Consequences of the Pauli exclusion principle for the Bose-Einstein condensation of atoms and excitons

TL;DR

This paper investigates how the Pauli exclusion principle limits the condensate fraction in Bose-Einstein condensation of atoms and excitons, revealing significant depletion effects at high densities and providing insights into low condensate fractions in helium II.

Contribution

It demonstrates the impact of fermionic constituents on bosonic condensates, introducing a new understanding of condensate depletion due to the Pauli exclusion principle.

Findings

Pauli exclusion limits the condensate fraction in atomic and excitonic BECs.

Condensate depletion increases significantly at high densities.

Results offer new insights into low condensate fractions in helium II.

Abstract

The bosonic atoms used in present day experiments on Bose-Einstein condensation are made up of fermionic electrons and nucleons. In this Letter we demonstrate how the Pauli exclusion principle for these constituents puts an upper limit on the Bose-Einstein-condensed fraction. Detailed numerical results are presented for hydrogen atoms in a cubic volume and for excitons in semiconductors and semiconductor bilayer systems. The resulting condensate depletion scales differently from what one expects for bosons with a repulsive hard-core interaction. At high densities, Pauli exclusion results in significantly more condensate depletion. These results also shed a new light on the low condensed fraction in liquid helium II.