Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices

TL;DR

This paper provides a comprehensive quantum many-body analysis of dark solitons in one-dimensional optical lattices, revealing quantum effects like soliton filling and inelastic collisions beyond mean-field theories.

Contribution

It introduces a fully quantum simulation of dark soliton dynamics in optical lattices using time-evolving block decimation, surpassing Bogoliubov approximations.

Findings

Quantum fluctuations fill in dark solitons over time.

Soliton collisions become inelastic due to quantum effects.

Natural orbital dynamics are explicitly calculated.

Abstract

We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [Phys. Rev. Lett. {\bf 103}, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.