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 reliable fabricated using advanced thin-film technologies and allow building macroscopic systems such as artificial atoms that behave entirely quantum-mechanically. 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 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 establishing quantum computers.
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 Qubits 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 of the lecture

• Introduction to superconductivity
• Josephson tunnel junctions
• Superconducting quantum interference devices (SQUIDs)
• SQUID based low-and high-frequency amplifiers
• Microwave properties of superconductors, superconducting resonators
• Qubits (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, there is no prerequisite knowledge. All relevant aspects on superconductivity will be introduced within the lecture. Basic knowledge about solid-state physics as gained by the introduction into solid-state physics (PEP5) or the advanced lecture on condensed matter physics (CMP) might be helpful.

Formalities

There are no tutorials. Every second week an exercise sheet is distributed containing excersises that have to be solved at home. Handing in of the solutions is within the lecture two weeks after distribution.

Credit points (2CPs) will be assigned due to

• attendance in the lecture which will be proved by signing an attendance list every week
• reaching at least 60% of the points that can be achieved on the exercise sheets.

Materials

• Notes_Lecture_01.pdf
• Notes_Lecture_02.pdf
• Notes_Lecture_03.pdf
• Notes_Lecture_04.pdf
• Notes_Lecture_05.pdf
• Notes_Lecture_06.pdf
• Notes_Lecture_07.pdf
• Notes_Lecture_08.pdf
• Notes_Lecture_09.pdf
• Notes_Lecture_10.pdf
• Notes_Lecture_11.pdf
• Notes_Lecture_12.pdf
• Notes_Lecture_13a.pdf
• Notes_Lecture_13b.pdf
• Slides_General_Information.pdf
• Slides_Lecture_01.pdf
• Slides_Lecture_02.pdf
• Slides_Lecture_03.pdf
• Slides_Lecture_04.pdf
• Slides_Lecture_05.pdf
• Slides_Lecture_06.pdf
• Slides_Lecture_07.pdf
• Slides_Lecture_09.pdf
• Slides_Lecture_10.pdf
• Slides_Lecture_12.pdf

Exercise sheets

• 1
  
  • Problem_Set_01.pdf
  • Solution_Problem_Set_01.pdf
• 2
  
  • Problem_Set_02.pdf
  • Solution_Problem_Set_02.pdf
• 3
  
  • Problem_Set_03.pdf
  • Solution_Problem_Set_03.pdf
• 4
  
  • Problem_Set_04.pdf
  • Solution_Problem_Set_04.pdf
• 5
  
  • Problem_Set_05.pdf
  • Solution_Problem_Set_05.pdf
• 6
  
  • Problem_Set_06.pdf
  • Solution_Problem_Set_06.pdf

Tutorials

• Gruppe 1 (Sebastian Kempf)
  22 Teilnehmer/innen