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