Harmonic Interaction Model and Its Applications in Bose–Einstein Condensation

Graeme Whyte, Patrik Öhberg, Johannes Courtial

We investigate the property of isotropic harmonic traps to Fourier transform a weakly interacting Bose–Einstein condensate (BEC) every quarter of a trap period. We solve the Gross–Pitaevskii equation numerically to investigate the time evolution of interacting BECs in the context of the Fourier transform, and we suggest potential applications.

William J. Mullin

Li Hao-Cai, Chen Hai-Jun, Xue Ju-Kui

The transition temperature, the depletion of the condensate atoms and the collective excitations of a Bose–Einstein condensation (BEC) with two- and three-body interactions in an anharmonic trap at finite temperature are studied in detail. By using the Popov version of the Hartree–Fock–Bogoliubov (HFB) approximation, an extended self-consistent model describing BEC with both two- and three-body interactions in a distorted harmonic potential at finite temperature is obtained and solved numerically. The results show that the transition temperature, the condensed atom number and the collective excitations are modified dramatically by the atomic three-body interactions and the distortion of the harmonic trap.

Adelchi Fabrocini

Alfred M. Levine, Anatoly B. Kuklov

The effect of Bose-Einstein condensation, achieved recently for alkaline gases in magnetic traps, should lead to a strong enhancement of non-linear harmonic generation. A nearly resonant light imposed on the gas of two-level atoms excites the intra-atomic transitions and causes generation of various harmonics. Normally, in the thermal state of the gas, a contribution of the inter-atomic interaction to the non-linear harmonic generation is negligible. However, if a Bose-Einstein condensate (BEC) is present, the inter-particle interaction cannot be ignored. Considering second harmonic generation, we show that, in the presence of the BEC, the intensity of the second harmonic is proportional to (aN n)/sup 2/, where N and n are the total number and the effective density of the condensed atoms, respectively, and a stands for the scattering length describing the process of scattering of two excited atoms by each other so that, after the collision, one excited atom enters the condensate. We consider the interaction between light, represented by the electric field E, and the atomic Bose field /spl Psi/ as well as the two body interaction treated within the scattering length approximation.

Hasan TATLIPINAR, Seçkin D. Günay