On the open-dissipative nature of photon Bose-Einstein condensates

Photon condensation was first observed in 2010 within a dye-filled microcavity at room temperature and gained interest since then. A deeper understanding is particularly needed as to whether the stationary states are equilibrium or nonequilibrium states. To this end we examine at first how the driven-dissipative nature of a photon Bose–Einstein condensate modifies the condensation process [1]. To this end, we consider a rate-equation model, which can be derived microscopically [2]. It depends on external parameters such as emission and absorption rates as well as cavity photon losses. In steady state, the photon occupation follows an open-dissipative Bose–Einstein distribution whose chemical potential is set self-consistently by the dye’s ground- and excited-state populations. We show that driven-dissipative parameters strongly alter the distribution and use these results to distinguish photonic condensation from both atomic condensation and lasing.

Although open-dissipative quantum fluids have extensively been studied numerically, analytical descriptions are rare. Here we show that generalizing the standard optimization method for closed condensates yields a projection optimization method, which is applicable for open-dissipative systems [3]. As an example we analyze a complex Gross–Pitaevskii equation that heuristically models a harmonically trapped photon Bose–Einstein condensate. Together with established methods from hydrodynamics, we obtain an approximate dynamical vortex solution and demonstrate how open-dissipative parameters affect both vortex size and stability. The resulting information is useful for possibly realizing vortices in photon Bose-Einstein condensates.

[1] J. Krauß, E. Stein, and A. Pelster, The European Physical Journal Special Topics (2026), https://doi.org/10.1140/epjs/s11734-026-02185-2

[2] M. Randonjić, W. Kopylov, A. Balaž, and A. Pelster, New J. Phys. 20, 055014 (2018).

[3] J. Krauß, M.A.G. dos Santos Filho, F.E.A. dos Santos, and A. Pelster, Phys. Rev. Res. 7, 033007 (2025).