Superfluidity and Critical Velocities in Nonequilibrium Bose-Einstein Condensates

We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.

Figure 1

Elementary excitation spectrum of a moving, spatially homogeneous, nonequilibrium condensate as described by the linearized generalized GPE around the steady-state solution. Parameters: $k_c/k_{\gamma }=4$, $r/\gamma =1$, $g/\gamma =1$, ${\Omega }_K/\gamma =50$, Panels (c),(d) and (e),(f) correspond to different values of the density, $n_{c}g/\gamma =0.1$ [(c),(d)] and $n_{c}g/\gamma =1$ [(e),(f)], respectively. Inset: magnified view of (d). Panels (a),(b): same as panels (e),(f) in the limit of a frequency-independent pumping ${\Omega }_K=\infty$. Momenta are measured in units of $k_{\gamma }=\sqrt{m\gamma /\hslash }$.

Figure 2

Growth rate of the maximally unstable mode as a function of condensate momentum $k_c$ and density $n_c$. The region above the dashed line corresponds to dynamically stable condensates. Same system parameters as in Figs. 1c, 1f.

Figure 3

Density perturbation created in a moving condensate by a stationary weak defect for three values of the condensate velocity $v/c_s=1.5$, 1, 0.4 across the critical value for superfluidity. Parameters: $n_{c}g/\gamma =n_{c}r/\gamma =1$, ${\Omega }_K/\gamma =50$.

Figure 4

Panel (a): Force exerted on a weak stationary defect by a moving condensate as a function of the condensate velocity $v$ for different values of the nonequilibrium parameter $\gamma /g{n}_c=0$, 0.1, 1, 2 (thin black solid line, blue solid line, green dashed line, red dotted line), in units of $F_{\xi }={\hslash }^2/m{\xi }^3$, where $\xi =\sqrt{{\hslash }^2/mg{n}_c}$. The ratios $P/\gamma$ and $r{n}_c/\gamma$ are kept constant. The other parameters are the same as in Fig. 3. Panels (b),(c): Real and imaginary parts of the complex wave vector $\tilde{k}$ of the zero-frequency Bogoliubov mode as a function of $v$. The wave vector is taken to be parallel to the flow velocity. The parameters correspond to the green curve of panel (a).

Figure 5

Real (linear color scale) and momentum space (logarithmic color scale) densities of a nonequilibrium condensate after a temporal evolution of $\gamma t=300$ for an initial momentum $k/k_{\gamma }=2$ and two different densities of defects. The dots in the real space panels indicate the position of the defects. The square in the momentum space panels indicates the initial momentum of the condensate. Parameters are the same as in Fig. 4, except for ${\Omega }_K/\gamma =10$.