Open system probes of many-body environments: Effects of quantum backaction

The reduced dynamics of an open system are uniquely determined by the spectral structure and correlations in the environment, providing a powerful means to probe a complex many-body quantum system through the lens of a simple quantum system. We recently showed how a central "probe" spin coupled to a 1D transverse-field Ising model (TFIM), via a quantum non-demolition (QND) interaction, exhibits Markovian evolution at all conformal fixed points including the quantum critical point. Crucially, we found that the non-Markovian flow of spin dephasing rate mimics the renormalization group flow in the many-body phase diagram. In this talk, we discuss the development of a quantum master equation for the same setup, without constraining the probe-TFIM interaction to be QND. We investigate both the decoherence rate and the steady-state emission spectrum of the probe to deconvolve the effects of quantum backaction on both single-time and two-time system observables. Further, using tensor network simulations, we benchmark our analytical predictions, including at finite-temperatures where exact solutions remain analytically intractable. Our results highlight intriguing connections between non-Markovianity and long-range correlations in reservoir-engineered quantum systems.