 Condensate density

For a homogeneous gas, the condensate density is the macroscopic occupation $N_0$ of its condensate mode divided by volume. More generally its spatial density is $N_0|{\phi }_0(x){|}^2$ for a normalized condensate orbital. The mode and occupation are defined by a macroscopic eigenvalue of the one-body density matrix, so a finite fixed-number state need not have a nonzero field expectation. Condensate density is distinct from the superfluid density defined by response to a phase twist; interactions can deplete the former even when the latter equals the total density at zero temperature in a uniform Galilean-invariant gas.