Finding the phase diagram of strongly-correlated disordered bosons using quantum quenches

TL;DR

This paper extends the use of quench spectroscopy to map the phase diagram of disordered Bose-Hubbard systems, distinguishing phases and probing rare regions through out-of-equilibrium dynamics.

Contribution

It introduces an in-depth analysis of quench spectral functions and demonstrates their effectiveness in identifying phases in disordered bosonic systems.

Findings

Quench spectroscopy distinguishes Mott insulator, superfluid, and Bose glass phases.

The phase diagram of disordered Bose-Hubbard is reconstructed using two experimental methods.

Spectral properties reveal information about rare regions in disordered systems.

Abstract

The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In arXiv:2105.05774 we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here, we extend this work by providing a more in-depth study of the behavior of the quench spectral functions associated to different observables and investigating an extended parameter regime. We provide a detailed introduction to quench spectroscopy for disordered systems and show how spectral properties can be probed using both local operators and two-point correlation functions. We benchmark the technique using the one-dimensional Bose-Hubbard model in the presence of a random external potential, focusing on the low-lying excitations, and demonstrate that quench spectroscopy can distinguish the Mott insulator, superfluid, and Bose glass phases. We then explicitly reconstruct the zero-temperature phase diagram of the disordered Bose-Hubbard at fixed filling using two independent methods, both experimentally accessible via time-of-flight imaging and quantum gas microscopy respectively, and demonstrate that quench spectroscopy can give valuable insights as to the distribution of rare regions within disordered systems.