Research
Quantum computing research
Quantum computers promise to revolutionize computing by performing certain tasks exponentially faster than classical computers. Quantum bits, or qubits, are the building blocks of quantum computers but suffer from decoherence due to unwanted couplings to environment. Our group is interested in studying open problems related to various quantum computing and microelectronics platforms. For example, our research aims to understand limiting factors of qubit coherence in quantum computing devices. In particular we have focused on topological and conventional superconductors in the condensed matter setting.
Topological quantum computing
In topological quantum computation, the quantum information is stored in non-local topological degrees of freedom with the promise of longer coherence times. Our group currently focuses on three leading hybrid semiconductor-superconductor platforms for topological quantum computing: (i) structures based on semiconductor or gate-defined nanowires, (ii) 2D or 3D topological insulator materials, and (iii) the use of strongly-correlated electrons in fractional quantum Hall states. Below we outline some of the important research questions in this field.
Mesoscopic effects in topological superconductors
The study of mesoscopic phenomena in conventional s-wave superconductors paved the way to the advances of superconducting qubits technology in quantum information. More recently, the theoretical prediction of topological superconductors in hybrid semiconductor-superconductor nanowires have brought topological quantum computation closer to reality. The theoretical study of mesoscopic phenomena in such topological superconductors has just started and is driven by the rapid experimental progress with the hope to one day realize a topologically protected qubit. The problem is highly non-trivial due to the presence of strong Coulomb interaction. Fortunately, we can use low-dimensional models and employ the techniques of bosonization, boundary conformal field theory, and DMRG to study these systems. This is an exciting new field that has many key differences from the "old" study of s-wave superconductors. Understanding the differences is essential for the development of topological qubit technologies.
Schematic picture of a Coulomb blockaded Majorana island that can be studied by using boundary conformal field theory techniques. Figure taken from arXiv:2002.06192.
Helical edge transport
Topological insulators proximitized by an s-wave superconductor provide another path to topologically protected quantum computing. Since the first experimental observation of edge transport in the two-dimensional topological insulator (2D TI) in a HgTe quantum well, there has been an explosion of new experiments and materials. In the next-generation HgTe systems, induced superconductivity and quantum point contacts have been studied recently. In parallel, new monolayer 2D materials have been discovered and new creative ways to engineer helical edge modes in "old" materials have been invented. For example, in the zeroth Landau level of graphene an interaction induced topological phase can be found in parallel magnetic field. Another breakthrough comes from GaAs double quantum wells in the strongly-correlated fractional quantum Hall regime, where differential gating allows one to create helical edge modes.
These exciting developments call for a study of disorder and interactions in these systems. For example, in the first HgTe 2D TI it is believed that the edge transport is strongly influence by charge puddles in the bulk. Understanding such effects is essential for making future devices based on the 2D TI systems. Additionally, the strong interactions brought by some of the new platforms raise challenging open questions.
Superconducting quantum computing
Microwave control plays an essential role in controlling the bosonic condensate degree of freedom in modern superconducting qubits. In the last decade or so, microwaves were also demonstrated a key tool in probing the fermionic subgap Andreev bound states in various Josephson junctions, for example in atomic contacts, many-channel nanobridge junctions, and nanowire junctions. Our group is particularly interested in studying the fermionic subgap degrees of freedom in superconducting junctions. Nanowire junctions are a particularly attractive platform since the exposed junctions are gate-tunable.
Simultaneously with the development of microwave techniques, there has been a tremendous activity on investigating subgap states induced by magnetic impurities in a host superconductor. The magnetic impurity creates a so-called Yu-Shiba-Rusinov (YSR) bound state below the superconducting gap. The recent studies of YSR states are motivated by the prediction and subsequent observation of Majorana end states in a chain of magnetic atoms deposited on a superconductor.
In the future, we envision productive interplay between these thus far separate branches of superconductivity. Our group is interested in harnessing the microwave techniques to understand YSR impurity states.
Magnetic impurities in a narrow-bridge Josephson junction (right). The associated Yu-Shiba-Rusinov (YSR) impurity subgap states can be probed and controlled with microwave irradiation. Figure taken from Phys. Rev. Research 1, 033091 (2020).