Nonlinear Phenomenology from Quantum Mechanics: Soliton in a Lattice

TL;DR

This paper investigates quantum solitons in optical lattices with bosonic atoms, using numerical and Monte Carlo methods to connect quantum states with experimental measurements, revealing localized classical-like solitons amidst quantum noise.

Contribution

It introduces a combined numerical and Monte Carlo approach to study quantum solitons, explicitly linking quantum states with measurement outcomes in optical lattices.

Findings

Quantum Monte Carlo captures individual experimental outcomes.

Quantum states remain translationally invariant despite localized measurements.

Localized classical solitons emerge in noisy experimental observations.

Abstract

We study a soliton in an optical lattice holding bosonic atoms quantum mechanically using both an exact numerical solution and quantum Monte Carlo simulations. The computation of the state is combined with an explicit account of the measurements of the numbers of the atoms at the lattice sites. In particular, importance sampling in the quantum Monte Carlo method arguably produces faithful simulations of individual experiments. Even though the quantum state is invariant under lattice translations, an experiment may show a noisy version of the localized classical soliton.