Theory of two-component superfluidity of microcavity polaritons

TL;DR

This paper develops a mean-field theory for two-component superfluidity of microcavity polaritons, analyzing how upper and lower polariton condensates coexist and how their properties change with detuning and population imbalance.

Contribution

It introduces a phenomenological parameter to describe population imbalance and analyzes its effects on critical temperature and sound velocity in polariton condensates.

Findings

Critical temperature is independent of population imbalance at zero detuning.

Variations in population imbalance affect sound velocity and critical temperature.

The theory provides analytic insights for future nonequilibrium polariton superfluid studies.

Abstract

We develop a microscopic mean-field theory describing the coexistence of Bose-Einstein condensates of upper and lower polaritons (UP/LP) in a semiconductor microcavity. Incorporating interbranch scattering within a modified polariton Hamiltonian, we introduce a phenomenological population-split parameter $\alpha$ that quantifies the relative LP/UP occupations. At zero detuning, the critical temperature becomes independent of $\alpha$, converging to a single value that marks the balanced, resonant regime. Away from resonance, variations in $\alpha$ lead to distinctive and experimentally resolvable changes in both the sound velocity $c_s$ and critical temperature $T_c$, relative to the single-component (LP-only) condensate limit. The system under study consists of excitons confined in a transition metal dichalcogenide (TMDC) monolayer, particularly WSe$_2$ embedded within a planar optical microcavity of GaAs where they strongly couple to cavity photons. Our analysis focuses on monolayer WSe$_2$ embdedded in a GaAs microcavity. We present results for GaAs/AlGaAs quantum wells embedded in a GaAs microcavity in the Appendix. While mean-field in scope, the framework provides analytic benchmarks and physical insight for future treatments that include dissipation and fluctuations in nonequilibrium polariton superfluids.