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Evidence for Metallic Behavior in an Atomic Bose-Hubbard System

David C. McKay, Matt White, Matthew Pasienski, Brian DeMarco

Published Aug 22, 2007• 0 citations
OpenAlex

Abstract

We have observed a metallic-like state, which persists to the zerotemperature limit, in a 3D Bose-Hubbard system of ultra-cold atoms trapped in an optical lattice. The damping rate of atomic motion— the analog of electrical resistance in a solid—in the confining parabolic potential fits well to a model that includes finite damping at zero temperature. The low-temperature behavior is consistent with the theory of quantum tunneling of phase slips, while at higher temperatures a cross-over consistent with the transition between quantum tunneling and thermal activation of phase slips is evident. The existence of a metallic phase in a bosonic system may have implications for the unusual dissipative phases apparent in solid-state superconducting films. The ground state of a system of bosons is predicted to be either superconducting or insulating (1). However, experiments on superconducting films have shown that a dissipative phase can exist to the lowest temperatures attainable. For example, experiments on

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We have observed a metallic-like state, which persists to the zerotemperature limit, in a 3D Bose-Hubbard system of ultra-cold atoms trapped in an optical lattice. The damping rate of atomic motion— the analog of electrical resistance in a solid—in the confining parabolic potential fits well to a model that includes finite damping at zero temperature. The low-temperature behavior is consistent with the theory of quantum tunneling of phase slips, while at higher temperatures a cross-over consistent with the transition between quantum tunneling and thermal activation of phase slips is evident. The existence of a metallic phase in a bosonic system may have implications for the unusual dissipative phases apparent in solid-state superconducting films. The ground state of a system of bosons is predicted to be either superconducting or insulating (1). However, experiments on superconducting films have shown that a dissipative phase can exist to the lowest temperatures attainable. For example, experiments on
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The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap and in optical superlattices are presented.
Quantum simulations are quickly becoming an indispensable tool for studying particle transport in correlated lattice models. One of the central topics in the study of transport is bad-metal behavior, characterized by the direct-current resistivity linear in temperature. In the fermionic Hubbard model, optical conductivity has been studied extensively, and a recent optical lattice experiment demonstrated bad-metal behavior in qualitative agreement with theory. Far less is known about transport in the bosonic Hubbard model. We investigate the conductivity in the Bose-Hubbard model and focus on the regime of strong interactions and high temperatures. We use numerically exact calculations for small lattice sizes. At weak tunneling, we find multiple peaks in the optical conductivity that stem from the Hubbard bands present in the many-body spectrum. This feature slowly washes out as the tunneling rate gets stronger. At high temperature, we identify a regime of TTT-linear resistivity, as expected. When the interactions are very strong, the leading inverse-temperature coefficient in conductivity is proportional to the tunneling amplitude. As the tunneling becomes stronger, this dependence takes quadratic form. At very strong coupling and half filling, we identify a separate linear resistivity regime at lower temperature, corresponding to the hard-core boson regime. Additionally, we unexpectedly observe that at half filling, in a big part of the phase diagram, conductivity is an increasing function of the coupling constant before it saturates at the hard-core-boson result. We explain this feature based on the analysis of the many-body energy spectrum and the contributions to conductivity of individual eigenstates of the system.
We study the quantum (zero-temperature) critical behaviors of confined particle systems described by the one-dimensional (1D) Bose-Hubbard model in the presence of a confining potential, at the Mott insulator to superfluid transitions, and within the gapless superfluid phase. Specifically, we consider the hard-core limit of the model, which allows us to study the effects of the confining potential by exact and very accurate numerical results. We analyze the quantum critical behaviors in the large trap-size limit within the framework of the trap-size scaling (TSS) theory, which introduces a new trap exponent $\ensuremath{\theta}$ to describe the dependence on the trap size. This study is relevant for experiments of confined quasi-1D cold atom systems in optical lattices. At the low-density Mott transition, TSS can be shown analytically within the spinless fermion representation of the hard-core limit. The trap-size dependence turns out to be more subtle in the other critical regions, when the corresponding homogeneous system has a nonzero filling fff, showing an infinite number of level crossings of the lowest states when increasing the trap size. At the n=1n=1n=1 Mott transition, this gives rise to a modulated TSS: The TSS is still controlled by the trap-size exponent $\ensuremath{\theta}$, but it gets modulated by periodic functions of the trap size. Modulations of the asymptotic power-law behavior is also found in the gapless superfluid region, with additional multiscaling behaviors.