Theory of two-component superfluidity in microcavity polaritons

We develop a microscopic theory of superfluidity in exciton–polaritons that accounts for the unusual coexistence of Bose–Einstein condensates in both the lower polariton (LP) and upper polariton (UP) branches of a semiconductor microcavity. While most experiments to date observe condensation in a single branch, recent evidence suggests that regimes of competition or partial coexistence may be possible. Motivated by this, we explicitly include both branches in a modified Hamiltonian with interbranch scattering, and analyze the resulting Bogoliubov excitation spectrum, sound velocity, and critical temperature.

To describe relative occupations of the LP and UP condensates, we introduce a population–split parameter α. Scanning across this parameter provides a controlled way to interpolate between one-component limits and genuine two-component coexistence. This framework allows us to construct phase–diagram–like plots of the sound velocity and critical temperature as functions of α, polariton density, detuning, and Rabi splitting. Our results demonstrate that two-component coherence consistently enhances superfluid properties compared to the one-component only case. In particular, we find nontrivial dependence of c_s and T_c on α. These predictions are good for GaAs/AlGaAs quantum wells, and they depend only on experimentally tunable parameters. This equilibrium framework establishes a predictive baseline for future nonequilibrium studies, including driven–dissipative extensions with pump, decay, and dephasing. More broadly, it provides a general strategy for exploring multicomponent polariton superfluidity, Josephson-like interbranch phase dynamics, and engineered quantum fluids of light.