# Bose-Einstein Condensation of Photons

Image of the radiation transmitted through one cavity mirror below (left) and above (right) the critical photon number. For the latter case a macroscopically ground state mode is visible.

Spectral intensity distribution of radiation from the dye-filled optical microresonator for different pump powers.Upon a spectrally broad thermal background above the critical power a spectrally sharp peak, the Bose-Einstein condensate, is observed at the position of the cavity cutoff. The inset shows theoretical spectra.

### Bose-Einstein condensation, the macroscopic ground state occupation of a system of bosonic particles below a critical temperature, was observed for an atomic gas first in 1995. Photons, the quantized particles of light, usually exibit no Bose-Einstein condensation, because for Planck's blackbody radiation the particle number is not conserved and the photons disappear at low temperature in the walls of the system. We investigate the thermodynamics of a two-dimensional photon gas in a dye-molecule filled optical microresonator. The resonator mirrors here provide both a confining trapping potential as well as a nonvanishing effective mass of the photon, so that the system is formally equivalent to harmonically confined two-dimensional gas of massive particles. By repeated absorption and emission processes in dye molecules, the photon gas thermalizes with the temperature of the dye solution, which is at room temperature. The so far observed properties of the photon Bose-Einstein condensate in many respects resemble those of atomic Bose-Einstein condensates, while the 10 order of magnitude smaller effective photon mass allows for transiton temperatures at room temperature.

### We have determined the particle number statistics of the photon condensate generated in the dye microresonator system. For small photon numbers, for condensed state conditions unusually high values of the normalized intensity correlation of up to g^{(2)}(0)=1.7 are observed, which significantly differs from the for usual Bose-Einstein-condensates or also lasers observed value g^{(2)}(0)=1. The background of the enhanced particle number fluctuations is that the photon condensate can effectively exchange particles with the photo-excitable dye molecules, as can be well described in the picture of the grand canonical statistical ensemble. The measurements provide direct evidence for a grand canonical Bose-Einstein condensate. For high condensate particle numbers, or also for small molecular numbers, again the usual value g^{(2)}(0)=1 is observed, which then corresponds to a canonical ensemble.

### In other works, we have determined the heat capacity of condensed light. Recently, also periodic lattice potentials for light trapped in the microresonator have been realized.

Dye molecules serve as heat bath and particle reservoir for the photon gas (left). If the effective size of the reservoir is high enough, grand canonical statistics fluctuations of the condensate particle number occur, which do not appear for a small reservoir size. The right panel shows measured data for g^{(2)}(0) for different effective reservoir sizes and condensate fractions.

Some references:

Bose-Einstein condensation of photons in an optical microcavity

J. Klärs, J. Schmitt, F. Vewinger, and M. Weitz

Nature **468**, 545 (2010)

Thermalization of a two-dimensional photonic gas in a ‘white wall’ photon box

J. Klärs, F. Vewinger, and M. Weitz

Nature Phys. **6**, 512 (2010)

Statistical physics of Bose-Einstein-condensed light in a dye microcavity

J. Klärs, J. Schmitt, T. Damm, F. Vewinger, and M. Weitz

Phys. Rev. Lett. **108**, 160403 (2012), arXiv:1201.0444

Observation of grand-canonical number statistics in a Photon Bose-Einstein condensate

J. Schmitt, T. Damm, D. Dung, F. Vewinger, J. Klärs, and M. Weitz

Phys. Rev. Lett. **112**, 030401(2014), arXiv:1311.6634, Physics Viewpoint

J. Schmitt, T. Damm, D. Dung, F. Vewinger, J. Klaers, and M. Weitz

Phys. Rev. A

**92**, 011602 (2015), arXiv: 1410.5713

**116**, 033604 (2016), arXiv: 1512.07148

T. Damm, J. Schmitt, Q. Liang, D, Dung, F. Vewinger, M. Weitz, and J. Klaers

**7**, 11340 (2016), arXiv: 1604.08747

Bose-Einstein-Kondensat aus Licht

J. Klärs, J. Schmitt, F. Vewinger und M. Weitz

Phys. Unserer Zeit

**42**, 58 (2011)