Applied Superconductivity 2: from superconducting quantum circuits to microwave quantum optics

The application of superconducting circuits for the realization of future quantum electronics has attracted strong interest, in particular regarding the implementation of quantum information processing systems. Here, we address the physics of superconducting quantum circuits and show how such circuits can be implemented based on superconducting thin films and nanostructures. We also discuss applications of superconducting quantum circuits in the study of fundamental light-matter interaction, the realization of quantum information processing systems and in quantum simulation. Finally, we consider the field of quantum communication and sensing with propagating quantum microwaves emitted from superconducting circuits. All these fields are nowadays intensively studied in the cutting edge collaborative research projects (e.g. EU Quantum Flagship, Excellence Cluster MCQST, Munich Quantum Valley, among others).

Regarding the application of superconductivity in quantum electronics, the following specific topics will be addressed:

• introduction to secondary quantumn effects
• superconducting quantum circuits: from resonators to qubits
• circuit Quantum electrodynamics: "Quantum optics on a chip"
• quantum information processing with superconducting circuits
• propagating quantum microwaves
• quantum microwave communication and cryptography
• quantum illumination and remote sensing

After successful completion of the module the students are able to:

• to describe and explain the secondary macroscopic quantum effects in Josephson junctions.
• to explain the physical foundations of superconducting quantum circuits (resonators, quantum bits, circuit QED).
• to list the key features of quantum information processing with superconducting circuits.
• to describe the basic properties of propagating quantum microwaves.
• to describe basic quantum communication and sensing protocols.

No preconditions in addition to the requirements for the Master’s program in Physics, preliminary knowledge from the lecture on Applied Superconductivity 1 is highly recommended.

The module consists of a lecture and exercise classes.

In the thematically structured lecture the learning content is presented by blackboard work, beamer presentation, etc. With cross-references between different topics the universal concepts in physics are shown. The students are involved in scientific discussions to stimulate their analytic and physics-related intellectual power.

In the exercise groups the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

Lecture Notes, exercise sheets, supplementary literature, PowerPoint slides, movies, lab tour, etc..

• Lecture notes and handouts
• R. Gross & A. Marx, Festkörperphysik, de Gruyter, 3. Auflage (2018)
• Claude Cohen-Tannoudji: Quantum Mechanics, Volume I, Wiley-Interscience (2006)
• M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2000)
• D. E. Walls, G. J. Milburn Quantum Optics 2nd edition, Springer (2008)

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

• Discuss seondary quantum effects in Josephson junctions. On which conditions do they play a crucial role?
• Derive the Hamilton operator for a Josephson junction. What are the conjugate variables?
• What do we mean by the nonlinear Josephson inductance?
• How can we realize quantum bits by using Josephson junctions?
• What do we mean by relaxation and dephasing of quantum bits? What are the underlying physical mechanisms?
• Discuss the basic properties of superconducting flux, charge and phase quantum bits. How can we manipulate them and read them out?
• Discuss the basic properties of superconducting microwave resonators
• What do we mean by superconducting circuit quantum electrodynamics?
• Discuss the Jaynes-Cummings model and its validity range. What do we mean by weak, strong and ultra-strong coupling?
• Discuss the basic properties of propagating quantum microwaves
• What are squeezed states and how can we generate them in the microwave regime?

In the exam no learning aids are permitted.

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.