Spatial entanglement from off-diagonal long-range order in a Bose-Einstein condensate

Abstract

We investigate spatial entanglement---particle-number entanglement between regions of space---in an ideal bosonic gas. We quantify the amount of spatial entanglement around the transition temperature for condensation $({T}_{C})$ by probing the gas with two localized 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.