I Master Equation Methods in Quantum Optics

H. J. Carmichael, Marlan O. Scully

Hou Bang-pin

The algebraic structure for the master equation of the generalized dissipative two-mode optical system has been set up in this paper. Based on the structure, the master equation is rewritten as a Schrdinger-like equation, then the exact solution to the master equation in the particle number representation has been obtained by using algebraic dynamical method.

Gautam Gangopadhyay, Deb Shankar Ray

Ravinder Rupchand Puri

Yudan Liu, Ellen Mulvihill, Eitan Geva

The generalized quantum master equation (GQME) approach provides a powerful general-purpose framework for simulating the inherently quantum mechanical dynamics of a subset of electronic reduced density matrix elements of interest in complex molecular systems. Previous studies have found that combining the GQME approach with quasiclassical mapping Hamiltonian (QC/MH) methods can dramatically improve the accuracy of electronic populations obtained via those methods. In this paper, we perform a complimentary study of the advantages offered by the GQME approach for simulating the dynamics of electronic coherences, which play a central role in optical spectroscopy, quantum information science, and quantum technology. To this end, we focus on cases where the electronic coherences predicted for the spin-boson benchmark model by direct application of various QC/MH methods are inaccurate. We find that similar to the case of electronic populations, combining the QC/MH methods with the GQME approach can dramatically improve the accuracy of the electronic coherences obtained via those methods. We also provide a comprehensive analysis of how the performance of GQMEs depends on the choice of projection operator and electronic basis and show that the accuracy and feasibility of the GQME approach can benefit from casting the GQME in terms of the eigen-basis of the observable of interest.

Francesco Campaioli, Jared H. Cole, Harini Hapuarachchi

Quantum master equations are an invaluable tool to model the dynamics of a plethora of microscopic systems, ranging from quantum optics and quantum information processing to energy and charge transport, electronic and nuclear spin resonance, photochemistry, and more. This tutorial offers a concise and pedagogical introduction to quantum master equations, accessible to a broad, cross-disciplinary audience. The reader is guided through the basics of quantum dynamics with hands-on examples that increase in complexity. The tutorial covers essential methods such as the use of the Lindblad master equation, Redfield relaxation, and Floquet theory, as well as techniques such as Suzuki-Trotter expansion and numerical approaches for sparse solvers. These methods are illustrated with code snippets implemented in and other languages, which can be used as a starting point for generalization and more sophisticated implementations. Published by the American Physical Society 2024