Generating functional approach for spontaneous coherence in semiconductor electron-hole-photon systems

Abstract

Electrons, holes, and photons in semiconductors are interacting fermions and bosons. In this system, a variety of ordered coherent phases can be formed through the spontaneous phase symmetry breaking because of their interactions. The Bose-Einstein condensation (BEC) of excitons and polaritons is one of such coherent phases, which can potentially crossover into the Bardeen-CooperSchrieffer (BCS) type ordered phase at high densities under quasi-equilibrium conditions, known as the BCS-BEC crossover. In contrast, one can find the semiconductor laser, superfluorescence (SF), and superradiance as relevant phenomena under nonequilibrium conditions. In this paper, we present a comprehensive generating functional theory that yields nonequilibrium Green's functions in a rigorous way. The theory gives us a starting point to discuss these phases in a unified view with a diagrammatic technique. Comprehensible time-dependent equations are derived within the Hartree-Fock approximation, which generalize the Maxwell-Semiconductor-Bloch equations under the relaxation time approximation. With the help of this formalism, we clarify the relationship among these cooperative phenomena and we show theoretically that the Fermi-edge SF is directly connected to the e-h BCS phase. We also discuss the emission spectra as well as the gain-absorption spectra.

High-energy side-peak emission of exciton-polariton condensates in high density regime

“…In semiconductor materials (with no cavity), it is well known that e–h Coulomb interactions can cause significant enhancement of the PL intensity around the Fermi edge at low temperature, even for a plasma state 31 32 . As found in our previous studies on the carrier population and optical gain spectra 17 18 , this effect was shown to survive also in our case ( Fig. 4B ).…”

“…One of the advantages of this approach is the applicability to high-density regimes because electrons and holes are explicitly treated with their Coulomb interactions, in contrast to the other approaches assuming excitons as bosonic particles such as dissipative Gross-Pitaevskii equations. By taking into account the pumping baths and the vacuum photon bath, a closed set of equations for the cavity photon field a 0 , the polarization function p k , and the number of electrons n e, k and holes n h, k can be derived 17 18 within the Hartree-Fock (HF) approximation for the steady state as…”

“…9(d) of ref. 18 ). We note that such asymmetric PL spectra are never obtained for non-interacting two-level atom models (see also the Supplementary Information and Fig.…”

“…At higher densities, conventional wisdom has been that strong coupling is lost, and the system reverts to a standard photon laser 15 16 . The mechanism of this loss of strong coupling is still not very well understood, with only a few theoretical 17 18 and fewer experimental works 19 analysing this regime in detail.…”

Quantum fluctuations in a strongly interacting Bardeen-Cooper-Schrieffer polariton condensate at thermal equilibrium

“…In this work we also consider the equilibrium situation only, as inspired by the recent experimental demonstration of a thermal equilibrium excitonpolariton BEC in a high-quality microcavity [29]. The extension of our work to include dissipations is possible, following the standard Keldysh technique [30][31][32].…”