Fadi Sun, Yi-Xiang Yu, Jinwu Ye, Wuming Liu
The Photoluminescent (PL) measurements on photons and the transport measurements on excitons are the two types of independent and complementary detection tools to search for possible exciton superfluids in electron-hole semi-conductor bilayer systems. It is important to establish the relations between between the two kinds of measurements. In this paper, using quantum Heisenberg-Langevin equations, we establish such a connection by calculating various exciton correlation functions in the putative exciton superfluids. These correlation functions include both normal and anomalous Greater, Lesser, Advanced, Retarded, and Time-ordered exciton Green functions and also various two exciton correlation functions. We also evaluate the corresponding normal and anomalous spectral weights and the Keldysh distribution functions. We stress the violations of the fluctuation and dissipation theorem among these various exciton correlation functions in the non-equilibrium exciton superfluids. We also explore the input-output relations between various exciton correlation functions and those of emitted photons such as the angle resolved photon power spectrum, phase sensitive two mode squeezing spectrum and two photon correlations. For a comparison, using conventional imaginary time formalism, we also calculate all the exciton correlation functions in an equilibrium dissipative exciton superfluid in the electron-electron coupled semi-conductor bilayers at the quantum Hall regime at the total filling factor $ \nu_T= 1 $. We stress the analogies and also important differences between the correlations functions in the two exciton superfluid systems.
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http://arxiv.org/abs/1112.5611
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