Phases, many-body entropy measures and coherence of interacting bosons in optical lattices

TL;DR

This paper investigates quantum phases of interacting bosons in optical lattices using many-body entropy measures and correlation functions, demonstrating their effectiveness in characterizing superfluid, Mott-insulator, and fermionized phases.

Contribution

It introduces and applies many-body Shannon entropy measures to identify and distinguish quantum phases of bosons in optical lattices, linking entropy with spatial correlations.

Findings

Many-body entropy measures effectively characterize different quantum phases.

Single-particle entropy fails to detect phase transitions.

Glauber correlation functions corroborate entropy-based phase identification.

Abstract

Already a few bosons with contact interparticle interactions in small optical lattices feature a variety of quantum phases: superfluid, Mott-insulator and fermionized Tonks gases can be probed in such systems. To detect these phases -- pivotal for both experiment and theory -- as well as their many-body properties we analyze several distinct measures for the one-body and many-body Shannon information entropies. We exemplify the connection of these entropies with spatial correlations in the many-body state by contrasting them to the Glauber normalized correlation functions. To obtain the ground-state for lattices with commensurate filling (i.e. an integer number of particles per site) for the full range of repulsive interparticle interactions we utilize the multiconfigurational time-dependent Hartree method for bosons (MCTDHB) in order to solve the many-boson Schr\"odinger equation. We demonstrate that all emergent phases -- the superfluid, the Mott insulator, and the fermionized gas can be characterized equivalently by our many-body entropy measures and by Glauber's normalized correlation functions. In contrast to our many-body entropy measures, single-particle entropy cannot capture these transitions.