}$. We demonstrate comprehensive quantum state control by preparing the molecules in a specific electronic, vibrational, rotational, and hyperfine state. Employing the tunability and strength of the permanent electric dipole moment of NaCs, we induce dipole moments of up to 2.6 D. Dipolar systems of NaCs molecu…
We study systems of two identical dipolar particles confined in quasi one-dimensional harmonic traps. Numerical results for the dependencies of the entanglement on the control parameters of the systems are provided and discussed in detail. In the limit of a strong interaction between the particles, the occupancies and the von Neumann entropies of the bosonic and fermionic ground states are derived in closed analytic forms by applying the harmonic approximation. The strong correlation regimes of the system with the dipolar bosons and the system with the charged ones are compared with each other…
We report the investigation on dipolar collisions in rotational state mixtures of ultracold bosonic $^{23}$Na$^{87}$Rb molecules. The large resonant dipole-dipole interaction between molecules in rotational states of opposite parities brings about significant modifications to their collisions, even when an electric field is not present. In this work, this effect is revealed by measuring the dramatically enhanced two-body loss rate constants in the mixtures. In addition, the dipolar interaction strength can be tuned by preparing the NaRb mixture in different rotational levels with microwave spe…
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…
We report the creation of ultracold bosonic dipolar $^{23}\textrm{Na}^{39}\textrm{K}$ molecules in their absolute rovibrational ground state. Starting from weakly bound molecules immersed in an ultracold atomic mixture, we coherently transfer the dimers to the rovibrational ground state using an adiabatic Raman passage. We analyze the two-body decay in a pure molecular sample and in molecule-atom mixtures and find an unexpectedly low two-body decay coefficient for collisions between molecules and $^{39}\textrm{K}$ atoms in a selected hyperfine state. The preparation of bosonic $^{23}\textrm{Na…
We reveal the existence of polarizing quantum phases for the enantiomers of cold, interacting chiral molecules in an optical helicity lattice by means of an extended Bose-Hubbard model. These recently proposed lattices have sites with alternating helicity which exert a discriminatory force on chiral molecules with different handedness. In our study of the phase diagram we find that a strong dipolar repulsion between molecules results in the separation of left and right enantiomers.
The thermodynamics of a quantum system of layers containing perpendicularly oriented dipolar molecules is studied within an oscillator approximation for both bosonic and fermionic species. The system is assumed to be built from chains with one molecule in each layer. We consider the effects of the intralayer repulsion and quantum statistical requirements in systems with more than one chain. Specifically, we consider the case of two chains and solve the problem analytically within the harmonic Hamiltonian approach which is accurate for large dipole moments. The case of three chains is calculate…
A two-component two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure fact…
We observe the suppression of inelastic dipolar scattering in ultracold Fermi gases of the highly magnetic atom dysprosium: the more energy that is released, the less frequently these exothermic reactions take place, and only quantum spin statistics can explain this counterintuitive effect. Inelastic dipolar scattering in non-zero magnetic fields leads to heating or to loss of the trapped population, both detrimental to experiments intended to study quantum many-body physics with strongly dipolar gases. Fermi statistics, however, is predicted to lead to a kinematic suppression of these harmful…
Ultracold dysprosium gases, with a magnetic moment ten times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 10…
