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arXiv:1901.09762 · Physical Review Letters

Disorderless Quasi-localization of Polar Gases in One-Dimensional Lattices

W. Li, Arya Dhar, Xiaolong Deng, Kenichi Kasamatsu, Luca Barbiero, Luis Santos

Published Jan 10, 2020• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.124.010404

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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.
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.
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.
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.
Strong enough intersite interactions may result in lack of ergodicity in disorder-free many-body lattice systems. Ultracold dipolar gases in optical lattices provide an experimentally accessible platform for exploring this physics. Dipolar intersite interactions are usually assumed to decay with a fixed power law. We show that in a one-dimensional polar lattice gas the actual decay depends on the transversal confinement. This affects profoundly the particle dynamics, which mimics rather that of a system with an externally controllable effective power-law interaction. Our results show that the crucial role of the interaction decay on disorder-free localization may be flexibly studied in experiments with polar gases.
The absence of energy dissipation leads to an intriguing out-of-equilibrium dynamics for ultracold polar gases in optical lattices, characterized by the formation of dynamically bound on-site and inter-site clusters of two or more particles, and by an effective blockade repulsion. These effects combined with the controlled preparation of initial states available in cold-gas experiments can be employed to create interesting out-of-equilibrium states. These include quasiequilibrated effectively repulsive 1D gases for attractive dipolar interactions and dynamically bound crystals. Furthermore, nonequilibrium polar lattice gases can offer a promising scenario for the study of quasi-many-body localization in the absence of quenched disorder. This fascinating out-of-equilibrium dynamics for ultracold polar gases in optical lattices may be accessible in on-going experiments.
Intersite dipolar interactions induce, even in absence of disorder, an intriguing nonergodic dynamics for dipolar bosons in an optical lattice. We show that the inherent dipole-induced density-dependent tunneling, typically neglected, plays a crucial role in this dynamics. For shallow-enough lattices, the delocalization stemming from the interaction-induced hopping overcomes the localization induced by intersite interactions. As a result, in stark contrast to the more studied case of hard-core bosons, delocalization is counterintuitively strengthened when the dipolar strength increases. Furthermore, the quasicancellation between bare and interaction-induced tunneling may lead, near a lattice-depth-dependent value of the dipole strength, to an exact decoupling of the Hilbert space between ergodic hard-core states and strongly nonergodic soft-core ones. Our results show that interaction-induced hopping should play a crucial role in future experiments on the dynamics of polar lattice gases.