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arXiv:2012.02663 · Physical Review A

Cluster dynamics in two-dimensional lattice gases with intersite interactions

Wei-Han Li, Arya Dhar, Xiaolong Deng, Luis Santos

Published Apr 23, 2021• 13 citations
arXivHTMLPDF

Abstract

Sufficiently strong intersite interactions in extended-Hubbard and XXZ spin models result in dynamically bound clusters at neighboring sites. We show that the dynamics of these clusters in two-dimensional lattices is remarkably different and richer than that of repulsively bound on-site clusters in gases without intersite interactions. Whereas on-site pairs move in the same lattice as individual particles, nearest-neighbor dimers perform an interacting quantum walk in a different lattice geometry, leading to a peculiar dynamics characterized by multiple timescales. Although this is generally true, it is especially relevant in some lattices, including triangular and diamond lattices for hard-core bosons, and square lattices for soft-core bosons, where dimers move resonantly in either a kagome or a Lieb lattice. As a result, dimers show two very different transport velocities---a fast one comparable to the motion of individual particles, and a very slow one associated to flatband quasilocalization. Moreover, these lattices permit the resonant motion of longer clusters, and, remarkably, trimers move faster than quasi-flatband dimers for sufficiently strong optical lattices. This rich interplay between multiscaled quantum walk dynamics, quasilocalization, and flatband physics may be readily observed in experiments with lanthanide atoms.

DOI
10.1103/physreva.103.043331

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Sufficiently strong intersite interactions in extended-Hubbard and XXZ spin models result in dynamically bound clusters at neighboring sites. We show that the dynamics of these clusters in two-dimensional lattices is remarkably different and richer than that of repulsively bound on-site clusters in gases without intersite interactions. Whereas on-site pairs move in the same lattice as individual particles, nearest-neighbor dimers perform an interacting quantum walk in a different lattice geometry, leading to a peculiar dynamics characterized by multiple timescales. Although this is generally true, it is especially relevant in some lattices, including triangular and diamond lattices for hard-core bosons, and square lattices for soft-core bosons, where dimers move resonantly in either a kagome or a Lieb lattice. As a result, dimers show two very different transport velocities---a fast one comparable to the motion of individual particles, and a very slow one associated to flatband quasilocalization. Moreover, these lattices permit the resonant motion of longer clusters, and, remarkably, trimers move faster than quasi-flatband dimers for sufficiently strong optical lattices. This rich interplay between multiscaled quantum walk dynamics, quasilocalization, and flatband physics may be readily observed in experiments with lanthanide atoms.
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.
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.
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Emerging dynamical constraints resulting from intersite interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the 1/r^{3} tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body localization is within reach of future experiments with magnetic atoms and polar molecules.
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One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.