Ultracold atoms in 1D optical lattices: mean field, quantum field, computation, and soliton formation

  • Authors:

  • R. V. Mishmash;L. D. Carr

  • Affiliations:

  • Department of Physics, University of California, Santa Barbara, CA 93106, United States and Department of Physics, Colorado School of Mines, Golden, CO 80401, United States;Department of Physics, Colorado School of Mines, Golden, CO 80401, United States

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2009

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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 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.