Theory projects

 

Unsolicited applications

In addition to the advertised projects, we are always happy about unsolicited applications. Please contact the principal investigator with whom you'd like to work with to discuss possible projects.

  graphene Copyright: © Phys.Rev. B 84, 041404(R)(2011)

B.Sc. Project Magnetic moments in strained bilayer graphene

Implementing a strain in bilayer graphene has been shown to result in massive low-energy modes at the corners of the Brillouin zone [Phys.Rev. B 84, 041404(R)(2011)]. In this thesis, you will investigate the effective low-energy Hamiltonian analytically. You will learn about berry curvature and how it relates to a formulation of a magnetic moment for these massive modes. Subsequently, you construct wavepakets and study their response to magnetic fields to develop an intuition of the effects of this so called topological magnetic moment.
Contacts: , Fabian Hassler

  Shapiro setup Copyright: © Lisa Arndt

B.Sc. Project Parametrically driven Duffing oscillator

A parametrically driven Duffing oscillator can exhibit self-sustained oscillations if the amplitude of the parametric drive exceeds a certain instability threshold. While classical, coherent oscillations are no longer possible below the threshold, the parametric drive still impacts the quantum fluctuations of the system. In this thesis, you will analyze and simulate a parametrically driven Duffing oscillator in the quantum regime. Among other methods, you will employ the Lindblad Master equation to gain a deeper insight into the dynamics of the system.
Contacts: , Fabian Hassler

  Shapiro setup Copyright: © Lisa Arndt

B.Sc. Project Hysteresis in underdamped Josephson junctions​

If the potential of a driven, nonlinear system exhibits more than one (local) minimum, it can show hysteretic behavior. This means that the state of the system depends not only on the current system parameters but also on its history. In this thesis, you will employ a variety of methods to investigate hysteretic effects in an underdamped Josephson junction.
Contacts: , Fabian Hassler

  Detector setup Copyright: © Fabian Hassler

M.Sc. Project Detector theory for microwave photonics with superconducting quantum circuits

In superconducting quantum systems, a significant part of the emitted microwave radiation can be collected and converted to an amplified output signal. This allows for a detailed study of the correlations of the radiation. The statistics of the radiation can offer a valuable insight into the quantum nature of the radiation. It demonstrates phenomena like squeezing or multi-photon processes. In order to study such phenomena theoretically, it is necessary to develop a fitting model for the detector. The goal of this project will be to explore different theoretical detector models for microwave photonics, including the initial detection of the photons, the amplification of the signal, and possible backaction due to the detector.
Contacts: , Fabian Hassler

  Hall bar Copyright: © David DiVincenzo

B.Sc. Project

Hall Effect Gyrator

This work will continue recent investigations in our group on the action of an essential component in quantum microwave science, the gyrator. Here you will do calculations of the real-time propagation of electromagnetic fields in this device. Contact: David DiVincenzo

  Qubit-Heterostructure Copyright: © Pascal Cerfontaine

B.Sc. Project Improved Quantum Dot Qubits

In this project you will explore theoretically variants of the semiconductor quantum dot to perform quantum gate fidelity and readout. There will be an emphasis on tailoring the spin-orbit action to achieve optimal performance, and on varying the electron number and confinement strength. Contact: David DiVincenzo

  Flux Qubit Copyright: © Gianluigi Catelani

B.Sc. and M.Sc. Projects Superconducting Qubits

In these projects you will study theoretically some basic properties (energy levels, wave functions, matrix elements) of superconducting qubits such as the fluxonium and the flux qubit. These properties can be accurately calculated numerically in most cases, especially if the problem reduces to that of a quantum particle in a one-dimensional potential. The goal here is to construct an approximate but accurate analytical solution to such a quantum-mechanical problem, using perturbation theory, the WKB approximation, etc. For a B.Sc. project, a symmetric double-well potential will be analyzed. Extension of the results to asymmetric potentials, and to two- or three-dimensional problems, can be considered for a M.Sc. project. Contact: Gianluigi Catelani (g.catelani@fz-juelich.de)