Phonon resonances in atomic currents through Bose-Fermi mixtures in optical lattices

TL;DR

This paper investigates how phonon resonances influence atomic currents in Bose-Fermi mixtures within optical lattices, revealing negative differential conductance and potential observability through numerical simulations.

Contribution

It introduces a theoretical framework for phonon-assisted hopping in tilted lattices and predicts observable phonon resonances in atomic currents.

Findings

Atomic current exhibits phonon resonances.

Negative differential conductance observed.

Resonances are detectable with realistic measurements.

Abstract

We present an analysis of Bose-Fermi mixtures in optical lattices for the case where the lattice potential of the fermions is tilted and the bosons (in the superfluid phase) are described by Bogoliubov phonons. It is shown that the Bogoliubov phonons enable hopping transitions between fermionic Wannier-Stark states; these transitions are accompanied by energy dissipation into the superfluid and result in a net atomic current along the lattice. We derive a general expression for the drift velocity of the fermions and find that the dependence of the atomic current on the lattice tilt exhibits negative differential conductance and phonon resonances. Numerical simulations of the full dynamics of the system based on the time-evolving block decimation algorithm reveal that the phonon resonances should be observable under the conditions of a realistic measuring procedure.