Exciton correlations and input-output relations in non-equilibrium exciton superfluids

TL;DR

This paper establishes a theoretical framework linking photoluminescence and transport measurements in non-equilibrium exciton superfluids, revealing correlations, spectral properties, and input-output relations, with applications to exciton-polariton systems.

Contribution

It introduces a comprehensive quantum theoretical approach to connect different measurement techniques and analyze exciton correlations in non-equilibrium superfluids, highlighting violations of fluctuation-dissipation relations.

Findings

Derived exciton correlation functions and Green functions.

Identified violations of fluctuation-dissipation theorem.

Established input-output relations for emitted photons.

Abstract

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. In fact, it was believed that the transport measurements can provide more direct evidences on superfluids than the spectroscopic measurements. It is important to establish the relations 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. Applications to possible superfluids in the exciton-polariton systems are also mentioned. 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.