Ultracold Atoms in 1D Optical Lattices: Mean Field, Quantum Field, Computation, and Soliton Formation
arXiv:0810.2593 · doi:10.1016/j.matcom.2009.08.025
Abstract
In this work, we highlight the correspondence between two descriptions of a system of ultracold bosons in a one-dimensional optical lattice potential: (1) the discrete nonlinear Schrödinger 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 Schrödinger 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.
14 pages, 2 figures; to appear in Journal of Mathematics and Computers in Simulation
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Cited by in corpus (7)
- Non-standard Hubbard models in optical lattices: a review
- Ultracold bosons with short-range interaction in regular optical lattices
- Emergent Time Scale in Entangled Quantum Dynamics of Ultracold Molecules in Optical Lattices
- Dark solitons near the Mott-insulator--superfluid phase transition
- Solitary excitations in one-dimensional spin chains
- Semiclassical dynamics of a dark soliton in a one-dimensional bosonic superfluid in an optical lattice
- Simulating DNLS models