Three limiting cases - one theory: Decoding quantum dynamics from continuous measurements via higher order spectra in cases of telegraph noise, Gaussian noise, and stochastic clicks

Probing the dynamics of a quantum system is always challenging as the probe itself is quantum resulting in stochastic measurement records. We discuss measurement schemes from quantum transport [1], optical spin noise spectroscopy [2], and single photon counting [3,4] that exhibit very diverse records like random telegraph noise, mainly Gaussian laser shot noise, or stochastic clicks. This raises the question for a suitable quantitative unified evaluation procedure that can relate signatures of the measurement to a theoretical treatment of the system. We solve the problem by calculating higher-order spectra up to fourth order of the measurement records [1]. System parameters follow from fitting theoretical to experimental spectra. We employ recently derived general quantum mechanical expression for higher-order spectra that depend only on the open-system Liouvillian and the measurement operator and correctly include measurement induced back-action [2]. We demonstrate that a transition from probing a system with a continuous laser beam to probing with stochastic single photons preserves all information of the higher order spectra. Our scheme thus allows for decoding quantum dynamics from measurements at ultra-low light levels [3,4] with potential applications in high-resolution spectroscopy, quantum sensing, and quantum electrodynamics.