© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1412.5298 · Physical Review B

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

Makoto Yamaguchi, Ryota Nii, Kenji Kamide, Tetsuo Ogawa, Y. Yamamoto

Published Mar 16, 2015• 21 citations

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 cross over into the Bardeen-Cooper-Schrieffer (BCS) type ordered phase at high densities under quasiequilibrium 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.

DOI: 10.1103/physrevb.91.115129

Related papers

BEC–BCS-laser crossover in Coulomb-correlated electron–hole–photon systems

Makoto Yamaguchi, Kenji Kamide, T. Ogawa +1 more

Many-body features caused by Coulomb correlations are of great importance for understanding phenomena pertaining to polariton systems in semiconductor microcavities, i.e. electron–hole–photon systems. Remarkable many-body effects are shown to exist in both thermal-equilibrium phases and non-equilibrium lasing states. We then show a unified framework for connecting the thermal-equilibrium and the non-equilibrium steady states based on a non-equilibrium Green's function approach. Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS)-laser crossovers are investigated by using this approach.

New Journal of Physics•Jun 1, 2012•48 citations

Second Thresholds in BEC-BCS-Laser Crossover of Exciton-Polariton Systems

Makoto Yamaguchi, Kenji Kamide, Ryota Nii +2 more

The mechanism of second thresholds observed in several experiments is theoretically revealed by studying the BEC-BCS-laser crossover in exciton-polariton systems. We find that there are two different types of second thresholds: one is a crossover within quasiequilibrium phases and the other is into nonequilibrium (lasing). In both cases, the light-induced band renormalization causes gaps in the conduction and valence bands, which indicates the existence of bound electron-hole pairs in contrast to earlier expectations. We also show that these two types can be distinguished by the gain spectra.

arXiv:1301.4838•Physical Review Letters•Jul 12, 2013•62 citations

BCS Wave-Function Approach to the BEC-BCS Crossover of Exciton-Polariton Condensates

Tim Byrnes, Tomoyuki Horikiri, Natsuko Ishida +1 more

The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.

arXiv:1005.3141•Physical Review Letters•Oct 26, 2010•71 citations

Fermi-edge superfluorescence from a quantum-degenerate electron-hole gas

Ji‐Hee Kim, G. Timothy Noe, Stephen McGill +4 more

Nonequilibrium can be a source of order. This rather counterintuitive statement has been proven to be true through a variety of fluctuation-driven, self-organization behaviors exhibited by out-of-equilibrium, many-body systems in nature (physical, chemical, and biological), resulting in the spontaneous appearance of macroscopic coherence. Here, we report on the observation of spontaneous bursts of coherent radiation from a quantum-degenerate gas of nonequilibrium electron-hole pairs in semiconductor quantum wells. Unlike typical spontaneous emission from semiconductors, which occurs at the band edge, the observed emission occurs at the quasi-Fermi edge of the carrier distribution. As the carriers are consumed by recombination, the quasi-Fermi energy goes down toward the band edge, and we observe a continuously red-shifting streak. We interpret this emission as cooperative spontaneous recombination of electron-hole pairs, or superfluorescence (SF), which is enhanced by Coulomb interactions near the Fermi edge. This novel many-body enhancement allows the magnitude of the spontaneously developed macroscopic polarization to exceed the maximum value for ordinary SF, making electron-hole SF even more "super" than atomic SF.

arXiv:1312.4070•Scientific Reports•Nov 21, 2013•26 citations

Maxwell-Bloch formulation for semiconductors: Effects of coherent Coulomb exchange

Charles M. Bowden, Govind Prasad Agrawal

A generalized Bloch-Maxwell formulation for laser-field-coupled semiconductors is derived from a two-band model which includes direct Coulomb interactions. The momentum-dependent, microscopic, electron-hole equations of motion in the time-dependent Hartree-Fock approximation and neglecting interband exchange interactions form the starting point for the formulation. A self-consistent set of coupled equations in four dynamical variables for the medium, together with the electric-field amplitude coupled through the Maxwell wave equation in a semiclassical approximation, are obtained to lowest order in the coherent Coulomb exchange interaction and the density-of-states distribution. Intrinsic optical bistability is predicted in a steady state due to a carrier density-dependent redshift of the band edge due explicitly to coherent Coulomb exchange. Integration of the dynamical equations for conditions which correspond to the ultrafast time regime exhibit intrinsic adiabatic inversion, adiabatic following, anomalous Rabi cycling, and unique, as well as fast, optical switching, all of which depend upon the coherent Coulomb exchange interaction.

