1. Microscopic model of photon condensation Milan Radonjić, Antun Balaž and Axel Pelster TU Berlin, 04.06.2015.

2. Outline The photon BEC experiment Microscopic model Master equation Equations of motion for averages To be, or not to be BEC (LASER)? Future work

3. The photon BEC experiment J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Nature (London) 468, 545 (2010)

4. Microscopic model Hamiltonian of the system: photon modes dye molecules electron-phonon coupling photon-dye interaction Dressed phonon Hamiltonian: to avoid renormalization of phonon frequency Similar model: P. Kirton and J. Keeling, Phys. Rev. Lett. 111, 100404 (2013)

5. Microscopic model Transformation to normal modes:

6. Microscopic model Treatment of electron-dressed phonon interaction via polaron transformation: electron-dressed phonon coupling

7. Microscopic model We treat dressed phonons as a bath in a thermal state: Bath effects are treated using standard second-order perturbation theory: First order yields coherent coupling

8. Microscopic model Modeling the bath spectral density function: coupling strength cut-off frequency

9. Microscopic model Second order yields dissipative effects: effect of pumping and decay retarded correlation function of thermal fluctuations of displacement operators Different from Kirton & Keeling, PRL 111, 100404 (2013) !!

10. Master equation Evolution equation: pumping spontaneous decay cavity losses

11. Equations of motion for averages Assumptions: Correlations of higher than second order are neglected!

12. Equations of motion for averages Degrees of freedom of dye molecules: coherent coupling relaxation We have competition between coherent and dissipative influence of the bath!

13. BEC or LASER? Weak influence of collisions with the solvent: Depends on the bath: LASER!

14. BEC or LASER? Strong influence of collisions with the solvent: Depends on the bath: BEC!

15. Future work Characterization of stationary states Correlation functions e.g. Phase diagrams Stability issues Temporal behavior/relaxation Higher order truncation schemes…