Continuous Measurement of a Non-Markovian Open Quantum System

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.

Published version, the section on continuous state tomography will be published in a separate manuscript

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Cited by in corpus (16)

• Non-Markovianity and memory effects in quantum open systems
• Artificial quantum thermal bath: Engineering temperature for a many-body quantum system
• Non-Markovian Quantum Dynamics in Strongly Coupled Multimode Cavities Conditioned on Continuous Measurement
• Stochastic Feshbach Projection for the Dynamics of Open Quantum Systems
• Modelling and Filtering for Non-Markovian Quantum Systems
• Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function
• Landau-Zener evolution under weak measurement: Manifestation of the Zeno effect under diabatic and adiabatic measurement protocols
• Noise, delocalization, and quantum diffusion in one-dimensional tight-binding models
• Quantum superballistic diffusion in presence of white noise
• A superconducting circuit probe for analog quantum simulators
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• Quantum jump metrology in a two-cavity network
• Efficient Quantum State Tracking in Noisy Environments
• Realization of A Non-Markov Chain in A Single 2D Crystal RRAM