Many-body effects in the excitation spectrum of weakly-interacting Bose-Einstein condensates in one-dimensional optical lattices

TL;DR

This paper investigates how quantum depletion influences the excitation spectrum of weakly-interacting Bose-Einstein condensates in one-dimensional optical lattices, revealing significant many-body effects beyond mean-field predictions.

Contribution

It introduces a linear-response approach based on MCTDHB to accurately analyze many-body excitations and demonstrates the importance of full many-body treatment even with minimal depletion.

Findings

Weak depletion (~1%) causes observable many-body effects in the spectrum.

Deviations from Bogoliubov-de Gennes predictions are significant.

Effects persist in larger lattice systems with more particles.

Abstract

In this work, we study many-body excitations of Bose-Einstein condensates (BECs) trapped in periodic one-dimensional optical lattices. In particular, we investigate the impact of quantum depletion onto the structure of the low-energy spectrum and contrast the findings to the mean-field predictions of the Bogoliubov-de Gennes (BdG) equations. Accurate results for the many-body excited states are obtained by applying a linear-response theory atop the MCTDHB (multiconfigurational time-dependent Hartree method for bosons) equations of motion, termed LR-MCTDHB. We demonstrate for condensates in a triple well that even weak ground-state depletion of around $1\%$ leads to visible many-body effects in the low-energy spectrum which deviate substantially from the corresponding BdG spectrum. We further show that these effects also appear in larger systems with more lattice sites and particles, indicating the general necessity of a full many-body treatment.