We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.
Dipolar particles in an elongated trap are expected to undergo a quantum phase transition from a linear to a zigzag structure with decreasing transverse confinement. We derive the low-energy effective theory of the transition showing that in the presence of quantum fluctuations the zigzag phase can be characterized by a long-ranged string order, while the local Ising correlations decay as a power law. This is also confirmed using density matrix renormalization group calculations on a microscopic model. The nonlocal order in the bulk gives rise to zero energy states localized at the interface between the ordered and disordered phases. Such an interface naturally arises when the particles are subject to a weak harmonic confinement along the tube axis. We compute the signature of the edge states in the single-particle tunneling spectra pointing to differences between a system with bosonic versus fermionic particles. Finally we assess the magnitude of the relevant quantum fluctuations in realistic systems of dipolar particles, including ultracold polar molecules as well as alkali atoms weakly dressed by a Rydberg excitation.
Recent advances in realizing nearly degenerate dipolar gases in optical lattices have enabled the study of quantum systems with long-range anisotropic interactions. Here, we investigate hard-core dipolar bosons on a two-dimensional square lattice described by an extended Bose--Hubbard model. Using path-integral quantum Monte Carlo simulations at fixed azimuthal angle
φ=45∘, we investigate density instabilities arising from first-order phase transitions. We start by mapping the ground-state phase diagram at half filling as a function of dipolar interaction strength and polar angle
θ. For weak interactions, the system remains superfluid for all
θ. Above a critical interaction strength, the superfluid phase becomes unstable and gives way to checkerboard, stripe, or incompressible phases depending on
θ. For
θ≳62∘, we find that half filling becomes unstable and only the empty state,
n=0, and the fully filled state,
n=1, are stable. Unlike recent experimental reports of a self-bound insulator at half filling, the homogeneous ground state does not support such a phase, but instead exhibits a direct first-order transition between
n=0 and
n=1. At finite temperature, thermal fluctuations shift the onset of density instabilities to larger
θ and stabilize intermediate fillings in the regime where half filling is unstable in the ground state. This leads to phase-separated states consisting of empty and fully filled regions that resemble the experimentally observed "self-bound insulator." In a harmonic trap, similar structures also emerge from phase coexistence associated with the underlying first-order transition.
Ultracold atomic gases in optical lattices provide an unique framework to study quantum phenomena in strongly correlated systems. In addition to the precise control over all relevant parameters in the experiment, these experiments can be mapped to a fundamental model from solid-state physics. For the bosonic version of this model, the so-called Bose-Hubbard model, a phase transition from a superfluid to a Mott insulator was theoretically predicted and later experimentally observed in an ultracold gas of Rb-87 atoms in three-dimensional as well as in one-dimensional optical lattices. Apart from homogeneous optical lattices one can introduce more complex lattice topologies such as two-color superlattices which give rise to a rich phase diagram including more exotic phases like the Bose-glass. We employ various powerful many-body techniques like exact diagonalization in complete and truncated Hilbert spaces and the Density-Matrix Renormalization Group (DMRG) algorithm to study the phase diagrams of the one-dimensional Bose-Hubbard and the one-dimensional Bose-Fermi-Hubbard Hamiltonian. Most theoretical studies of these systems discuss the phase diagrams with respect to the generic parameters of the Hubbard model. These Hubbard parameters, however, depend non-trivially on the control parameters used in experiments. The focus of this work is on the ab-initio calculation of the phase diagram of ultracold Rb-87 in one-dimensional optical superlattices starting directly from the experimental setup. To this end, we first employ band-structure calculations to extract the Hubbard parameters from the experimental parameters. Then, we use state-of-the-art DMRG techniques to solve the many-body problem for realistic particle numbers and lattice sizes that occur in experiments. Our results show that by using the intensities of the two laser fields forming the two-color superlattice as control parameters while keeping all other experimental parameters fixed, it is possible to access all relevant quantum phases of the system. Furthermore, we found out that the critical values of the laser intensities for the different phase transitions depend strongly on a third parameter that has to be included for a realistic description of the experiment. This third parameter is the strength of a harmonic trapping potential which accounts for the Gaussian shape of the laser fields and an additional magnetic potential used to confine the atoms in the center of the trap.
We present an analytic Bogoliubov description of a Bose-Einstein condensate of polar molecules trapped in a quasi-two-dimensional geometry and interacting via internal state-dependent dipole-dipole interactions. We derive the mean-field ground-state energy functional, and we derive analytic expressions for the dispersion relations, Bogoliubov amplitudes, and static structure factors. This method can be applied to any homogeneous, two-component system with linear coupling and direct, momentum-dependent interactions. The properties of the mean-field ground state, including polarization and stability, are investigated, and we identify three distinct instabilities: a density-wave rotonization that occurs when the gas is fully polarized, a spin-wave rotonization that occurs near zero polarization, and a mixed instability at intermediate fields. The nature of these instabilities is clarified by means of the real-space density-density correlation functions, which characterize the spontaneous fluctuations of the ground state, and the momentum-space structure factors, which characterize the response of the system to external perturbations. We find that the gas is susceptible to both density-wave and spin-wave responses in the polarized limit but only a spin-wave response in the zero-polarization limit. These results are relevant for experiments with rigid rotor molecules such as RbCs, $\mathrm{\ensuremath{\Lambda}}$-doublet molecules such as ThO that have an anomalously small zero-field splitting, and doublet-$\mathrm{\ensuremath{\Sigma}}$ molecules such as SrF where two low-lying opposite-parity states can be tuned to zero splitting by an external magnetic field.
We investigate the mean-field phase diagram of the Bose-Hubbard model with infinite-range interactions in two dimensions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and dispersively coupled to a cavity mode with the same wavelength as the lattice. We determine the ground-state phase diagram for a grand-canonical ensemble by means of analytical and numerical methods. Our results mostly agree with the ones reported in Dogra et al. [N. Dogra, F. Brennecke, S. D. Huber, and T. Donner, Phys. Rev. A 94, 023632 (2016)], and have a remarkable qualitative agreement with the quantum Monte Carlo phase diagrams of Flottat et al. [T. Flottat, L. de Forges de Parny, F. H\'ebert, V. G. Rousseau, and G. G. Batrouni, Phys. Rev. B 95, 144501 (2017)]. The salient differences concern the stability of the supersolid phases, which we discuss in detail. Finally, we discuss differences and analogies between the ground-state properties of all-connected bosons with the ones predicted for repulsively interacting dipolar bosons in two dimensions.