PHY/ECE 624, Open Quantum Systems, Spring 2023
SynopsisIn several experimental frameworks, a high level of control on quantum systems has been accomplished. Due to practical constraints and our aim of manipulating these systems efficiently, they are inevitably open in the sense that they are coupled to the environment. This generally leads to dissipation and decoherence, which pose challenges for modern quantum technology. On the other hand, one can design environment couplings to achieve novel effects and, e.g., to stabilize useful entangled states for quantum computation and simulation. The description of open systems goes beyond the unitary dynamics covered in introductory quantum mechanics courses; it involves intriguing new mathematical aspects and physical phenomena.This course provides an introduction to open quantum systems. We will start by discussing quantum mechanics of composite systems, which leads us from pure states to density operators and from unitary dynamics to quantum channels. At this stage, we can already gain an understanding of decoherence, dephasing, and error correction. We will then derive and discuss the Lindblad master equation, which describes the evolution of Markovian systems. It covers, for example, systems weakly coupled to large baths or closed quantum systems with external noise. As we will see in applications for specific models, it can explain dissipation, decoherence, and thermalization. We will talk about prominent experimental platforms for quantum computation and simulation from this viewpoint. The analog of Hamiltonians for closed systems are Liouville super-operators for open systems. As they are non-Hermitian, interesting mathematical aspects arise. We will discuss fundamental properties like the spectrum and their connection to phase transitions in the nonequilibrium steady states. We will close with a summary of analytical and numerical methods for the investigation of open many-body systems, addressing third quantization, perturbation theory, exact diagonalization, quantum trajectories, tensor networks, and the Keldysh formalism. Depending on the available time, we may also address examples for non-Markovian dynamics and corresponding techniques. The course is intended for students from physics, quantum engineering, quantum chemistry, and math. We expect basic knowledge of quantum mechanics, e.g., on the level of PHY 464 or ECE 521 (Schrödinger equation, bra-ket notation, spin, tensor product). Lecture Notes[Are provided on the Sakai site PHYSICS.624.02.Sp23]LiteratureRecommended reading for large parts of the course:
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