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Direct reconstruction of the quantum master equation dynamics of a trapped ion qubit

The physics of Markovian open quantum systems can be described by quantum master equations. These are dynamical equations, that incorporate the Hamiltonian and jump operators, and generate the system's time evolution. Reconstructing the system's Hamiltonian and and its coupling to the environment from measurements is important both for fundamental research as well as for performance-evaluation of quantum machines. In this paper we introduce a method that reconstructs the dynamical equation of open quantum systems, directly from a set of expectation values of selected observables. We benchmark our technique both by a simulation and experimentally, by measuring the dynamics of a trapped $^{88}\text{Sr}^+$ ion under spontaneous photon scattering.