Physical Review A•May 1, 1995•38 citations

Observation of superfluorescence from a quantum ensemble of coherent excitons in a ZnTe crystal: Evidence for spontaneous Bose-Einstein condensation of excitons

D. C. Dai, Andrew P. Monkman

Superfluorescence (SF) is the emission from a dense coherent system in population inversion formed from an initially incoherent ensemble. This is characterized by an induction time (${\ensuremath{\tau}}_{\mathrm{D}}$) for the spontaneous development of the macroscopic quantum coherence. Here we report detailed observation of SF on an ultrafast timescale from a quantum ensemble of coherent excitons in highly excited intrinsic-bulk ZnTe single crystal at 5 K, showing a characteristic ${\ensuremath{\tau}}_{\mathrm{D}}$ from 40 ps to 10 ps, quantum noise and fluctuations, and quantum beating and ringing. From this clear observation of SF from a spontaneous coherence of excitons bound to impurities and defect states, we infer that this is indicative of the formation of a spontaneous Bose-Einstein condensation (BEC) of excitons on an ultrafast timescale. The population density and dephasing time (${T}_{2}$ or ${T}_{2}^{*}$) of exciton are two controlling factors in the generation of SF from the BEC.

arXiv:1107.5273•Physical Review B•Sep 19, 2011•65 citations

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 cross over into the Bardeen-Cooper-Schrieffer (BCS) type ordered phase at high densities under quasiequilibrium 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.

Many-body features caused by Coulomb correlations are of great importance for understanding phenomena pertaining to polariton systems in semiconductor microcavities, i.e. electron–hole–photon systems. Remarkable many-body effects are shown to exist in both thermal-equilibrium phases and non-equilibrium lasing states. We then show a unified framework for connecting the thermal-equilibrium and the non-equilibrium steady states based on a non-equilibrium Green's function approach. Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS)-laser crossovers are investigated by using this approach.

The mechanism of second thresholds observed in several experiments is theoretically revealed by studying the BEC-BCS-laser crossover in exciton-polariton systems. We find that there are two different types of second thresholds: one is a crossover within quasiequilibrium phases and the other is into nonequilibrium (lasing). In both cases, the light-induced band renormalization causes gaps in the conduction and valence bands, which indicates the existence of bound electron-hole pairs in contrast to earlier expectations. We also show that these two types can be distinguished by the gain spectra.

The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.

Nonequilibrium can be a source of order. This rather counterintuitive statement has been proven to be true through a variety of fluctuation-driven, self-organization behaviors exhibited by out-of-equilibrium, many-body systems in nature (physical, chemical, and biological), resulting in the spontaneous appearance of macroscopic coherence. Here, we report on the observation of spontaneous bursts of coherent radiation from a quantum-degenerate gas of nonequilibrium electron-hole pairs in semiconductor quantum wells. Unlike typical spontaneous emission from semiconductors, which occurs at the band edge, the observed emission occurs at the quasi-Fermi edge of the carrier distribution. As the carriers are consumed by recombination, the quasi-Fermi energy goes down toward the band edge, and we observe a continuously red-shifting streak. We interpret this emission as cooperative spontaneous recombination of electron-hole pairs, or superfluorescence (SF), which is enhanced by Coulomb interactions near the Fermi edge. This novel many-body enhancement allows the magnitude of the spontaneously developed macroscopic polarization to exceed the maximum value for ordinary SF, making electron-hole SF even more "super" than atomic SF.

A generalized Bloch-Maxwell formulation for laser-field-coupled semiconductors is derived from a two-band model which includes direct Coulomb interactions. The momentum-dependent, microscopic, electron-hole equations of motion in the time-dependent Hartree-Fock approximation and neglecting interband exchange interactions form the starting point for the formulation. A self-consistent set of coupled equations in four dynamical variables for the medium, together with the electric-field amplitude coupled through the Maxwell wave equation in a semiclassical approximation, are obtained to lowest order in the coherent Coulomb exchange interaction and the density-of-states distribution. Intrinsic optical bistability is predicted in a steady state due to a carrier density-dependent redshift of the band edge due explicitly to coherent Coulomb exchange. Integration of the dynamical equations for conditions which correspond to the ultrafast time regime exhibit intrinsic adiabatic inversion, adiabatic following, anomalous Rabi cycling, and unique, as well as fast, optical switching, all of which depend upon the coherent Coulomb exchange interaction.

Superfluorescence (SF) is the emission from a dense coherent system in population inversion formed from an initially incoherent ensemble. This is characterized by an induction time (${\ensuremath{\tau}}_{\mathrm{D}}$) for the spontaneous development of the macroscopic quantum coherence. Here we report detailed observation of SF on an ultrafast timescale from a quantum ensemble of coherent excitons in highly excited intrinsic-bulk ZnTe single crystal at 5 K, showing a characteristic ${\ensuremath{\tau}}_{\mathrm{D}}$ from 40 ps to 10 ps, quantum noise and fluctuations, and quantum beating and ringing. From this clear observation of SF from a spontaneous coherence of excitons bound to impurities and defect states, we infer that this is indicative of the formation of a spontaneous Bose-Einstein condensation (BEC) of excitons on an ultrafast timescale. The population density and dephasing time (

{T}_{2}

or

{T}_{2}^{*}

) of exciton are two controlling factors in the generation of SF from the BEC.