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arXiv:1203.5094 · New Journal of Physics

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

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

Published Jun 19, 2013• 25 citations
arXivHTMLPDF

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.

DOI
10.1088/1367-2630/15/6/063026

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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.
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We show that the recently developed optical lattices with Peierls substitution---which can be modeled as a lattice with a complex tunneling coefficient---may be used to induce controllable quantum transport of ultracold atoms. In particular, we show that by ramping up the phase of the complex tunneling coefficient in a spatially uniform fashion, a finite quasi-steady-state current (QSSC) ensues from the exact dynamics of noninteracting fermions. The direction and magnitude of the current can be controlled by the overall phase difference but not the details of the ramp. The entanglement entropy does not increase when the QSSC lasts. Due to different spin statistics, condensed noninteracting bosons do not support a finite QSSC under the same setup. We also find that an approximate form of the QSSC survives when perturbative effects from interactions, weak harmonic background traps, and finite temperature are present, which suggests that our findings should be observable with available experimental capabilities.
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We propose a setup in which Andreev-like reflections predicted for 1D transport systems could be observed time dependently using cold atoms in a 1D optical lattice. Using time-dependent density matrix renormalization group methods we analyze the wave packet dynamics as a density excitation propagates across a boundary in the interaction strength. These phenomena exhibit good correspondence with predictions from Luttinger liquid models and could be observed in current experiments in the context of the Bose-Hubbard model.
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