PhD subjects

Interfacing superconducting circuits with spins in the solid state has the potential to leverage the flexibility of superconducting circuits with the long coherence times offered by spins. This project aims to demonstrate circuit-mediated two qubit gates between electron spin qubits.

The thesis will develop a new type of microwave photon counter, based on a multi-qubit superconducting chip. Using correlations between these qubits should enable to considerably suppress dark counts, which are the main source of noise in these new sensors. Once operational, the counter shall be used for individual spin detection.

Even-denominator states of the fractional quantum Hall effect (e.g. ??=5/2) are expected to host excitations that have non-abelian anyonic statistics, making them promising candidates for the realization of topological quantum computing [1]. While the demonstration of these non-abelian statistics has long been an extremely challenging endeavor, recent experiments in GaAs semiconductor heterostructures have shown that the edge thermal conductance of the ??=??/?? state is quantized in half-integer values of the thermal conductance quantum [2,3]. This half-integer quantization is known to be an universal signature of non-abelian statistics, including of Majorana fermions [4]. However, many of the suspected candidates for the ground state of ??=5/2 have complex edge structures exhibiting counterpropagating neutral modes, which can modify the edge thermal conductance and give them non-integer values similar to that of a non-abelian edge. A very recent experiment [3] has circumvented the issue by finding a way to separate the contributions of the different channels at the edge, confirming the existence of a non-abelian channel with half-integer quantized electrical and thermal conductance. The next obvious interrogation is whether this result is truly universal: does it hold for different material, and different even-denominator states?

In this project, we propose to address these questions by performing heat transport measurements in fractional quantum Hall states in bilayer graphene. Bernal-stacked bilayer graphene (BLG) has recently shown to host a large variety of robust even-denominator fractional quantum Hall states [5-8], both hole- and electron-type. This provides an excellent test-bed on which to probe the thermal conductance, as these fractions are expected to be described by different (possibly non-abelian) ground states; furthermore, the ability to apply electric displacement fields allows a further degree of control over the even-denominator states, which can be investigated in terms of heat transport.

This experimental project relies on ultra-low temperature, high magnetic field thermal transport [9] based on high sensitivity-sensitivity electrical measurements. We are looking for highly motivated candidates whoe are interested in all aspects of the project, both experimental (sample fabrication, low noise measurements, cryogenics) and theoretical.

[1] Nayak, et al., RMP 80, 1083 (2008) [2] Banerjee, et al., Nature 559, 205 (2018)
[3] Dutta, et al., Science 377, 1198 (2022) [4] Kasahara, et al., Nature 559, 227 (2018)
[5] Ki, et al., Nano Letters 14, 2135 (2014) [6] Li, et al., Science 358, 648 (2017)
[7] Zibrov, et al., Nature 549, 360 (2017) [8] Huang, et al., PRX 12, 031019 (2022)
[9] Le Breton, …, & Parmentier, PRL 129, 116803 (2022)