Spatial Entanglement From Off-Diagonal Long Range Order in a BEC

Abstract

We investigate spatial entanglement - particle-number entanglement between regions of space - in an ideal Bosonic gas. We quantify the amount spatial entanglement around the transition temperature for condensation by probing the gas with two localised two-level systems. We show that spatial entanglement in the gas is directly related to filling of the ground state energy level and therefore to the off-diagonal long-range order of the system and the onset of condensation.

7 pages, 3 figures. Extended from 4 to 7 pages. More detailed derivations of key formula. Extended introduction and background. Results remain unchanged