The influence of the radiative decay of excitonic molecules on a possible quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecule's is examined with respect to the radiative renormalization of the excitonic molecule energy (excitonic molecule Lamb shift). For the excitonic molecule wave function, a Schrödinger equation which contains polariton effects is derived and analyzed. Both the inverse excitonic molecule radiative lifetime γ m and the biexciton Lamb shift Δ m depend strongly on the total excitonic molecule momentum K. The energy renormalization Δ m (K) leads to the excitonic molecule effective mass modification and can result in a camel-back structure at K = 0, which opposes a BEC of excitonic molecules at K = 0. Introduction Observations of a quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecules (EM) have been attempted [1, 2, 3] following its theoretical prediction [4, 5] (for reviews see, e.g. [6, 7]). Recent approaches [8, 9] with high-precision techniques renewed the interest in this phenomenon. Traditionally, one tries to detect BEC of the EMs in luminescence. In the new approach the appearance of coherence in the thermal system of the EMs has been tested by means of four-wave mixing and treated as a fundamental manifestation of BEC. (See the paper by Hasuo et al . in this book.) Both optical methods for the BEC detection imply that the optical transition to the corresponding intermediate exciton (IE) state is dipole-active. In this case the EM state is unstable against optical decay with a “giant” oscillator strength [6].
The influence of the radiative decay of excitonic molecules on a possible quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecule's is examined with respect to the radiative renormalization of the excitonic molecule energy (excitonic molecule Lamb shift). For the excitonic molecule wave function, a Schrödinger equation which contains polariton effects is derived and analyzed. Both the inverse excitonic molecule radiative lifetime γ m and the biexciton Lamb shift Δ m depend strongly on the total excitonic molecule momentum K. The energy renormalization Δ m (K) leads to the excitonic molecule effective mass modification and can result in a camel-back structure at K = 0, which opposes a BEC of excitonic molecules at K = 0. Introduction Observations of a quasiequilibrium Bose–Einstein condensation (BEC) of excitonic molecules (EM) have been attempted [1, 2, 3] following its theoretical prediction [4, 5] (for reviews see, e.g. [6, 7]). Recent approaches [8, 9] with high-precision techniques renewed the interest in this phenomenon. Traditionally, one tries to detect BEC of the EMs in luminescence. In the new approach the appearance of coherence in the thermal system of the EMs has been tested by means of four-wave mixing and treated as a fundamental manifestation of BEC. (See the paper by Hasuo et al . in this book.) Both optical methods for the BEC detection imply that the optical transition to the corresponding intermediate exciton (IE) state is dipole-active. In this case the EM state is unstable against optical decay with a “giant” oscillator strength [6].
Introduction. Polaritons and Semiconductor Microcavities As we have mentioned previously, BEC of excitons or biexcitons and lasing can be seen as two limits of the same theory. Lasing occurs in the case of strong electron-photon coupling (recombination rate fast compared with interparticle-scattering rate) while excitonic BEC occurs in the case of weak electron-photon coupling (recombination rate slow compared with the interparticle-scattering rate.) A laser can be seen as a Bose condensate in which the long-range phase coherence exists in the photon states [1], while in the exciton condensate the coherence exists in the electronic states. This is one of the reasons for some of the confusing debates in the early history of excitonic Bose condensation – in many systems there is not a sharp distinction between an excitonic condensate and supperradiance, i.e., luminescence with enhanced intensity due to stimulated emission [2-4]. In the previous chapters, we have so far considered a laser light source only as a source of excitons by means of quantum transitions. In Chapter 6, the laser radiation was taken into account as a given external factor. This chapter is dedicated to phenomena related to a strong and noticeable exciton-photon interaction, when the light significantly influences the energy spectrum of the high-density excitons [5-9]. As we will see, this leads to many fascinating effects related to instabilities. A strong exciton-photon interaction implies a strong polariton effect, in which photon and exciton states are mixed (as in Fig. 1.3). When this mixing is strong, it is not obvious how to define the ground state of the system.
Abstract Superfluidity, first discovered in liquid 4He, is closely related to Bose–Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations—the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton–polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton–polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton–polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton–polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.
Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.
This reference book explains the fundamentals of Bose Einstein Condensation (BEC) in excitons and polaritons. It presents five chapters exploring fundamental concepts and recent developments on the subject. Starting with a historical overview of BEC, the book progresses into the origins and behaviors of excitons and polaritons. Chapters also cover the unique thermalization and relaxation kinetics of excitons, and the distinctive features of polaritons, such as lasing, superfluidity, and quantized vortices. The chapters dedicated to BEC in excitons and polaritons detail experimental techniques, theoretical modeling, recent advancements, and practical applications in a simplified way for beginners. This book serves as a resource for researchers, physicists, and students interested in the phenomena of BEC, providing insights into both the theoretical foundations and the practical implications of excitons and polaritons.
Great progress has been made in recent years in experimental studies of excitonic molecules, both in direct-band and indirect-band semiconductors. The exciton systems in these semiconductors differ substantially. In direct-band semiconductors with dipole-allowed optical transitions, the direct-recombination times are extremely small. Consequently the processes of binding of excitons into excitonic molecules and their decay occur under strongly nonequilibrium conditions. Hence one can obtain the fundamental information on biexcitons in these semiconductors by nonlinear optical methods. This review discusses the processes on which the various methods are based: two-photon resonance excitation of biexcitons, induced one-photon conversion of an exciton into a biexciton, two-photon resonance Raman scattering involving biexciton states, etc., and their application to studying biexcitons with the example of CdS. Problems of bistability involving biexcitons are also briefly discussed. In indirect semiconductors, where recombination occurs with the emission of a phonon, the lifetimes of excitons are large, and quasiequilibrium can be established in the exciton system. Under these conditions the information on the properties of the molecules is obtained by analyzing their radiative-decay spectra. The problem of detecting biexcitons in indirect semiconductors, radiative decay of molecules, and the effect on their stability of external electric, strain, and magnetic fields are discussed in detail with the examples of Si and Ge. Also the results of investigating the quantum statistical behavior of a dense gas of spin-oriented excitons (in a magnetic field under conditions in which the biexcitons are destabilized) are briefly presented (using the example of uniaxially compressed germanium), and the question of the possibility of their Bose condensation is discussed.
He, is closely related to Bose-Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations-the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton-polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton-polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton-polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton-polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.