Variational Theories with Many-Body Correlations for Dilute Bose–Einstein Condensates

航 河野

正仁 上田, Masahito Ueda

Brett D. Esry

Anasuya Kundu

Shorttitle: The first experimental achievement of Bose Einstein condensation (BEC) in dilute alkali gases in 1995 has developed a renewed interest both theoretical and experimental. Lot of work has already been done over the last decade to study the different aspects of this condensation, mainly based on mean-field theories, hyperspherical approaches and quantum Monte Carlo methods. This thesis work presents an approximate many-body approach to investigate mainly the static (ground state) properties of the condensate, incorporating realistic inter-atomic interactions. Potential harmonic expansion method (PHEM), which includes two-body correlations only and disregards three or higher body correlations, has been adopted to analyze this condensate. This is ideally suited for BEC, which is required to be extremely dilute for its experimental realization. This treatment and analysis should be useful for the physics community especially working with weakly interacting ultra cold atoms, bosons and fermions as well.

S. A. Sofianos, Tapan Kumar Das, Barnali Chakrabarti +3 more

A two-body correlated basis set is used to develop a many-body theory which is valid for any number of bosons in the trap. The formalism incorporates the van der Waals interaction and two-body correlations in an exact way. The theory has successfully been applied to Bose-Einstein condensates---dilute weakly interacting and also dilute but having a large scattering length. Even in the extreme dilute condition, we observe the breakdown of the shape-independent approximation and the interatomic correlation plays an important role in the large particle-number limit. This correlated many-body calculation can handle, within the two-body correlation approximation, the entire range of atom number of experimentally achieved condensates. Next we successfully push the basis function for large scattering lengths where the mean-field results are manifestly bad. The sharp increase in correlation energy clearly shows the beyond-mean-field effect. We also calculate one-particle densities for various scattering lengths and particle numbers. Our many-body calculation exhibits the finite-size effect in the one-body density.

Marvin D. Girardeau, Ewan M. Wright

A number-conserving hybrid Bose-Fermi variational theory is developed and applied to investigation of the Bose-Einstein condensate crossover to the Tonks gas in toroidal and long cylindrical traps of high aspect ratio, where strong many-body correlations and condensate depletion occur.