Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)
Continuously Sustained Bose-Einstein Photon Condensate in a Semiconductor Quantum Well Open Microcavity
Ross C. Schofield, Ming Fu, Edmund Clarke, Ian A. Farrer, Himadri Shekhar Dhar, Rick Mukherjee, Jon Heffernan, Florian Mintert, Robert A. Nyman, Rupert F. Oulton
Bose-Einstein condensates (BECs) of light are widely studied systems for investigating a variety of physical phe-nomena, from coherence [1] to phase transitions [2]. Up to this point photon BEC systems have all used organic dyes [3], typically Rhodamine 6G, which imposes several limitations. Namely, long-lived dark states that require low repetition rate pulsed operation to prevent population shelving, molecular degradation over time due to photo-bleaching, and weak photon-photon interaction. Here we report photon condensation using an inorganic semiconductor quantum well. Distinct from polariton condensates [4], this is the first observation of photon condensation in an inorganic semiconductor open microcavity system.
Bose-Einstein condensates (BECs) of light are widely studied systems for investigating a variety of physical phe-nomena, from coherence [1] to phase transitions [2]. Up to this point photon BEC systems have all used organic dyes [3], typically Rhodamine 6G, which imposes several limitations. Namely, long-lived dark states that require low repetition rate pulsed operation to prevent population shelving, molecular degradation over time due to photo-bleaching, and weak photon-photon interaction. Here we report photon condensation using an inorganic semiconductor quantum well. Distinct from polariton condensates [4], this is the first observation of photon condensation in an inorganic semiconductor open microcavity system.
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~ g ̃ ≳ 10–3), which is large enough to access the rich physics of interactions within BECs, such as superfluid light.
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, which is large enough to access the rich physics of interactions within BECs, such as superfluid light or vortex formation.
Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity is a macroscopically populated coherent quantum state subject to concurrent pumping and decay. Debates about the fundamental nature of the condensed phase in this open quantum system still persist. Here, we gain a new insight into the spontaneous condensation process by imaging long-lifetime exciton polaritons in a high-quality inorganic microcavity in the single-shot optical excitation regime, without averaging over multiple condensate realisations. In this highly non-stationary regime, a condensate is strongly influenced by the `hot' incoherent reservoir, and reservoir depletion is critical for the transition to the ground energy and momentum state. Condensates formed by more photonic exciton polaritons exhibit dramatic reservoir-induced density filamentation and shot-to-shot fluctuations. In contrast, condensates of more excitonic quasiparticles display smooth density and are second-order coherent. Our observations show that the single-shot measurements offer a unique opportunity to study formation of macroscopic phase coherence during a quantum phase transition in a solid state system.
We review recent experiments on the Bose-Einstein condensation of photons in a dye-filled optical microresonator. The most well-known example of a photon gas, photons in blackbody radiation, does not show Bose-Einstein condensation. Instead of massively populating the cavity ground mode, photons vanish in the cavity walls when they are cooled down. The situation is different in an ultrashort optical cavity imprinting a low-frequency cutoff on the photon energy spectrum that is well above the thermal energy. The latter allows for a thermalization process in which both temperature and photon number can be tuned independently of each other or, correspondingly, for a nonvanishing photon chemical potential. We here describe experiments demonstrating the fluorescence-induced thermalization and Bose-Einstein condensation of a two-dimensional photon gas in the dye microcavity. Moreover, recent measurements on the photon statistics of the condensate, showing Bose-Einstein condensation in the grand-canonical ensemble limit, will be reviewed. Introduction Quantum statistical effects become relevant when a gas of particles is cooled, or its density is increased, to the point where the associated de Broglie wavepackets spatially overlap. For particles with integer spin (bosons), the phenomenon of Bose-Einstein condensation (BEC) then leads to macroscopic occupation of a single quantum state at finite temperatures [1]. Bose-Einstein condensation in the gaseous case was first achieved in 1995 by laser and subsequent evaporative cooling of a dilute cloud of alkali atoms [2, 3, 4], as detailed in Chapter 3 of this volume. The condensate atoms can be described by a macroscopic singleparticle wavefunction, similar to the case of liquid helium [1]. Bose-Einstein condensation has also been observed for exciton-polaritons, which are hybrid states of matter and light [5, 6, 7] (see Chapter 4), magnons [8] (see Chapter 25), and other physical systems. Other than material particles, photons usually do not show Bose-Einstein condensation [9]. In blackbody radiation, the most common Bose gas, photons at low temperature disappear, instead of condensing to a macroscopically occupied ground-state mode. In this system, photons have a vanishing chemical potential, meaning that the number of photons is determined by the available thermal energy and cannot be tuned independently from temperature.
We review, aiming at an audience of final year undergraduates, the phenomena observed in, and properties of, microcavity exciton–polariton condensates. These are condensates of mixed light and matter, consisting of superpositions of photons in semiconductor microcavities and excitons in quantum wells. Because of the imperfect confinement of the photon component, exciton–polaritons have a finite lifetime, and have to be continuously re-populated. Therefore, exciton–polariton condensates lie somewhere between equilibrium Bose–Einstein condensates and lasers. We review in particular the evidence for condensation, the coherence properties studied experimentally, and the wide variety of spatial structures either observed or predicted to exist in exciton–polariton condensates, including quantised vortices and other coherent structures. We also discuss the question of superfluidity in a non-equilibrium system, reviewing both the experimental attempts to investigate superfluidity to date, and the theoretical suggestions of how it may be further elucidated.
The fascination of macroscopic quantum coherence formed in a degenerate Bose gas drives the worldwide work on atomic Bose-Einstein condensates. Semiconductor polaritons1 are another promising system to explore the physics of degenerate Bose gases in a stronger interaction regime. It is also a system easily produced and probed through optical methods. In this work we present the first observation of the onset of a quantum coherence formed out of an initially thermal population of polaritons in a microcavity quantum well system. The quantum coherence is measured by a time domain second order coherence g(2)(0) of the light emitted from the polaritons. Second and higher order coherence functions are crucial in quantum optics to distinguish among various pure states of light, such as coherent state or squeezed state, from classical thermal light2. They have been measured indirectly in the spatial domain for atomic BECs3,4. In our system, with supporting evidence from measurements of the input-output, dispersion, and time evolution of the emission, the phase transition was identified by a decrease of g(2)(0) ≈2, the value for a thermal state, toward g(2)(0) ≈1 for a coherent state. This is a direct evidence of the formation of a macroscopic quantum coherence in the lower polariton ground state.