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Reports on Progress in Physics

A quantum kinetic theory of photon Bose–Einstein condensation in semiconductors

José Luis Figueiredo, Ross C. Schofield, Ming Fu, Robert A. Nyman, Rupert F. Oulton, Hugo Terças, Florian Mintert

Published Apr 28, 2026• 1 citation
Publisher

Abstract

Abstract Photon condensation in semiconductor microcavities is a transformative technique for engineering quantum states of light at room temperature by tailoring strong but incoherent light-matter interactions. While continuous-wave and electrical pumping offer exceptional prospects for miniaturized quantum photonic technologies, harnessing these requires conceptual advances in understanding non-equilibrium light-matter dynamics in semiconductors. We resolve this challenge through an ab initio quantum kinetic theory capturing how Coulomb interactions of optically excited carriers and phonon scattering mediate photon thermalization and condensation in semiconductors. Our microscopic model shows that at high carrier densities, thermalization is dominated by carrier–carrier Coulomb scattering, in clear contrast to the rovibrational relaxation that governs dye-based photon condensates. The theory predicts a rich nonequilibrium phase diagram with thermal, Bose-condensed, multimode, and lasing phases, quantitatively in agreement with recent experiments. Crucially, we identify how cavity detuning controls transitions between equilibrium and gain-dominated regimes, enabling tailored design of coherent light sources. This work thus provides the foundation for semiconductor-based quantum photonic devices operating beyond conventional laser paradigms.

DOI
10.1088/1361-6633/ae65da

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Abstract Photon condensation in semiconductor microcavities is a transformative technique for engineering quantum states of light at room temperature by tailoring strong but incoherent light-matter interactions. While continuous-wave and electrical pumping offer exceptional prospects for miniaturized quantum photonic technologies, harnessing these requires conceptual advances in understanding non-equilibrium light-matter dynamics in semiconductors. We resolve this challenge through an ab initio quantum kinetic theory capturing how Coulomb interactions of optically excited carriers and phonon scattering mediate photon thermalization and condensation in semiconductors. Our microscopic model shows that at high carrier densities, thermalization is dominated by carrier–carrier Coulomb scattering, in clear contrast to the rovibrational relaxation that governs dye-based photon condensates. The theory predicts a rich nonequilibrium phase diagram with thermal, Bose-condensed, multimode, and lasing phases, quantitatively in agreement with recent experiments. Crucially, we identify how cavity detuning controls transitions between equilibrium and gain-dominated regimes, enabling tailored design of coherent light sources. This work thus provides the foundation for semiconductor-based quantum photonic devices operating beyond conventional laser paradigms.
Photon condensation in semiconductor microcavities is a transformative technique for engineering quantum states of light at room temperature by tailoring strong but incoherent light-matter interactions. While continuous-wave and electrical pumping offer exceptional prospects for miniaturized quantum photonic technologies, harnessing these requires conceptual advances in understanding nonequilibrium light-matter dynamics in semiconductors. We resolve this challenge through an \textit{ab initio} quantum kinetic theory capturing how Coulomb interactions of optically excited carriers and phonon scattering mediate photon thermalization and condensation in semiconductors. Our microscopic model shows that at high carrier densities, thermalization is dominated by carrier-carrier Coulomb scattering, in clear contrast to the rovibrational relaxation that governs dye-based photon condensates. The theory predicts a rich nonequilibrium phase diagram with thermal, Bose-condensed, multimode, and lasing phases, quantitatively in agreement with recent experiments. Crucially, we identify how cavity detuning controls transitions between equilibrium and gain-dominated regimes, enabling tailored design of coherent light sources. This work thus provides the foundation for semiconductor-based quantum photonic devices operating beyond conventional laser paradigms.
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.
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.
We report a time-resolved study of the thermalization dynamics and the lasing to photon Bose-Einstein condensation crossover by in situ monitoring the photon kinetics in a dye microcavity. When the equilibration of the light to the dye temperature by absorption and reemission is faster than photon loss in the cavity, the optical spectrum becomes Bose-Einstein distributed and photons accumulate at low-energy states, forming a Bose-Einstein condensate. The thermalization of the photon gas and its evolution from nonequilibrium initial distributions to condensation is monitored in real time. In contrast, if photons leave the cavity before they thermalize, the system operates as a laser.
Abstract Many bosons can occupy a single quantum state without a limit. It is described by the quantum-mechanical Bose–Einstein statistic, which allows Bose–Einstein condensation at low temperatures and high particle densities. Photons, historically the first considered bosonic gas, were late to show this phenomenon, observed in rhodamine-filled microcavities and doped fibre cavities. These findings have raised the question of whether condensation is also common in other laser systems with potential technological applications. Here we show the Bose–Einstein condensation of photons in a broad-area vertical-cavity surface-emitting laser with a slight cavity-gain spectral detuning. We observed a Bose–Einstein condensate in the fundamental transversal optical mode at a critical phase-space density. The experimental results follow the equation of state for a two-dimensional gas of bosons in thermal equilibrium, although the extracted spectral temperatures were lower than the device’s. This is interpreted as originating from the driven-dissipative nature of the photon gas. In contrast, non-equilibrium lasing action is observed in the higher-order modes in more negatively detuned device. Our work opens the way for the potential exploration of superfluid physics of interacting photons mediated by semiconductor optical nonlinearities. It also shows great promise for enabling single-mode high-power emission from a large-aperture device.
Many bosons can occupy a single quantum state without a limit. This state is described by quantum-mechanical Bose-Einstein statistics, which allows the formation of a Bose-Einstein condensate at low temperatures and high particle densities. Photons, historically the first considered bosonic gas, were late to show this phenomenon, which was observed in rhodamine-filled microlaser cavities and doped fiber cavities. These more recent findings have raised the natural question as to whether condensation is common in laser systems, with potential technological applications. Here, we show the Bose-Einstein condensation of photons in a broad-area vertical-cavity surface-emitting laser with positive cavity mode-gain peak energy detuning. We observed a Bose-Einstein condensate in the fundamental transversal optical mode at the critical phase-space density. The experimental results follow the equation of state for a two-dimensional gas of bosons in thermal equilibrium, although the extracted spectral temperatures were lower than those of the device. This is interpreted as originating from the driven-dissipative nature of the device and the stimulated cooling effect. In contrast, non-equilibrium lasing action is observed in the higher-order modes in a negatively detuned device. Our work opens the way for the potential exploration of superfluid physics of interacting photons mediated by semiconductor optical non-linearities. It also shows great promise for enabling single-mode high-power emission from a large aperture device.