Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons

Abstract

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.

Accepted in Physical Review A (2013)

References in corpus (5)

• Resonance States and Quantum Tunneling of Bose Einstein condensates in a 3D shallow trap
• Stability of attractive bosonic cloud with van der Waals interaction
• Destruction of attractive bosonic cloud due to high spatial coherence in tight trap
• Bose atoms in a trap: a variational Monte Carlo formulation for the universal behavior at the Van der Waals length scale
• Pair-correlation properties and momentum distribution of finite number of interacting trapped bosons in three dimension

Cited by in corpus (6)

• Controlling quantum random walk with a step-dependent coin
• Condensate fraction and critical temperature of interacting Bose gas in anharmonic trap
• Level spacing statistics and spectral correlations in the diffuse van der Waals clusters
• Relaxation of Shannon entropy for trapped interacting bosons with dipolar interactions
• Correlation dynamics of dipolar bosons in 1D triple well optical lattice
• Use of two-body correlated basis functions with van der Waals interaction to study the shape-independent approximation for a large number of trapped interacting bosons