Bose-Einstein condensation (BEC), where a large number of bosons occupy a single quantum state, was theoretically predicted early in the 20th century but its direct observation in dilute atomic gases only came much later due to the need for extremely low temperatures inversely proportional to the boson mass. However, BEC has been observed in various systems with bosonic quasiparticles exhibiting high curvature dispersion and low effective mass, allowing condensation at higher temperatures. Examples include magnons, excitons, plasmons, and cavity polaritons. Photons, being massless with linear energy dispersion and a trivial ground state, were initially considered unlikely candidates for BEC. While the number of photons isn't conserved in a thermal equilibrium blackbody radiation model, BEC has been demonstrated in systems such as rhodamine-filled microcavities and doped fiber cavities, raising the question of its feasibility in other laser systems with technological applications. This study investigates the possibility of achieving photon BEC in a readily available semiconductor device—the large-aperture vertical-cavity surface-emitting laser (VCSEL)—operating at room temperature.

Previous research has demonstrated photon BEC in rhodamine-filled microcavities and doped fiber cavities. These systems exhibited textbook effects of non-interacting bosons, including thermodynamic and caloric properties and quantum-statistical effects. The driven-dissipative nature of these systems and the phase boundaries between photon BEC and non-equilibrium lasing have also been extensively studied. However, limitations like weak and slow thermo-optical nonlinearity in rhodamine-based systems have hindered the observation of superfluid effects. The search for BEC conditions in other laser systems, such as semiconductor lasers, is motivated by the potential for technological applications and the availability of materials with significant and fast nonlinearities. Prior work in semiconductor lasers has shown some evidence of BEC-like phenomena, but a definitive demonstration in a widely used device like a VCSEL at room temperature has remained elusive.

The study used an epitaxially grown oxide-confined VCSEL with a large 23-µm diameter aperture, emitting around 980 nm. The device comprised two distributed Bragg reflectors (DBRs), p-doped and n-doped, creating a p-i-n junction with a multiple quantum well (QW) active region sandwiched between them. Oxide apertures provided spatial current confinement. The VCSEL was driven at room temperature with direct current, setting a non-equilibrium carrier distribution in the QW region. The quasi-Fermi levels for electrons and holes, proportional to the applied voltage, described the carrier distributions using separate Fermi distributions. The key conditions for photon BEC in a VCSEL were considered: chemical equilibrium (chemical potential of photons equal to the difference between electron and hole quasi-Fermi levels) and detailed balance between emission and absorption (described by the van Roosbroeck-Shockley relation). The modified Bose-Einstein (BE) distribution of photons was derived from laser rate equations, incorporating a correction parameter representing the ratio of photon decay rate from the passive cavity to the spontaneous emission rate, reflecting the degree of thermalization. Devices with different cavity-QW gain detunings (Δ = ε − EQW) were probed. A back focal plane imaging technique was used to access the momentum dispersion, enabling spectral analysis of momentum dispersions. Spatial resolution was achieved to observe the homogeneity of the photon gas. Thermodynamic properties were explored by extracting occupancies of transversal energy states from the momentum-space electroluminescence data, accounting for density of states, photon lifetimes, and optical setup efficiency. The equation of state (EOS) was examined to determine whether it followed the behavior of a two-dimensional (2D) Bose gas.

The researchers observed a homogeneous BEC of photons in a VCSEL device with a detuning of Δ1 = −5.2 meV. Above a critical BEC threshold, the fundamental mode (k⊥ = 0) dominated the spectrum, contrasting with the higher-order mode lasing observed in a device with a more negative detuning (Δ2 = −14 meV). The momentum-space spectrum of the BEC device showed a thermalized distribution, transitioning to dominance by the ground state above the critical current. The real-space spectra confirmed the homogeneity of the photon gas in the BEC regime. The experimental energy distributions were successfully fitted with Bose-Einstein distributions, although the extracted effective temperatures were lower than the device temperature, indicating a non-equilibrium state. The effective chemical potential was negative and approached zero near the condensation threshold. The population of the ground state showed a threshold-like increase, while the excited states saturated, typical of a Bose-condensed gas. The equation of state determined from the experimental data followed the theoretical prediction for a 2D Bose gas, with minor deviations attributed to the finite collection angle of the optical setup and imperfect thermalization. The critical particle number for condensation was experimentally determined and matched theoretical expectations. Linewidth narrowing and the appearance of spatial coherence further supported the BEC transition.

The lower-than-expected temperature of the photon gas suggests that the system is not in full thermal and chemical equilibrium with the active region of the device. Stimulated cooling, a phenomenon predicted for driven-dissipative bosonic condensates in the fast thermalization limit, could explain this observation. The observed monotonic increase of the photon gas temperature with driving current might be due to an increase in the ratio of the photon decay rate to spontaneous emission rate. The experimental EOS agrees well with the theoretical EOS for a 2D Bose gas, supporting the existence of a BEC, despite the non-equilibrium nature of the system. The lack of clear indications of photon interactions is attributed to the dominance of current- and temperature-induced refractive index changes over cavity energy shifts. Further research is needed to investigate the superfluid properties of the system and explore the non-Hermitian aspects of the condensation.

This study successfully demonstrated a Bose-Einstein condensate of photons in a readily available, electrically driven VCSEL at room temperature. The findings support the theoretical model for a two-dimensional Bose gas, despite the system being in a non-equilibrium state. This achievement opens new possibilities for investigating superfluid phenomena and the potential development of single-mode high-power lasers with excellent beam quality using established VCSEL technology. Future research could focus on directly probing the dynamics of the condensed photons, examining fluctuation properties, and exploring topological effects in complex lattice geometries.

The study acknowledges the non-equilibrium nature of the photon gas and its potential influence on interpreting the results. The deviations from the ideal 2D Bose gas EOS, attributed to the finite collection angle and imperfect thermalization, need further investigation. The influence of spatial inhomogeneities in the current density and chemical potential across the VCSEL aperture on the extracted thermodynamic properties was discussed, but further analysis is warranted. The impact of the relatively short photon lifetime on thermalization and the potential for stimulated cooling is a subject for further studies.