Regensburg 2019 – scientific programme

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HL: Fachverband Halbleiterphysik

HL 39: Quantum dots and wires: Optical properties I

HL 39.2: Talk

Thursday, April 4, 2019, 09:45–10:00, H34

An information theoretical approach to the many-particle hierarchy problem: application to quantum dot microcavity lasers — •Boris Melcher, Boris Gulyak, and Jan Wiersig — Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany

Using the maximum entropy principle [E. T. Jaynes, Phys. Rev. 106, 620 (1957), Phys. Rev. 108, 171 (1957)], we develop a stand-alone approach to numerically determine the full density matrix of open quantum systems. By doing so, the many-particle hierarchy problem that arises in conventional equation of motion techniques and makes it necessary to utilize factorization and truncation schemes such as the cluster expansion method [H. A. M. Leymann et al., Phys. Rev. B 89, 085308 (2014)], is completely avoided. Instead, a finite set of input information is used to calculate the least biased density matrix self-consistently, and thus making all relevant expectation values and correlation functions as well as the full statistics directly accessible.

As a benchmark, we compare the maximum entropy method results for a four-level single quantum dot microcavity laser where the full density matrix is still available by numerically solving the von Neumann-Lindblad equation and demonstrate excellent agreement in terms of entropy, mean photon number, autocorrelation function, and photon statistics. Finally, we show that our approach can be used as a tool for learning about the relevant processes of quantum systems.