Abstract
We use the maximum entropy principle to circumvent the many-particle hierarchy problem that arises in conventional equation of motion techniques. Our efficient approach enables us 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. We compare the maximum entropy method results with the numerically exact solution of the von Neumann-Lindblad equation for a four-level system resonantly coupled to one cavity mode and demonstrate excellent agreement in terms of entropy, mean photon number, autocorrelation function, and photon statistics. Moreover, we show that our approach can be used as a tool for learning about the relevant processes of quantum systems.
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