Interaction-induced conducting–non-conducting transition of ultra-cold atoms in one-dimensional optical lattices

Chih-Chun Chien,Daniel Gruss,Michael Zwolak,Massimiliano Di Ventra

doi:10.1088/1367-2630/15/6/063026

Abstract

The study of time-dependent, many-body transport phenomena is increasingly within reach of ultra-cold atom experiments. We show that the introduction of spatially inhomogeneous interactions, e.g., generated by optically controlled collisions, induce negative differential conductance in the transport of atoms in one-dimensional optical lattices. Specifically, we simulate the dynamics of interacting fermionic atoms via a micro-canonical transport formalism within both a mean-field and a higher-order approximation, as well as with a time-dependent density-matrix renormalization group (DMRG). For weakly repulsive interactions, a quasi-steady-state atomic current develops that is similar to the situation occurring for electronic systems subject to an external voltage bias. At the mean-field level, we find that this atomic current is robust against the details of how the interaction is switched on. Further, a conducting–non-conducting transition exists when the interaction imbalance exceeds some threshold from both our approximate and time-dependent DMRG simulations. This transition is preceded by the atomic equivalent of negative differential conductivity observed in transport across solid-state structures.

Highlights

Advances in experimental studies of quantum transport of ultra-cold atoms in optical lattices [1,2,3,4,5] draw attention to different aspects of systems out of equilibrium
This, in turn, reveals interesting phenomena otherwise difficult to observe in conventional solid state systems
A key to realize interaction-induced transport is controllable inhomogeneous interactions – a novel possibility offered by optically tunable collisions of ultra-cold atoms

Summary

INTRODUCTION

Advances in experimental studies of quantum transport of ultra-cold atoms in optical lattices [1,2,3,4,5] draw attention to different aspects of systems out of equilibrium. A mean-field approximation predicts that this decrease leads to a conducting-to-nonconducting transition after the interaction strength exceeds some threshold (dependent on the filling). This transition may be explained by a mismatch of energy spectra between the interacting and non-interacting parts of the system, but this argument does not rule out other possible current-carrying states. The many-body negative differential conductance remains at all levels of approximation This is the counterpart to negative differential conductivity observed in solid-state structures [12, 13], where changes in the carrier density or subdivisions of the Brillouin zones cause non-monotonic dependence of the current on the external field strength. We focus on fermions but notice that, for the Bose-Hubbard model, Ref. [16] considers the sudden connection of a superfluid and a Mott insulator with different chemical potentials and found a mass current as well

INTERACTION-INDUCED TRANSPORT

RESULTS AND DISCUSSIONS

HIGHER-ORDER CORRELATIONS AND TD-DMRG

CONCLUSION