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Conference on Lasers and Electro-Optics

Theory of an exciton matter laser

P. Stenius, Ataç İmamoğlu

Published Nov 27, 2002• 0 citations
Publisher

Abstract

Summary form only given.Recent experiments show signatures of exciton Bose-Einstein condensation in semiconductors. Thus a device that creates a coherent population of excitons while being pumped by a thermal source may be possible. Such an exciton matter laser could consist of a quantum well, possibly embedded in an optical microcavity. In it hot excitons slightly below the bandgap are created by a thermal distribution of free electrons and holes (generated by electrical injection or optical pumping). The excitons interact with (LA) phonons. At low densities excitons are bosonic, and their scattering is affected by statistical enhancement into states with large occupation. Under certain conditions the excitons can condense into a single state, with statistics similar to a coherent state. Light emitted by radiative recombination has the coherence properties of the condensate and is similar to laser light. However, the electronic population in the device does not need to be inverted. We consider 1S heavy-hole excitons in a two-dimensional harmonic trap, realized by a quantum well where interface roughness inevitably localizes low-energy excitons, or by strain fields in lattice mismatched structures. We treat the lowest two trap levels quantum mechanically, and the higher lying states act as a reservoir. Our model is valid at low density, where phase space filling and collisions are negligible. While simplistic, the model displays the main features of an exciton matter laser. Our model is described by the master equation.

DOI
10.1109/iqec.1998.680089

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Conceptually, a single-mode laser light may be perceived as a quantum-degenerate state because all of its photons occupy one and the same light-mode state. One can utilize this property in direct-gap semiconductor in order to excite, e.g., quantum-degenerate excitons that are Coulomb-bound electronhole pairs. For example, if a classical laser resonant with an exciton resonance, the resulting excitation injects a quantum-degenerate state of coherent excitons. This process is fully explained by the semiconductor Bloch equations [1] where the quantum-degenerate coherent excitons are simply described by a polarization. One can rigorously generalize [2] this state-injection concept to realize quantum-optical spectroscopy beyond simple excitons because also laser’s quantum fluctuations are injected as such to the quantumdegenerate electron-hole pairs, before the onset of Coulomb and phonon-induced scattering. More explicitly, the quantum aspects of a single-mode pump laser are defined by a boson operator B while the Coulomb-bound electron-hole pairs are described by an exciton operator X that is bosonic only approximately. When the pump laser has quantum-optical correlations †J K

