Soliton in a lattice derived from quantum mechanics

Starting from the tenet that measurements are the agent that calls forth nonlinear phenomenology from linear quantum mechanics, we study solitons in an optical lattice carrying a Bose-Einstein condensate. We juxtapose the Bose-Hubbard model and the corresponding classical model. For certain parameter values the stationary lowest-energy state of the classical model is a localized soliton, while the quantum mechanical ground state is translationally invariant. However, if the numbers of the atoms at each lattice site are measured, a distribution of the atoms closely resembling the classical soliton is found. We demonstrate this with a Quantum Monte Carlo (QMC) analysis of the ground state, noting that every sample obtained from our particular QMC method is also a faithful simulation of what a measurement would give for the atom numbers at the lattice sites.