Conductivity spectrum of ultracold atoms in an optical lattice

TL;DR

This study measures the conductivity spectrum of ultracold neutral fermions in an optical lattice, revealing how transport properties depend on system parameters and providing insights into dissipation and thermodynamics.

Contribution

It introduces a method to measure both real and imaginary conductivity spectra of ultracold atoms in an optical lattice, linking spectral features to thermodynamic and dissipative properties.

Findings

Conductivity decreases with increased effective mass.

High-temperature conductivity approaches a T-linear regime.

Finite lattice depth is necessary for current relaxation.

Abstract

We measure the conductivity of neutral fermions in a cubic optical lattice. Using in-situ fluorescence microscopy, we observe the alternating current resultant from a single-frequency uniform force applied by displacement of a weak harmonic trapping potential. In the linear response regime, a neutral-particle analogue of Ohm's law gives the conductivity as the ratio of total current to force. For various lattice depths, temperatures, interaction strengths, and fillings, we measure both real and imaginary conductivity, up to a frequency sufficient to capture the transport dynamics within the lowest band. The spectral width of the real conductivity reveals the current dissipation rate in the lattice, and the integrated spectral weight is related to thermodynamic properties of the system through a sum rule. The global conductivity decreases with increased band-averaged effective mass, which at high temperatures approaches a T-linear regime. Relaxation of current is observed to require a finite lattice depth, which breaks Galilean invariance and enables damping through collisions between fermions.