Superconducting Quantum Devices SQUIDs, Qubits, and Quantum-Limited Amplifiers

Introduction

Superconducting quantum devices (SQDs) are electrical circuits utilizing the unique features of superconductivity such as dissipationless direct current flow, ideal diamagnetism, magnetic flux quantization and Cooper pair tunneling. SQDs can nowadays be reliablely fabricated using advanced thin-film technologies and allow building macroscopic systems such as artificial atoms that show quantum-mechanical behaviour. The scalability, reproducibility and controllability of these systems facilitate to study complex quantum-mechanical systems while having the unique possibility to adjust key system parameters such as coupling strengths, operation frequencies or energy scales. SQDs are therefore an outstanding experimental playground for investigating new physics under well-defined experimental boundary conditions. Besides this, SQDs are used as most sensitive devices for measuring or amplifying different physical quantities and are hotly tipped as very promising candidates for the implementation of a quantum computer.

This lecture gives a comprehensive introduction into the physics and applications of superconducting quantum devices. In particular, we discuss the physics of Josephson tunneling junctions which are of similar importance for SQDs than transistors for modern semiconductor circuits. We cover superconducting quantum interference devices (SQUIDs) that are presently the most sensitive wideband devices for measuring various physical quantities such as voltage, current or magnetic field that can be naturally converted into magnetic flux. We discuss different kinds of superconducting quantum bits and give an introduction into quantum computing using SQDs. Finally, we deal with SQD-based quantum-limited amplifiers that are presently the only devices overcoming existing noise limits of conventional semiconductor electronics.

Content

• Introduction to superconductivity (perfect conductivity, ideal diagmagnetism, BCS theory, macroscopic wave function, magnetic flux quantization, Josephson effects)
• Josephson tunnel junctions (realization of Josephson junctions, RCSJ-model, mechanical analogon, long and short Josephson junctions, behaviour in external magnetic fields, quantum-mechanical description of a Josephson junction)
• Superconducting quantum interference devices (SQUIDs) (theoretical description of dc- and rf-SQUIDs, SQUID design, SQUID readout, SQUID applications)
• SQUID based low-and high-frequency amplifiers
• Microwave properties of superconductors, superconducting resonators
• Superconducting Quantum Bits (Cooper pair box, flux qubit, phase qubit, transmon qubit, etc.)
• Quantum-limited amplifiers, quantum measurements, quantum-mechanical description of amplifiers
• Quantum computing, Deutsch and Shore algorithm, quantum error correction
• Digital superconducting electronics

Prerequisite knowledge

Besides a general understanding of quantum mechanics and solid-state physics as gained by the module PEP5 , there is no prerequisite knowledge. All relevant aspects on superconductivity will be introduced within the lecture. Detailed knowledge about solid-state physics as gained by the advanced lecture on condensed matter physics (CMP) might be helpful.

Lecture organization

• 6 credit points (6CPs) are available when passing the exam.
• Each week, a problem set with one to three problems will be published. Solving these problem sets is optional but might be the best way for getting ready for the exam.
• The problem sets are discussed within the plenary tutorial.
• Registration for the plenary tutorial via webpage (mandatory!)

Material

• Klausur_Information_2020_07_21.pdf
• Klausur_Leitsystemplan_2020_07_15.pdf
• Klausur_SQD2020_Datenerhebung_Veranstaltungsteilnehmer.pdf
• Klausur_SQD2020_Datenschutzinformation.pdf
• Klausur_SQD2020_Zutritts-und-Teilnahmeregelungen.pdf
• Notes_Chapter_01.pdf
• Notes_Chapter_02.pdf
• Notes_Chapter_03.pdf
• Notes_Chapter_04.pdf
• Notes_Chapter_05.pdf
• Notes_Chapter_06.pdf
• Notes_Chapter_07.pdf
• Notes_Chapter_08.pdf
• Slides_Chapter_00.pdf
• Slides_Chapter_01.pdf
• Slides_Chapter_02.pdf
• Slides_Chapter_04.pdf
• Slides_Chapter_05.pdf
• Slides_Chapter_06.pdf
• Slides_Chapter_07.pdf

Exercise sheets

• 01
  
  • Problem_Set_01.pdf
  • Solution_Problem_Set_01.pdf
• 02
  
  • Problem_Set_02.pdf
  • Solution_Problem_Set_02.pdf
• 03
  
  • Problem_Set_03_corrected.pdf
  • Solution_Problem_Set_03.pdf
• 04
  
  • Problem_Set_04.pdf
  • Solution_Problem_Set_04.pdf
• 05
  
  • Problem_Set_05.pdf
  • Solution_Problem_Set_05.pdf
• 06
  
  • Problem_Set_06.pdf
  • Solution_Problem_Set_06.pdf
• 07
  
  • Problem_Set_07.pdf
  • Solution_Problem_Set_07.pdf
• 08
  
  • Problem_Set_08.pdf
  • Solution_Problem_Set_08.pdf
• 09
  
  • Problem_Set_09.pdf
  • Solution_Problem_Set_09.pdf
• 10
  
  • Problem_Set_10.pdf
  • Solution_Problem_Set_10.pdf
• 11
  
  • Problem_Set_11.pdf
  • Solution_Problem_Set_11.pdf
• 12
  
  • Problem_Set_12.pdf
  • Solution_Problem_Set_12.pdf

Übungsgruppen

• Gruppe 1 (Dr. Mathias Wegner)
  30 Teilnehmer/innen
  INF 227 (KIP), SR 3.403 / 3.404, Mi 16:15 - 18:00