Two dimensional photon gases trapped in dye-filled microcavities can undergo thermalization and nearly ideal equilibrium Bose-Einstein condensation. However, they are inherently drivendissipative systems that can exhibit an intricate interplay between the thermalizing influence of the environment given by the dye solution and the pump and loss processes driving the system out of equilibrium. We show that this interplay gives rise to a robust mechanism for two-mode emission, when the system is driven by an off-centered pump beam. Namely, after the system starts lasing in the dominantly pumped excited mode, in a second transition a photon condensate is formed in the ground mode, when the pump power is increased further. This effect is a consequence of the redistribution of excited dye molecules via the lasing mode in combination with thermalization. We propose to exploit this effect for engineering controlled two-mode emission and demonstrate that by tailoring the transverse potential landscape for the photons, the threshold pump power can be tuned by orders of magnitude.

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