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arXiv:2112.10386 · Physical review. B./Physical review. B

Quantum phases of dipolar bosons in one-dimensional optical lattices

Rebecca Kraus, Titas Chanda, Jakub Zakrzewski, Giovanna Morigi

Published Jul 25, 2022• 12 citations
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Abstract

We theoretically analyze the phase diagram of a quantum gas of bosons that interact via repulsive dipolar interactions. The bosons are tightly confined by an optical lattice in a quasi-one-dimensional geometry. In the single-band approximation, their dynamics is described by an extended Bose-Hubbard model where the relevant contributions of the dipolar interactions consist of density-density repulsion and correlated tunneling terms. We evaluate the phase diagram for unit density using numerical techniques based on the density-matrix renormalization group algorithm. Our results predict that correlated tunneling can significantly modify the parameter range of the topological insulator phase. At vanishing values of the onsite interactions, moreover, correlated tunneling promotes the onset of a phase with a large number of low-energy metastable configurations.

DOI
10.1103/physrevb.106.035144

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We theoretically analyze the phase diagram of a quantum gas of bosons that interact via repulsive dipolar interactions. The bosons are tightly confined by an optical lattice in a quasi-one-dimensional geometry. In the single-band approximation, their dynamics is described by an extended Bose-Hubbard model where the relevant contributions of the dipolar interactions consist of density-density repulsion and correlated tunneling terms. We evaluate the phase diagram for unit density using numerical techniques based on the density-matrix renormalization group algorithm. Our results predict that correlated tunneling can significantly modify the parameter range of the topological insulator phase. At vanishing values of the onsite interactions, moreover, correlated tunneling promotes the onset of a phase with a large number of low-energy metastable configurations.
We determine the quantum ground state of dipolar bosons in a quasi-one-dimensional optical lattice and interacting via sss-wave scattering. The Hamiltonian is an extended Bose-Hubbard model which includes hopping terms due to the interactions. We identify the parameter regime for which the coefficients of the interaction-induced hopping terms become negative. For these parameters we numerically determine the phase diagram for a canonical ensemble and by means of density matrix renormalization group. We show that at sufficiently large values of the dipolar strength there is a quantum interference between the tunneling due to single-particle effects and the one due to the interactions. Because of this phenomenon, incompressible phases appear at relatively large values of the single-particle tunneling rates. This quantum interference cuts the phase diagram into two different, disconnected superfluid phases. In particular, at vanishing kinetic energy, the phase is always superfluid with a staggered superfluid order parameter. These dynamics emerge from quantum interference phenomena between quantum fluctuations and interactions and shed light into their role in determining the thermodynamic properties of quantum matter.
We study the phase diagram of the one-dimensional boson gas trapped inside an optical lattice with contact and dipolar interaction, taking into account next-nearest terms for both tunneling and interaction. Using the density-matrix renormalization group, we calculate how the locations of phase transitions change with increasing dipolar interaction strength for average density $\ensuremath{\rho}=1$. Furthermore, we show the emergence of pair-correlated phases for a large dipolar interaction strength and $\ensuremath{\rho}\ensuremath{\ge}2$, including a supersolid phase with an incommensurate density wave ordering manifesting the corresponding spontaneous breaking of the translational symmetry.
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.
We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state results from the interplay between the lattice geometry and the long-range interactions, which we account for by means of a classical spin mean-field approach limited by the size of the considered unit cells. This extended classical spin mean-field theory accounts for the long-range density-density interaction without truncation. We consider three different lattice geometries: square, honeycomb, and triangular. In the limit of zero hopping the ground state is always a devil’s staircase of solid (gapped) phases. Such crystalline phases with broken translational symmetry are robust with respect to finite hopping amplitudes. At intermediate hopping amplitudes, these gapped phases melt, giving rise to various lattice supersolid phases, which can have exotic features with multiple sublattice densities. At sufficiently large hoppings the ground state is a superfluid. The stability of phases predicted by our approach is gauged by comparison to the known quantum phase diagrams of the Bose-Hubbard model with nearest-neighbour interactions as well as quantum Monte Carlo simulations for the dipolar case on the square and triangular lattice. Our results are of immediate relevance for experimental realisations of self-organised crystalline ordering patterns in analogue quantum simulators, e.g., with ultracold dipolar atoms in an optical lattice.
We study the quantum ground state of ultracold bosons in a two-dimensional square lattice. The bosons interact via the repulsive dipolar interactions and sss-wave scattering. The dynamics is described by the extended Bose-Hubbard model including correlated hopping due to the dipolar interactions, and the coefficients are found from the second quantized Hamiltonian using the Wannier expansion with realistic parameters. We determine the phase diagram using the Gutzwiller ansatz in the regime where the coefficients of the correlated hopping terms are negative and can interfere with the tunneling due to single-particle effects. We show that this interference gives rise to staggered superfluid and supersolid phases at vanishing kinetic energy, while we identify parameter regions at finite kinetic energy where the phases are incompressible. We compare the results with the phase diagram obtained with the cluster Gutzwiller approach and with the results found in one dimension using the density-matrix renormalization group.
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.