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Open Quantum Systems
Provider: Science

Activity no.: 5931-25-11-31There are 21 available seats 
Enrollment deadline: 02/02/2025
PlaceNiels Bohr Institute
Date and timeFebruary 2025 - April 2025
Regular seats30
ECTS credits5.00
Contact personStine Stenfatt West    E-mail address: west@nbi.ku.dk
Enrolment Handling/Course OrganiserKlaus Mølmer    E-mail address: klaus.molmer@nbi.ku.dk
Semester/BlockBlock 3
Exam requirementsThe course will be completed by each student preparing and delivering a presentation to the class on a topic discussed in a recent research publication.
Grading scaleApproved / Not approved
Aim and content
Aim and Content
Please state the purpose of the course
You must also present a thorough course description of the course content, i.e. a description of what will happen during the run of the course The purpose of the course is to present various methods to describe so-called open quantum systems, i.e. systems that interact with their environment, leading to decay, dissipation, leakage of information. Applications include assessment of errors in quantum computers, sensing with non-classical states of matter, understanding the dynamics (e.g., light-matter interaction, transport) of quantum systems in nonequilibrium settings.
1. Motivation, brief review of physical quantum systems and their environments: atoms and light, spins and phonons, superconducting qubits and spin baths, cavities and resonators with internal and leakage losses, motional oscillators and their “mounts”, quantum dots, defects and phonons, … .
2. Markov approximation, (Lindblad) master equation, quantum regression theorem. Alternative forms of master equations, Redfield, Nakajima-Zwanzig equation, Vernon-Feynman influence functional theory.
3. Photodetection theory and elements of general quantum measurement theory, quantum trajectories, quantum sensing with continuously probed quantum systems.
4. Reservoir engineering, combined coherent and dissipative generation of useful quantum states, strategies to reduce environment coupling, “quantum error correction”.
5. Elements of Quantum Thermodynamics. Work and Heat, fluctuations, transport.

Formel requirements
Bachelor level in physics, Quantum Mechanics 1 and 2 (basic formalism, perturbation theory).

Learning outcome
Knowledge:
• Know the essential environmental influences on different quantum systems
• Know the formalism to solve dynamics of quantum systems with dissipation and loss
• Know the connection between deterministic average dynamics and stochastic conditional dynamics

Skills:
• Ability to model and solve the master equation for simple quantum systems, e.g., with QuTip.
• Ability so model and solve stochastic wave function dynamics for an observed quantum system, e.g., with QuTip.
• Build and work with Master Equation and Stochastic Schrödinger Equation solvers.

Competences:
• Being able to assess and account for the interplay between dissipation and unitary dynamics of a quantum system, based on reading if current literature
• Being able to judge the importance of full versus simplified approaches (when can coupling to an environment be simplified or even neglected).

Teaching and learning methods
The course will teach the main methods and concepts in lectures using review style articles and special results and examples will be discussed and worked through by the students with starting point in recent research articles. The students will summarize results and methods to the class by short lectures and on-line summaries.

Lecturers
In addition to main lectures offered by Klaus Mølmer and Assistant Professor Frederik Nathan NQCP/NBI, we will invite contributions from the expert communities at and around NBI (Quantum Section Condensed Matter Section, QDev, Quantop, Hy-Q, NQCP) .

Workload
Preparation: 102.5
Lectures: 14
Class Instruction: 7
Theoretical Exercises: 14

0 DKK, 6000 DKK or 6000 DKK + 180 % , according to enrollment in Danish or foreign University or, e.g., private company. See KU Science Faculty rules, https://science.ku.dk/phd/courses/databases/Pricing_PhD_courses_at_SCIENCE_2024.pdf

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