Unified framework for open quantum dynamics with memory

Area of Science:

• Quantum mechanics
• Quantum dynamics
• Condensed matter physics

Background:

• Quantum systems coupled to baths exhibit memory effects, often studied via Nakajima-Zwanzig memory kernels or influence functions.
• Formal connections between these two formalisms for describing quantum dynamics have been previously unknown.

Purpose of the Study:

• To establish the formal connections between Nakajima-Zwanzig memory kernels and influence functions.
• To develop a non-perturbative method for constructing memory kernels from influence functions.
• To provide a framework for interpreting approximate path integral methods and enabling Hamiltonian learning.

Main Methods:

• Examining the system propagator for N-level systems linearly coupled to Gaussian baths.
• Developing a non-perturbative, diagrammatic approach to construct memory kernels from influence functions.
• Utilizing reduced system trajectories for Hamiltonian learning.

Main Results:

• Explicit connections between Nakajima-Zwanzig memory kernels and influence functions were established.
• A novel non-perturbative, diagrammatic method was devised to construct memory kernels from influence functions.
• A Hamiltonian learning procedure was proposed to extract bath spectral density from system trajectories.

Conclusions:

• The established connections advance the understanding of non-Markovian quantum dynamics.
• The developed methods offer new avenues in quantum sensing and engineering.
• This work serves as a foundation for future theoretical and experimental advancements in quantum dynamics.