This thesis is devoted to the study of dipolar lattice gases, i.e. many-body quantum systems of particles with a strong magnetic or electric dipole moment in optical lattices. Such systems are adequately described by the extended Hubbard model, which accounts for inter-site dipole-dipole interactions (DDI). These interactions, due to their long-range and anisotropic character, result in rich groundstate physics and intriguing dynamics as we illustrate in this thesis for the particular case of bosons in one- and quasi-one-dimensional lattices. We start by focusing on the non-trivial role played by the transversal confinement in one-dimensional dipolar lattice gases. We show that weakening the transversal confinement enhances beyond-nearest-neighbor interactions. Then, we analyze how this affects the ground-state physics of hard-core bosons with repulsive dipolar interactions and reveal quantitative differences to the standard case of the DDI falling off as 1/r^3 where r is the inter-particle distance. With attractive interactions, a new quantum liquid phase of self-bound lattice droplets emerges without the need for super-exchange processes. In the soft-core regime, proper consideration of the transversal confinement not only quantitatively shifts phase boundaries, but introduces novel phases with peculiar correlations in the site occupancies that may be either topological or topologically trivial. Furthermore, we study the effect of the transversal confinement on the dynamical properties of one-dimensional hard-core bosons at half-filling. We show in particular that the localization-to-delocalization transition induced by Hilbert space fragmentation resembles that of a system with an effective power-law decay different from 1/r^3 which can be controlled by the transversal confinement. To conclude this thesis, we analyze ground-state properties of hard-core dipolar bosons in a square ladder at unit rung filling with an energy bias between the two legs. We show that the interplay between the energy bias and the dipolar tail results in a peculiar topological quantum floating phase.
Polar lattice gases are usually assumed to have an intersite interaction that decays with the interparticle distance
r as
1/r3. However, a loose-enough transversal confinement may strongly modify the dipolar decay in one-dimensional lattices. We show that this modification alters significantly the ground-state properties of hard-core dipolar bosons. For repulsive intersite interactions, the corrected decay alters the conditions for devil's staircase insulators, affecting significantly the particle distribution in the presence of an overall harmonic confinement. For attractive interactions, it results in a reduction of the critical dipole interaction for the formation of self-bound clusters, and for a marked enhancement of the region of liquefied lattice droplets.
Recent experiments on ultracold dipoles in optical lattices open exciting possibilities for the quantum simulation of extended Hubbard models. When considered in one dimension, these models present at unit filling a particularly interesting ground-state physics, including a symmetry-protected topological phase known as Haldane insulator. We show that the tail of the dipolar interaction beyond nearest-neighbors, which may be tailored by means of the transversal confinement, does not only modify quantitatively the Haldane insulator regime and lead to density waves of larger periods, but results as well in unexpected insulating phases. These insulating phases may be topological or topologically trivial, and are characterized by peculiar correlations of the site occupations. These phases may be realized and observed in state-of-the-art experiments.
One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically bound nearest-neighbor dimers enhances the role of the 1/r^{3} dipolar tail, resulting in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.
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.
The disorder-free localization that occurred in the study of relaxation dynamics in far-from-equilibrium quantum systems has been widely explored. Here we investigate the interplay between the dipole-dipole interaction (DDI) and disorder in the hard-core polar bosons in a one-dimensional lattice. We find that the localized dynamics will eventually thermalize in the clean gas but can be stabilized with the existence of a small disorder proportional to the inverse of DDI strength. From the effective dimer Hamiltonian, we show that the effective second-order hopping of quasiparticles between nearest-neighbor sites is suppressed by the disorder with strength similar to the effective hopping amplitude. The significant gap between the largest two eigenvalues of the entanglement spectrum indicates the dynamical confinement. We also find that the disorder related sample-to-sample fluctuation is suppressed by the DDI. Finally, we extend our research from the uncorrelated random disorder to the correlated quasiperiodic disorder and from the two-dimer model to the half-filling system, obtaining similar results.
We study by quantum Monte Carlo simulations the low-temperature phase diagram of dipolar bosons confined to one dimension, with dipole moments aligned along the direction of particle motion. A hard-core repulsive potential of varying range ($\ensuremath{\sigma}$) is added to the dipolar interaction, in order to ensure stability of the system against collapse. In the $\ensuremath{\sigma}\ensuremath{\rightarrow}0$ limit the physics of the system is dominated by the potential energy and the ground state is quasicrystalline; as $\ensuremath{\sigma}$ is increased the attractive part of the interaction weakens and the equilibrium phase evolves from quasicrystalline to a nonsuperfluid liquid. At a critical value ${\ensuremath{\sigma}}_{c}$, the kinetic energy becomes dominant and the system undergoes a quantum phase transition from a self-bound liquid to a gas. In the gaseous phase with $\ensuremath{\sigma}\ensuremath{\rightarrow}{\ensuremath{\sigma}}_{c}$, at low density attractive interactions bring the system into a ``weak'' superfluid regime. However, gas-liquid coexistence also occurs, as a result of which the topologically protected superfluid regime is not approached.