Extracting information from non adiabatic dynamics: excited symmetric states of the Bose-Hubbard model

TL;DR

This paper introduces a Fourier transform method to extract low-energy many-body eigenstates from non-adiabatic dynamics in the Bose-Hubbard model, considering symmetry and disorder effects relevant to experiments.

Contribution

It presents a novel approach to analyze excited states in the Bose-Hubbard model using Fourier transforms and symmetry considerations, including disorder effects.

Findings

Successfully extracts eigenstates from time series data.

Provides classification of excitations without disorder.

Decomposes states into elementary one-particle processes.

Abstract

Using Fourier transform on a time series generated by unitary evolution, we extract many-body eigenstates of the Bose-Hubbard model corresponding to low energy excitations, which are generated when the insulator-superfluid phase transition is realized in a typical experiment. The analysis is conducted in a symmetric external potential both without and with and disorder. A simple classification of excitations in the absence disorder is provided. The evolution is performed assuming the presence of the parity symmetry in the system rendering many-body quantum states either symmetric or antisymmetric. Using symmetry-breaking technique, those states are decomposed into elementary one-particle processes.