Ultracold atoms in 1D optical lattices: mean field, quantum field, computation, and soliton formation
In this work, we highlight the correspondence between two descriptions of a system of ultracold bosons in a one-dimensional optical lattice potential: (I) the discrete nonlinear Schrodinger equation, a discrete mean-field theory, and (2) the Bose-Hubbard Hamiltonian, a discrete quantum-field theory. The former is recovered from the latter in the limit of a product of local coherent states. Using a truncated form of these mean-field states as initial conditions, we build quantum analogs to the dark soliton solutions of the discrete nonlinear Schrodinger equation and investigate their dynamical properties in the Bose-Hubbard Hamiltonian. We also discuss specifics of the numerical methods employed for both our mean-field and quantum calculations, where in the latter case we use the time-evolving block decimation algorithm due to Vidal. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
soliton discrete nonlinear schrodinger equation bose-hubbard hamiltonian time-evolving block decimation entanglement