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

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

2011-01-03

arxiv.org/abs/1101.0483v2

Pramana-Journal of Physics 77, 697 (2011)

Physics

Condensed Matter

Quantum Gases

Scientific paper

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(a D - 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.

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