•Jan 1, 2013•0 citations
Summary form only given.Recent experiments show signatures of exciton Bose-Einstein condensation in semiconductors. Thus a device that creates a coherent population of excitons while being pumped by a thermal source may be possible. Such an exciton matter laser could consist of a quantum well, possibly embedded in an optical microcavity. In it hot excitons slightly below the bandgap are created by a thermal distribution of free electrons and holes (generated by electrical injection or optical pumping). The excitons interact with (LA) phonons. At low densities excitons are bosonic, and their scattering is affected by statistical enhancement into states with large occupation. Under certain conditions the excitons can condense into a single state, with statistics similar to a coherent state. Light emitted by radiative recombination has the coherence properties of the condensate and is similar to laser light. However, the electronic population in the device does not need to be inverted. We consider 1S heavy-hole excitons in a two-dimensional harmonic trap, realized by a quantum well where interface roughness inevitably localizes low-energy excitons, or by strain fields in lattice mismatched structures. We treat the lowest two trap levels quantum mechanically, and the higher lying states act as a reservoir. Our model is valid at low density, where phase space filling and collisions are negligible. While simplistic, the model displays the main features of an exciton matter laser. Our model is described by the master equation.
Semiconductor excitons obey Bose-Einstein statistics in the low-density limit. In this paper, a two-level quantum model for an exciton condensate subject to radiative decay is presented. The condensate state has a well-defined exciton number and a slow phase diffusion rate analogous to a coherent state created by a (photon) laser. Since excitons recombine radiatively, the statistics of the device can be observed by photodetection. Our analytical and numerical results at steady state reveal that the change in population statistics of the ground state is gradual across the threshold region, above which a condensate forms. When radiative losses are present, the condensate mode is ``quasicoherent;'' in the limit of no losses a coherent state is approached. Far below threshold the ground state is well described by a thermal distribution. The higher level, that is the ``pump,'' remains thermally distributed at all times.
Abstract When particles with integer spin accumulate at low temperature and high density, they undergo Bose–Einstein condensation (BEC). Atoms, magnons, solid-state excitons, surface plasmon polaritons and excitons coupled to light exhibit BEC, which results in high coherence due to massive occupation of the respective system’s ground state. Surprisingly, photons were shown to exhibit BEC recently in organic-dye-filled optical microcavities, which—owing to the photon’s low mass—occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalize and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalization in our system where we can clearly distinguish laser action from BEC. Semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages: the lack of dark electronic states in inorganic semiconductors allows these BECs to be sustained continuously; and quantum wells offer stronger photon–photon scattering. We measure an unoptimized interaction parameter ( g~\tilde{{{{{g}}}}}g~​ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
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.
When particles with integer spin accumulate at low temperature and high density they undergo Bose-Einstein condensation (BEC). Atoms, solid-state excitons and excitons coupled to light all exhibit BEC, which results in high coherence due to massive occupation of the respective system's ground state. Surprisingly, photons were shown to exhibit BEC much more recently in organic dye-filled optical microcavities, which, owing to the photon's low mass, occurs at room temperature. Here we demonstrate that photons within an inorganic semiconductor microcavity also thermalise and undergo BEC. Although semiconductor lasers are understood to operate out of thermal equilibrium, we identify a region of good thermalisation in our system where we can clearly distinguish laser action from BEC. Based on well-developed technology, semiconductor microcavities are a robust system for exploring the physics and applications of quantum statistical photon condensates. Notably, photon BEC is an alternative to exciton-based BECs, which dissociate under high excitation and often require cryogenic operating conditions. In practical terms, photon BECs offer their critical behaviour at lower thresholds than lasers. Our study shows two further advantages of photon BEC in semiconductor materials: the lack of dark electronic states allows these BECs to be sustained continuously; and semiconductor quantum wells offer strong photon-photon scattering. We measure an unoptimised interaction parameter, g~=0.0023±0.0003\tilde{g}=0.0023\pm0.0003g~​=0.0023±0.0003, which is large enough to access the rich physics of interactions within BECs, such as superfluid light or vortex formation.
Physics A fascinating property of the quantum world is that particles come equipped with a dual, wavelike nature, which becomes apparent at low temperatures and high densities. For a certain type of particle, bosons, this results in the formation of a giant wave, a Bose-Einstein condensate (BEC). BECs have been realized in laser-trapped ultracold gases of alkali elements, but bosons that exist elsewhere in nature are also expected to condense. An exciton is a composite boson consisting of an electron and a hole (a missing electron) in a semiconductor. High et al. take a page out of the atomic physicists' book and demonstrate the condensation of excitons in a trap. A spatially varying electric field traps the excitons' dipole moments, which are nonzero because of the spatial separation of electrons and holes in a GaAs/AlGaAs coupled quantum well (such so-called indirect excitons also have the advantage of a long lifetime necessary for cooling). When the temperature is lowered below ~2 K, the excitons collect at the trap center, and the entire trap volume becomes coherent, signifying the onset of a BEC. The realization of a BEC in a trapped semiconductor system is expected to enable explorations complementary to those possible with ultracold atomic gases. Nano Lett. 12 , 10.1021/nl300983n (2012).
Conceptually, a single-mode laser light may be perceived as a quantum-degenerate state because all of its photons occupy one and the same light-mode state. One can utilize this property in direct-gap semiconductor in order to excite, e.g., quantum-degenerate excitons that are Coulomb-bound electronhole pairs. For example, if a classical laser resonant with an exciton resonance, the resulting excitation injects a quantum-degenerate state of coherent excitons. This process is fully explained by the semiconductor Bloch equations [1] where the quantum-degenerate coherent excitons are simply described by a polarization. One can rigorously generalize [2] this state-injection concept to realize quantum-optical spectroscopy beyond simple excitons because also laser’s quantum fluctuations are injected as such to the quantumdegenerate electron-hole pairs, before the onset of Coulomb and phonon-induced scattering. More explicitly, the quantum aspects of a single-mode pump laser are defined by a boson operator B while the Coulomb-bound electron-hole pairs are described by an exciton operator X that is bosonic only approximately. When the pump laser has quantum-optical correlations †J K