Feedback control of photon statistics, and rst steps toward a phonon laser modelling
Externally pumped nanostructures based in nano-cavities exhibit a wealth of features, including bifurcations and instabilities, due to the complex behaviour and interplay between phonons, photons and electrons. In our presentation, we discuss our approach to include non-Markovian contributions into the concepts of time delayed feedback control. In particular, we focus on the stabilization of exotic photon and phonon states beyond typical bath approximations.
In the first part, besides a general introduction to the equation of motion approach , a microcavity system, consisting of an emitter, a control field and a feedback loop system is investigated. Starting from the Lang-Kobayashi model, we quantize the cavity field and show stable and unstable photon-statistics solution in a stationary limit in dependence on the transmission and reflection coefficients of the external mirrors. Possible pump mechanisms are discussed, also.
In the second part, first steps of the modelling of a phonon laser is presented. Recent progress in the realization of phonon-lasers, involving non-equilibrium phonons, motivate theoretical frameworks beyond typical bath approximations (second order Born- Markov approximation) [2,3]. The concept of a phononlaser and possible control mechanisms are shown, such as coherent pumping via a heating and a cooling beam. Additionally, phonon statistics in phonon cavities are incorporated as a measure of the nonequilibrium of the phononic system.
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 J. Kabuss, A. Carmele, M. Richter, and A. Knorr, submitted to Phys. Rev. B (2011)