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I found in Nature magazine that photon can have Bose-Einstein condensation.

But I have a question how to derive the critical temperature for photon? Because the chemical potential of photon is zero and rest mass is also zero. And what's the microscopic mechanism of BEC of photon?

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    $\begingroup$ Photons do not form a Bose-Einstein condensate in free space. The abstract of the paper itself makes this very clear: "However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state.". One has to fill the cavity with some matter for BEC to occur. $\endgroup$ – CuriousOne Oct 16 '14 at 6:01
  • $\begingroup$ @CuriousOne Thanks, I know in free space Photons do not form a Bose-Einstein condensate , then how to derive the critical temperature of BEC in cavity like this paper? $\endgroup$ – 346699 Oct 16 '14 at 7:04
  • $\begingroup$ I can't tell you about the theory. In my opinion this doesn't really count as a BEC of photons. It may be a BEC of the mixed quantum state of the photons and the material in the cavity. From my perspective the far more interesting question is if photons have a "cosmological rest mass", i.e. if there can be a low temperature state of the universe in the far future, in which the free photon gas will do something unexpected (like form local BEC "lumps"). $\endgroup$ – CuriousOne Oct 16 '14 at 7:37
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The photons in the experiment are confined in a cavity, which gives effective mass to photons. With that, you could calculate the critical temperature as usual.

Although it is non-trivial to distinguish between lasing and Bose-Einstein condensation, they claim that they see "thermalization" via a lot of absorption and emission events with dye molecules, which is one of the main distinctions between lasing and Bose-Einstein condensation.

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