Superfluid Density of an Open Dissipative Condensate

I calculate the superfluid density of a nonequilibrium steady state condensate of particles with finite lifetime. Despite the absence of a simple Landau critical velocity, a superfluid response survives, but dissipation reduces the superfluid fraction. I also suggest an idea for how the superfluid density of an example of such a system, i.e., microcavity polaritons, might be measured.

Figure 1

Types of Feynman diagram required for the response function to one-loop order. Straight lines indicate noncondensate excitations. Filled symbols involve the condensate, arising from either interactions (circles) or coupling to currents (squares). Wavy lines indicate source fields coupling to the current vertices.

Figure 2

Normal density vs temperature for a variety of pump and decay rates, and obeying the equilibrium fluctuation dissipation theorem. Relative pump and decay rates are scaled so all three curves correspond to the same condensate density, while the influence of pump and decay varies.

Figure 3

Panel (a), microcavity sample ($\mu c$) placed between (imbalanced) anti-Helmholtz coils to induce a field ${\mathit{B}}_{\mathrm{real}}$. Panel (b), velocity and angular velocity vs radius for ${\mathit{A}}_{\mathrm{synth}}$ as discussed in the text.