Phase sensitive two mode squeezing and photon correlations from exciton superfluid

There have been experimental and theoretical studies on Photoluminescence (PL) from possible exciton superfluid in semiconductor electron-hole bilayer systems. However, the PL contains no phase information and no photon correlations, so it can only lead to suggestive evidences. It is important to identify smoking gun experiments which can lead to convincing evidences. Here we study two mode phase sensitive squeezing spectrum and also two photon correlation functions. We find the emitted photons along all tilted directions are always in a two mode squeezed state between $ \vec{k} $ and $ - \vec{k} $. There are always two photon bunching, the photon statistics is super-Poissonian. Observing these unique features by possible future phase sensitive homodyne experiment and HanburyBrown-Twiss type of experiment could lead to conclusive evidences of exciton superfluid in these systems.