Nonequilibrium dynamics of optical-lattice-loaded Bose-Einstein-condensate atoms: Beyond the Hartree-Fock-Bogoliubov approximation

Journal Article · Mon Mar 01 00:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.033610· OSTI ID:20640887

Rey, Ana Maria ^[1]; Hu, B L; Roura, Albert ^[1]; Calzetta, Esteban ^[2]; Clark, Charles W ^[3]

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1. Department of Physics, University of Maryland, College Park, Maryland 20742 (United States)
2. Universidad de Buenos Aires-Ciudad Universitaria, 1428 Buenos Aires (Argentina)
3. Electron and Optical Physics Division, National Institute of Standards and Technology, Technology Administration, U.S. Department of Commerce, Gaithersburg, Maryland 20899-8410 (United States)

In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose-Einstein condensate selectively loaded into every third site of a one-dimensional optical lattice. The motivation of this work is the recent experimental realization of this system. Patterned loading methods may be useful for quantum computing with trapped atoms. This system also serves to illustrate many basic issues in nonequilibrium quantum-field theory pertaining to the dynamics of quantum correlations and fluctuations which goes beyond the capability of a mean-field theory. By numerically evolving in time the initial-state configuration using the Bose-Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atoms and wells. One can also use it to test various approximate methods. Under the 2PI CTP scheme with this initial configuration, three different approximations are considered: (a) the Hartree-Fock-Bogoliubov (HFB) approximation (b) the next-to-leading-order 1/N expansion of the 2PI effective action up to second order in the interaction strength, and (c) a second-order perturbative expansion in the interaction strength. We present detailed comparisons between these approximations and determine their range of validity by contrasting them with the exact many-body solution for a moderate number of atoms and wells. As a general feature we observe that because the second-order 2PI approximations include multiparticle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution, which a mean-field collisionless approach fails to produce. While the second-order approximations show a clear improvement over the HFB approximation, our numerical results show that they fail at late times, when interaction effects are significant.

• OSTI ID: 20640887
• Journal Information: Physical Review. A, Vol. 69, Issue 3; Other Information: DOI: 10.1103/PhysRevA.69.033610; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ACTION INTEGRAL
ATOMS
BOSE-EINSTEIN CONDENSATION
CAPTURE
COMPARATIVE EVALUATIONS
COOLING
CORRELATIONS
DAMPING
EXACT SOLUTIONS
EXPANSION
FLUCTUATIONS
HAMILTONIANS
HARTREE-FOCK METHOD
HARTREE-FOCK-BOGOLYUBOV THEORY
INFORMATION THEORY
MANY-BODY PROBLEM
MEAN-FIELD THEORY
ONE-DIMENSIONAL CALCULATIONS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
SCATTERING
TRAPPING