microscopic model of photon condensation milan radonjić, antun balaž and axel pelster tu berlin,...
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Microscopic model of photon condensation
Milan Radonjić,Antun Balaž and Axel Pelster
TU Berlin, 04.06.2015.
Outline
• The photon BEC experiment
• Microscopic model
• Master equation
• Equations of motion for averages
• To be, or not to be BEC (LASER)?
• Future work
The photon BEC experiment
J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Nature (London) 468, 545 (2010)
Microscopic modelHamiltonian of the system:
photon modes dye moleculeselectron-phonon couplingphoton-dye interaction
Dressed phonon Hamiltonian:
to avoid renormalizationof phonon frequency
Similar model: P. Kirton and J. Keeling, Phys. Rev. Lett. 111, 100404 (2013)
Microscopic model
Transformation to normal modes:
Microscopic model
Treatment of electron-dressed phonon interactionvia polaron transformation:
electron-dressed phonon coupling
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
Microscopic model
Modeling the bath spectral density function:
coupling strength cut-off frequency
Microscopic modelSecond order yields dissipative effects:
effect of pumping and decay retarded correlation functionof thermal fluctuations ofdisplacement operators
Different from Kirton & Keeling, PRL 111, 100404 (2013) !!
Master equation
Evolution equation:
pumping spontaneous decaycavitylosses
Equations of motion for averagesAssumptions:
Correlations of higher than second order are neglected!
Equations of motion for averagesDegrees of freedom of dye molecules:
coherentcoupling relaxation
We have competition between coherent and dissipative influence of the bath!
BEC or LASER?
Weak influence of collisions with the solvent:
Depends on the bath:
LASER!
BEC or LASER?
Strong influence of collisions with the solvent:
Depends on the bath:
BEC!
Future work
• Characterization of stationary states
• Correlation functions e.g.
• Phase diagrams
• Stability issues
• Temporal behavior/relaxation
• Higher order truncation schemes…
(1) (2), ,g g K