Maximum-entropy method applied to the many-particle hierarchy problem in quantum-dot-microcavity systems

• Applicant: Professor Dr. Jan Wiersig
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 327790415

• Final Report Year: 2021

Final Report Abstract

The general objective of the project was to apply the maximum-entropy method to driven-dissipative quantum many-particle systems, with the focus on semiconductor quantum-dotmicrocavities. Most of the goals of the project have been accomplished and further interesting results beyond the original plan have been obtained. The individual results are as follows: The maximum-entropy method is an efficient scheme to compute full statistics and substatistics, such as the photon statistics of a microcavity laser, from the knowledge of moments given by equation-of-motion approaches. The entropy and the Lagrange multipliers, which appear as a by-product of the maximum-entropy method, can be used to characterize the quantum system under study. For instance, the zero of the first Lagrange multiplier is a good marker for the laser threshold in (nearly) “thresholdless” microcavity lasers. The maximum-entropy method can be used to circumvent the many-particle hierarchy problem for the case of steady-state solutions (but thermodynamic nonequilibrium). The efficient approach allows to numerically determine the full density matrix of driven-dissipative quantum many-particle systems and gain access to all relevant expectation values and the full statistics and not only moments and correlation functions. A factorization of moments and a costly time integration is thereby completely avoided. The approach can be used as a trial-and-error tool for learning and identifying the relevant processes of physical systems. Our considerations suggest that bimodal lasers are ideal sources of bunched photons.

Publications

• Determination of the full statistics of quantum observables using the maximum-entropy method. Phys. Rev. A, 98:053857, 2018
  B. Gulyak, B. Melcher, and J. Wiersig
  
• Superthermal photon bunching in terms of simple probability distributions. Phys. Rev. A, 97:053835, 2018
  T. Lettau, H. A. M. Leymann, B. Melcher, and J. Wiersig
  
• Information-theoretical approach to the many-particle hierarchy problem. Phys. Rev. A, 100:013854, 2019
  B. Melcher, B. Gulyak, and J. Wiersig