Bose-Einstein condensation in magnetic traps. Introduction to the theory

J. Rogel-Salazar, Seok Jin Choi, G.H.C. New +1 more

In this tutorial we present an introduction to some theoretical methods of quantum field theory applied to the description of a trapped Bose–Einstein condensate. First of all, we give a brief account of the main characteristics of the phenomenon of condensation and present the many-body Hamiltonian of the system. We outline some of the most important approaches used in the characterization of a condensed Bose gas, including the mean-field theory and the Hartree–Fock–Bogoliubov method. Finally we illustrate the use of these techniques addressing some important issues in quantum atom optics. We characterize the quantum state of a Bose–Einstein condensate (BEC) at zero temperature. We also describe a process of Beliaev coupling between quasiparticles using a method that includes terms beyond the usual Bogoliubov approach.

Claus Zimmermann, József Fortágh, Herwig Ott +2 more

Chen Ning Yang

Michael J. Steel, Weiping Zhang

Summary form only given. Since the experimental realization of Bose-Einstein condensation in the magnetically trapped quantum atomic gases, there have now been an enormous quantity of theory devoted to the properties of the trapped Bose-Einstein condensates (BEC). Motivated by the existing experiments, the bulk of the theoretical work has assumed a harmonic trap. Although recently a few papers have considered the consequences of exposing a BEC to a periodic optical potential, BEC confined in an optical lattice is still a new topic in this area. In the work, we develop theory to study the stationary and propagating properties of a Bose-Einstein condensate in an optical lattice. Instead of using an infinite optical lattice, we study the realistic case where the BEC is formed in a finite trapping potential and then is exposed to an infinite periodic potential created by off-resonance multiple laser beams.

Weiping Zhang, Daniel F. Walls

A three-component vector quantum field theory is developed to describe the electronic-spin-resonance interaction of a magnetically trapped Bose-Einstein condensate with a radio frequency field. The theory is directly applied to simulate the recent experiment of Mewes et al. for an output coupler for a Bose-Einstein condensate in a magnetic trap [Phys. Rev. Lett. 78, 582 (1997)]. By employing the mean-field approach, we study the collective dynamics of the multicomponent matter field via the nonlinear Schr\"odinger equation. Including the effect of gravity, we study the spin-resonance Rabi oscillations for the three-component Bose-Einstein condensate in three ground-state hyperfine levels and simulate the dynamic expansion of the condensate components coupled out of the magnetic trap.

Dan Stamper-Kurn, Dallin Durfee, M.‐O. Mewes +3 more