Josephson junction arrays of topological superconductors as quantum simulators

• Applicant: Professor Dr. Fabian Hassler
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2014 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 254002731

The notion of a quantum simulator stems from the idea to study the properties of a complicated system through another system which is easier to control and which is described by the same or a similar Hamiltonian. In this sense, a quantum simulator is a special-purpose analog processor. Topological superconductors are a novel quantum phase. A conventional superconductor can essentially be understood as a macroscopic quantum state of bosonic particles which are formed by pairs of electrons, the so-called Cooper pairs, thus boosting quantum coherence effects to the macroscale and making them easy to detect. Topological superconductors offer additionally fermionic degrees of freedom (called Majorana fermions) which still are completely coherent with the bosonic condensate. The prospects of Josephson junction arrays---arrays of small superconducting islands which are tunnel-coupled to each other---utilizing conventional superconductors for quantum simulation purposes have been analyzed in the past and have turned out to be rather versatile. However, due to the fact that there are only bosonic degrees of freedom present one is bound to simulate bosonic rather than fermionic systems. The latter being of prime interest as the constituents of matter are fermionic particles. In the course of this project, we will analyze the prospects of Josephson junction arrays built from topological superconductors for quantum simulation purposes. We will concentrate essentially on two models: In the first model, the bosonic degrees of freedom serve simply to implement a long-range interaction between the fermionic modes. We will study both the (static) phase diagram of this model with long-range interactions as well as its dynamic properties after a quantum quench, i.e., the time evolution after a sudden change in one of the system parameters. Additionally, we will study a system where there is a symmetry between the bosonic and the fermionic degrees of freedom, a so-called supersymmetry. With this choice of models, we can show the full potential of topological superconductors for quantum simulation purposes. The project will take an important step to evaluating the possibility to realize quantum simulators employing both bosonic as well as fermionic degrees of freedom in superconducting systems.

• DFG Programme: Research Grants