Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices

TL;DR

This paper analyzes the absorption spectrum of strongly interacting bosons in disordered optical lattices, revealing that perturbation theory accurately describes the infrared absorption rate across all frequencies, with implications for experiments.

Contribution

It demonstrates that perturbation theory effectively models the absorption spectrum of disordered bosons in 1D lattices, including the Bose-glass phase, across all frequency regimes.

Findings

Infrared absorption rate is quadratic in frequency in the thermodynamic limit.

Perturbation theory describes the spectrum well at all frequencies.

Results are relevant for interpreting optical lattice experiments.

Abstract

We compute the absorption spectrum of strongly repulsive one-dimensional bosons in a disordered or quasi-periodic optical lattice. At commensurate filling, the particle-hole resonances of the Mott insulator are broadened as the disorder strength is increased. In the non-commensurate case, mapping the problem to the Anderson model allows us to study the Bose-glass phase. Surprisingly we find that a perturbative treatment in both cases, weak and strong disorder, gives a good description at all frequencies. In particular we find that the infrared absorption rate in the thermodynamic limit is quadratic in frequency. This result is unexpected, since for other quantities like the conductivity in one dimensional systems, perturbation theory is only applicable at high frequencies. We discuss applications to recent experiments on optical lattice systems, and in particular the effect of the harmonic trap.