Quantum information entropies of ultra-cold atomic gases in a harmonic trap

Abstract

The position and momentum space information entropies of weakly interacting trapped atomic Bose-Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems contain $N$ atoms confined in a $D(\le 3)$-dimensional harmonic trap has a universal form as $S_t^{(D)}=N(aD-b\ln N)$, where $a\simeq 2.332$ and $b=2$ for interacting bosonic systems and $a\simeq 1.982$ and $b=1$ for ideal fermionic systems. These results obey the entropic uncertainty relation given by the Beckner, Bialynicki-Birula and Myceilski.

References in corpus (4)

• Theory of ultracold Fermi gases
• Realization of Bose-Einstein condensates in lower dimensions
• Pauli Blocking of Collisions in a Quantum Degenerate Atomic Fermi Gas
• Quantum information entropies of the eigenstates and the coherent state of the Pöschl-Teller potential