# Applied Superconductivity (Josephson Effects, Superconducting Electronics and Superconducting Quantum Circuits)

## Module PH2157

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of SS 2020

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions | ||||
---|---|---|---|---|

SS 2021 | SS 2020 | SS 2019 | SS 2018 | SS 2013 |

### Basic Information

PH2157 is a semester module in English or German language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

- Specific catalogue of special courses for condensed matter physics
- Specific catalogue of special courses for Applied and Engineering Physics
- Focus Area Experimental Quantum Science & Technology in M.Sc. Quantum Science & Technology
- Complementary catalogue of special courses for nuclear, particle, and astrophysics
- Complementary catalogue of special courses for Biophysics

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workload | Contact hours | Credits (ECTS) |
---|---|---|

300 h | 90 h | 10 CP |

Responsible coordinator of the module PH2157 in the version of SS 2020 was Rudolf Gross.

### Content, Learning Outcome and Preconditions

#### Content

Despite the fact that sometimes superconductivity is still considered exotic, superconductivity meanwhile has a number of important applications. In this module the most relevant present and future applications of superconductivity are discussed, starting from what is commonly referred to as the macroscopic quantum model of superconductivity. 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. They are intensively studied in various collaborative research projects (e.g. SFB 631, cluster of excellence NIM). In this module 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 the application of superconducting quantum circuits in the study of fundamental light-matter interaction, the realization of solid state based quantum information processing systems and in quantum simulation.

Regarding the application of superconductivity in electronics and for sensors the course addresses the following topics:

- macroscopic quantum model of superconductivity
- Josephson effects
- Josephson junctions and Superconducting Quantum Interference Devices (SQUIDs)
- Josephson voltage standard
- superconducting digital electronics
- superconducting particle detectors & microwave applications
- solid-state based quantum information processing devices

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 octics on a chip"
- quantum information processing with superconducting circuits
- propagating quantum microwaves

#### Learning Outcome

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

- to describe and apply the physical foundations related to superconducting electronics and sensors as well as superconducting quantum devices and circuits.
- to explain the macroscopic quantum model of superconductivity and to apply it to the description of weakly coupled superconductors.
- to illustrate and interprete the Josephson effects.
- to list and explain the basic properties of Josephson junctions and Superconducting QUantum Interference Devices (SQUIDs).
- to explain the operation principle of the Josephson voltage standard.
- to describe the foundations of superconducting digital electronics.
- to illustrate the operational principle and physical foundations of superconducting particle detectors and microwave devices.
- to describe 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 and of quantum communication by propagating quantum microwaves.

#### Preconditions

No prerequisites that are not already included in the prerequisites for the Master’s programmes.

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

Type | SWS | Title | Lecturer(s) | Dates | Links |
---|---|---|---|---|---|

VO | 4 | Applied Superconductivity: Josephson Effects, Superconducting Electronics and Superconducting Quantum Circuits | Fedorov, K. Gross, R. |
Mon, 14:15–15:45, WMI 143 Wed, 14:15–15:45, WMI 143 |
documents |

UE | 2 | Tutorial to Applied Superconductivity: Josephson Effects, Superconducting Electronics and Superconducting Quantum Circuits | Fedorov, K. Gross, R. | dates in groups |
documents |

#### Learning and Teaching Methods

The modul consists of a lecture and exercise classes.

In the thematically structured lecture the learning content is presented by blackboard work, beamer presentation). 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.

#### Media

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

#### Literature

- Lecture notes and handouts
- R. Gross & A. Marx, Festkörperphysik, de Gruyter, 3. Auflage (2018)
- Tinkham: Introduction to Superconductivity
- K. K. Likharev: Dynamics of Josephson Junctions and Circuits Gordon and Breach Science Publishers, New York (1986)
- T. P. Orlando, K. A. Delin: Foundations of Applied Superconductivity, Addison-Wesley, New York (1991)
- Fossheim, Sudbo: Superconductivity - Physics and Applications
- Buckel, Kleiner: Supraleitung
- de Gennes: Superconductivity of Metals and Alloys
- Claude Cohen-Tannoudji: Quantum Mechanics, Volume I, Wiley-Interscience (2006)

### Module Exam

#### Description of exams and course work

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:

- Explain the foundations of the macroscopic quantum model of superconductivity
- Discuss how the current-phase and energy-phase relation can be derived from the macroscopic quantum model of superconductivity
- Show how the London equations and the fluxoid quantization can be derived from the current-phase and energy-phase relation
- How can we describe the basic properties of weakly coupled superconductors in the framework of the macroscopic quantum model?
- What are Josephson junctions and which basic equations can we use for their description?
- What are the characteristic length and time scales of Josephson junctions?
- Discuss the dynamics of Josephson junctions in the voltage state. Which equations can be used to describe their dynamics?
- Discuss the behavior of Josephson junction in an applied magnetic field and at an applied ac voltage
- Explain the physical foundations, the operation principle and applications of superconducting quantum interference devices
- Explain the physical foundations and operation principle of superconducting particle and microwave detectors
- -
- 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

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

#### Exam Repetition

The exam may be repeated at the end of the semester.