Ever since the first observation of Bose-Einstein condensation in the nineties, ultracold quantum gases have been the subject of intense research, providing a unique tool to understand the behavior of matter governed by the laws of quantum mechanics. Ultracold bosonic atoms loaded in an optical lattice are usually described by the Bose-Hubbard model or a variant of it. In addition to the common insulating and superfluid phases, other phases (like density waves and supersolids) may show up in the presence of a short-range interparticle repulsion and also depending on the geometry of the lattice. We herein explore this possibility, using the graph of a convex polyhedron as "lattice" and playing with the coordination of nodes to promote the wanted finite-size ordering. To accomplish the job we employ the method of decoupling approximation, whose efficacy is tested in one case against exact diagonalization. We report zero-temperature results for two Catalan solids, the tetrakis hexahedron and the pentakis dodecahedron, for which a thorough ground-state analysis reveals the existence of insulating "phases" with polyhedral order and a widely extended supersolid region. The key to this outcome is the unbalance in coordination between inequivalent nodes of the graph. The predicted phases can be probed in systems of ultracold atoms using programmable holographic optical tweezers.
We analyze the energy spectrum of the three-site Bose-Hubbard model. It is shown that this spectrum is a mixture of the regular and irregular spectra associated with the regular and chaotic components of the classical Bose-Hubbard model. We find relative volumes of these components by using the pseudoclassical approach. Substituting these values in the Berry-Robnik distribution for the level spacing statistics we obtain good agreement with the numerical data.
We show that the Bose-Hubbard approximation fails due to the emergence of chaos, even when excited modes are far detuned and the standard validity condition is satisfied. This is formally identical to the Melnikov-Arnold analysis of the stochastic pump model. Previous numerical observations of Bose-Hubbard breakdown are precisely reproduced by our simple model and can be attributed to many body enhancement of chaos.
The long-range and anisotropic nature of the dipolar interaction provides the so-called supersolid phases in Bose-Einstein condensates (BECs) in an optical lattice. However, in a certain area of dipole interaction parameters, BECs can form into a droplet. In this paper, in order to qualitatively understand the droplet formations, we propose a toy model that allows us to estimate the size and shape of droplets in dipolar Bose-Hubbard system in the optical lattice. We compare results of the toy model with numerical solutions of the mean-field calculation.
We develop a novel approach to understand the phases of one-dimensional Bose-Hubbard models. We integrate the simplicity of the mean-field theory and the numerical power of the density matrix renormalization group method to build an effective numerical technique with moderate computational resources to determine superfluid order parameters and correlation functions of large one-dimensional systems. We demonstrate the applicability of this method to directly identify superfluid, Mott insulator, and density wave phases in Bose-Hubbard models.
Using a field-theoretic approach within the Schwinger-Keldysh formalism, we study a Bose-Hubbard model in the presence of a driving field and dissipation due to one-body losses. We recover the bistability diagram from the Gross-Pitaevski equation and analyze the different phases with respect to their elementary excitations and correlations. We find the low-density solution to be subdivided into a dynamically instable, a gapped, and a gapless regime. The correlations decay exponentially, but a substantial increase of correlation length marks the regime of gapless excitations.
The spin squeezing protocols allow the dynamical generation of massively correlated quantum many-body states, which can be utilized in entanglement-enhanced metrology and technologies. We study a quantum simulator generating twisting dynamics realized in a two-component Bose-Hubbard model with dipolar interactions. We show that the interplay of contact and long-range dipolar interactions between atoms in the superfluid phase activates the anisotropic two-axis counter-twisting mechanism, accelerating the spin squeezing dynamics and allowing the Heisenberg-limited accuracy in spectroscopic measu…
We study the dynamics of an interacting Bose-Hubbard chain coupled to a non-Markovian environment. Our basic tool is the reduced generating functional expressed as a path integral over spin-coherent states. We calculate the leading contribution to the corresponding effective action, and by minimizing it, we derive mean-field equations that can be numerically solved. With this tool at hand, we examine the influence of the system's initial conditions and interparticle interactions on the dissipative dynamics. Moreover, we investigate the presence of memory effects due to the non-Markovian enviro…
