Semiconductor Quantum Electronics

Semiconductor-based quantum electronic devices and circuits play a pivotal role in the current development of processors for quantum computing, in particular since they can be integrated with the highly versatile existing microelectronics. Furthermore, these devices are fabricated using identical technology. The aim of this module is to introduce the students to the current concepts for semiconductor-based nanoelectronics for quantum applications, with a focus on electrostatically defined quantum dots and donors as the elementary quantum bits (qubits). The module will introduce the basic physics, the fabrication and the operational principles of these qubits and will discuss the current status of both approaches with respect, e.g., to relaxation, decoherence and scalability. For the manipulation of these qubits, magnetic resonance is used, which will be briefly reviewed.

Specific topics will include:

Review of fundamental semiconductor physics

  crystal structure, band structure, excitons, dopants

Materials for semiconductor quantum electronics

  Si, SiGe, III-V semiconductors including GaAs/AlGaAs, isotope engineering, heterostructures

Fabrication of devices for quantum electronics

  molecular beam epitaxy, electron beam lithography, single ion implantation, STM lithography

Two-dimensional electron gases

  electrostatics, diffusive and ballistic transport, g-factor

Review of spin physics

  electron and nuclear spins, magnetic resonance, relaxation and decoherence

Electrostatically defined quantum dots

electronic transport, Coulomb diamond, single electron transistor, capacitance model, spin states, spin-to-charge conversion, Kondo effect

Spin interaction with the environment

  spin orbit interaction, hyperfine interaction

Coupled quantum dots

  electronic properties, spin blockade, hyperfine effects

Spin physics of dopants

  g-factor, hyperfine coupling, quadrupole interaction

Electrically detected magnetic resonance

Single donor spins

  readout via SET, coupling of donors, hyperfine effects

Comparison of quantum electronic systems discussed

Quantum processors

  topologies, quantum state transfers, the current state-of-the-art of such processors, challenges

Hybrid quantum systems

  with microwaves, optical photons and/or phonons

After participation in the Module the student is able to:

1. Understand the rationale for building semiconductor-based quantum electronic devices and circuits.

2. Explain the fundamental principles of quantum-dot- and donor-based quantum bits, including the physics of two-dimensional electron gases.

3. Understand which semiconductor nanostructures are used to generate, manipulate and detect electron and spin qubits, why they are used and how they are fabricated.

4. Explain the fundamentals of magnetic resonance and its elementary pulse sequences.

5. Sketch how these qubits are operated and what is observed.

6. Understand how quantum processors are being developed from elementary one- and two-qubit systems.

7. Understand and quantify the current limits of these qubits with respect to relaxation and decoherence.

8. Judge new concepts for semiconductor-based qubits.

No preconditions in addition to the requirements for the Master's programs in Physics (Condensed Matter) or in Quantum Science and Technology.

The module consists of a lecture series and exercise classes.

The blackboard is used for the introduction of physical concepts and quantitative analyses. Overhead projection is used for the discussion of experimental set-ups and results. Students are required to read selected research publications.

Combined Power Point and blackboard presentation plus research publications.

• Thomas Ihn, Semiconductor Nanostructures, Oxford University Press
• Yuli Nazarov and Yaroslav M. Blanter, Quantum Transport, Cambridge University Press
• R. Hanson et al., Reviews of Modern Physics 79, 1217 (2007)
• Floris A. Zwanenburg et al., Silicon Quantum Electronics, Reviews of Modern Physics 85, 961 (2013)
• and topical research papers

There will be an oral exam of 25 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:

• How do you fabricate a quantum dot?
• With which accuracy can you place a single donor? Which technology would you use?
• What is spin diffusion and how can you suppress it?
• Sketch and explain the stability diagram of a coupled quantum dot!
• What are the pros and cons of using a heavier donor such as 75As as compared to 31P?
• How would you realize coherence transfer to a nuclear spin?

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