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Nonequilibrium Dynamics of Optical-Lattice-Loaded Bose-Einstein-Condensate Atoms: Beyond the Hartree-Fock-Bogoliubov Approximation



A M. Rey, B- L. Hu, E Calzetta, A Roura, Charles W. Clark


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 (BEC) 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 at NIST where the placement of atoms in an optical lattice is controlled by using an intermediate superlattice. This patterned loading method is a useful technique for the proposed implementation of AMO quantum computing. This system also provides an interesting theoretical arena for the study of quantum coherence and fluctuations phenomena in many body physics. The evolution of this system regarding its quantum coherence is of crucial importance in quantum computer onsiderations. It 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 stateconfiguration using the Bose- Hubbard Hamiltonian an exact quantum solution is available for this system in the case of few atomsand wells. One can also use it to test out the various approximation methods constructed. 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 multi-particle scattering in a systematic way, they are able to capture damping effects exhibited in the exact solution that a mean field collisionless approach fails to produce. While the second orderapproximations show a clear improvement over the HFB approximation our numerical result shows that they do not work so well at latetimes, when interaction effects are significant.
Physical Review A (Atomic, Molecular and Optical Physics)
69 No. 3


closed-time path (CTP), dynamics, Hartree-Fock-Bogoliubov approximation, HFB, optical lattice, two-particle irreducible (2PI)


Rey, A. , Hu, B. , Calzetta, E. , Roura, A. and Clark, C. (2004), Nonequilibrium Dynamics of Optical-Lattice-Loaded Bose-Einstein-Condensate Atoms: Beyond the Hartree-Fock-Bogoliubov Approximation, Physical Review A (Atomic, Molecular and Optical Physics) (Accessed May 28, 2023)
Created March 1, 2004, Updated February 17, 2017