By using a correlated many body method and using the realistic van der Waals potential we study several statistical measures like the specific heat, transition temperature and the condensate fraction of the interacting Bose gas trapped in an anharmon
ic potential. As the quadratic plus a quartic confinement makes the trap more tight, the transition temperature increases which makes more favourable condition to achieve Bose-Einstein condensation (BEC) experimentally. BEC in 3D isotropic harmonic potential is also critically studied, the correction to the critical temperature due to finite number of atoms and also the correction due to inter-atomic interaction are calculated by the correlated many-body method. Comparison and discussion with the mean-field results are presented.
A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum limit of
the entropy uncertainty relation (EUR) is approached by making $N$ very small in our numerical work. We examine the effect of correlations in the calculation of information entropy. Comparison with the mean-field result shows that the correlated basis function is indeed required to characterize the important features of the information entropies. We also accurately calculate the point of critical instability of an attractive BEC, which is in close agreement with the experimental value. Next we calculate two-body entropies in position and momentum spaces and study quantum correlations in the attractive BEC.
We propose a novel mathematical approach for the calculation of near-zero energy states by solving potentials which are isospectral with the original one. For any potential, families of strictly isospectral potentials (with very different shape) havi
ng desirable and adjustable features are generated by supersymmetric isospectral formalism. The near-zero energy Efimov state in the original potential is effectively trapped in the deep well of the isospectral family and facilitates more accurate calculation of the Efimov state. Application to the first excited state in 4He trimer is presented.
We study coherence of a trapped bosonic cloud with attractive finite-range interaction in a tight harmonic trap. One-body density and pair-distribution function in the ground state for different trap sizes are calculated. We also calculate healing le
ngth and the correlation length which signify the presence of high spatial coherence in a very tight trap leading to the destruction of the condensate for a fixed particle number. This is in marked variance with the usual collapse of the attractive metastable condensate when N > Ncr . Thus we investigate the critical frequency and critical size of the trap for the existence of attractive Bose-Einstein condensation. The finite-range interaction gives a nonlocal effect in the effective many-body potential, and we observe a high-density stable branch besides the known metastable branch. Moreover, the new branch shows universal behavior even in the very tight trap.
A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to infinite traps commonly used). The realistic van der Waals interaction is adopted as th
e interatomic interaction. We calculate experimentally measurable decay rates of the lowest quasi-bound state in the shallow trap. The most striking result is the observation of a new metastable branch besides the usual one for attractive BEC in a pure harmonic trap. As the particle number increases the new metastable branch appears, then gradually disappears and finally usual metastable branch (associated with the attractive BEC in a harmonic trap) appears, eventually leading to the collapse of the condensate.
