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arXiv:2210.02470 · Physical review. B./Physical review. B

Dipole condensates in tilted Bose-Hubbard chains

Ethan Lake, Hyun‐Yong Lee, Jung Hoon Han, T. Senthil

Published May 16, 2023• 42 citations
arXivHTMLPDF

Abstract

The authors study a Bose-Hubbard model whose dynamics conserves the total center of mass, a situation which arises in strongly tilted optical lattices. Center of mass conservation is shown to dramatically alter the nature of the quantum phase diagram, which hosts several types of unusual gapless phases. These results hint at a wealth of interesting phenomena waiting to be uncovered in the physics of kinetically constrained many-body systems.

DOI
10.1103/physrevb.107.195132

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•Jan 1, 2011•0 citations
The authors study a Bose-Hubbard model whose dynamics conserves the total center of mass, a situation which arises in strongly tilted optical lattices. Center of mass conservation is shown to dramatically alter the nature of the quantum phase diagram, which hosts several types of unusual gapless phases. These results hint at a wealth of interesting phenomena waiting to be uncovered in the physics of kinetically constrained many-body systems.
We study Fermi-Hubbard models with kinetically constrained dynamics that conserves both total particle number and total center of mass, a situation that arises when interacting fermions are placed in strongly tilted optical lattices. Through a combination of analytics and numerics, we show how the kinetic constraints stabilize an exotic non-Fermi liquid phase described by fermions coupled to a gapless bosonic field, which in several respects mimics a dynamical gauge field. This offers a novel route towards the study of non-Fermi liquid phases in the precision environments afforded by ultracold atom platforms.
We study a simple model of interacting bosons on a ddd-dimensional cubic lattice whose dynamics conserves both total boson number and total boson dipole moment. This model provides a simple framework in which several remarkable consequences of dipole conservation can be explored. As a function of chemical potential and hopping strength, the model can be tuned between gapped Mott insulating phases and various types of gapless condensates. The condensed phase realized at large hopping strengths, which we dub a Bose-Einstein insulator, is particularly interesting: despite having a Bose condensate, it is insulating, and despite being an insulator, it is compressible.
When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such constrained dynamics by realizing a dipole-conserving Bose-Hubbard model, where single atoms are immobile but pairs of particles can move cooperatively while preserving the system's center of mass, i.e. the overall dipole moment of the particle distribution. Starting from a one-dimensional chain of ultracold bosonic atoms in an optical lattice, we generate localized dipole excitations consisting of a hole and a doublon using site-resolved optical potentials and characterize their quantum walks and scattering dynamics. Our study provides a bottom-up investigation of a Hamiltonian with kinetic constraints, and paves the way for exploring low-energy phases of fractonic matter in existing experimental platforms.
Fractonic constraints can lead to exotic properties of quantum many-body systems. Here, we investigate the dynamics of fracton excitations on top of the ground states of a one-dimensional, dipole-conserving Bose-Hubbard model. We show that nearby fractons undergo a collective motion mediated by exchanging virtual dipole excitations, which provides a powerful dynamical tool to characterize the underlying ground-state phases. We find that, in the gapped Mott insulating phase, fractons are confined to each other as motion requires the exchange of massive dipoles. When crossing the phase transition into a gapless Luttinger liquid of dipoles, fractons deconfine. Their transient deconfinement dynamics scales diffusively and exhibits strong but subleading contributions described by a quantum Lifshitz model. We examine prospects for the experimental realization in tilted Bose-Hubbard chains by numerically simulating the adiabatic state preparation and subsequent time evolution and find clear signatures of the low-energy fracton dynamics.
Observations of center-of-mass dynamics offer a straightforward method to identify strongly interacting quantum phases of atoms placed in optical lattices. We theoretically study the dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center-of-mass motion even with insulating states in the center. We identify short- and long-time-scale mechanisms for edge-state transport in insulating phases. We also argue that the center-of-mass velocity can aid in identifying a Bose-glass phase. Our zero-temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center-of-mass dynamics expected at nonzero temperature.
In Chapter 1 we set up the physical and mathematical framework for the description of interacting bosons on a lattice. After a brief introduction to the basic concepts of Bose-Einstein condensation, and how the condensate can be manipulated using optical lattices, we derive the Bose-Hubbard Hamiltonian (BHH) which is the paradigm model as far as the quantum description is concerned. Then the semiclassical limit of the BHH – the discrete nonlinear Schroedinger equation (DNLS) – as well as the mean-field (classical) description, the so-called Gross-Pitaevskii equation (GPE), is discussed. We give an overview of the relevant literature and of the various physical systems that are captured by the BHH including, among others, arrays of Josephson junctions and bond vibrations in small molecules. The chapter ends with an outline of the remaining thesis. In Chapter 2, we look at some interesting experiments done in cold bosonic systems. Ostensibly, done to realize the dc and ac Josephson effect in a system of cold bosons, it was soon found that the system can show some rather interesting non-linear behavior. This includes features such as solitons and breathers , but most interestingly, it shows the damping of the center-of-mass motion. Theoretical explanations are given for both the experiments. The damping of center-of-mass of the system is seen as a result of modulational instability. We give a different interpretation to this opening up lines for further investigations. We outline these at the end of the chapter. In Chapter 3, we discuss various experiments which contradicted the idea of a sharp modulational instability. Rather, the loss of coherence is smeared out over a large domain. We then reproduce some calculations from the literature showing how the dissipation can be thought of as arising from quantum phase slips. We calculate the tunneling rates for quantum phase slips and show a phase diagram demarcating stable and unstable regions of current which have been have obtained from mean-field calculations via the Gutzwiller ansatz. In Chapter 4, we look at the problem in details analyzing it as a Tomonaga-Luttinger liquid. The framework of Tomonaga-Luttinger liquid is actually a non-perturbative tool through which we can investigate an one-dimensional interacting bosonic fluid. We look at two possible mechanisms of decay of current- We look at the effect of a weak link in a Josephson Junction array as well as local quantum phase slips on a bosonic superfluid. We find that quantum phase slips are actually irrelevant under renormalisation group in both cases and the supercurrent is revived. In chapter 5, we look at the non-linear dynamics of the structures in greater detail, thus elucidating chaos. This mechanism of chaos is different from all realizations of chaos known so far and is a result of phase fluctuations, which are encoded by quantum phase slips.