Continuous Measurement of a Non-Markovian Open Quantum System

TL;DR

This paper introduces a formalism for continuous measurement of complex, non-Markovian quantum systems, enabling better understanding and control of their decoherence dynamics through a novel spectroscopy method.

Contribution

It develops a generalized dispersive measurement framework for non-Markovian systems and introduces SHEM formalism and weak spectroscopy for environmental characterization.

Findings

Derived SHEM for non-Markovian decoherence dynamics

Proposed weak spectroscopy to identify non-Markovian environments

Demonstrated the formalism's applicability to complex quantum systems

Abstract

Continuous quantum measurement is the backbone of various methods in quantum control, quantum metrology, and quantum information. Here, we present a generalized formulation of dispersive measurement of a complex quantum systems. We describe the complex system as an open quantum system that is strongly coupled to a non-Markovian environment, enabling the treatment of a broad variety of natural or engineered complex systems. The system is monitored via a probe resonator coupled to a broadband (Markovian) reservoir. Based on this model, we derive a formalism of Stochastic Hierarchy Equations of Motion (SHEM) describing the decoherence dynamics of the system conditioned on the measurement record. Furthermore, we demonstrate a spectroscopy method based on weak quantum measurement to reveal the non-Markovian nature of the environment, which we term weak spectroscopy.