Many quantum technologies dedicated to quantum computation and quantum information processing rely on either superconductor or semiconductor nanostructures [1,2]. These systems take advantage of quantum phenomena at the nanoscale level to bring up new functionalities. The scientific community is thus always on the lookup for such new phenomena, and sometimes a combination of both worlds results in outstanding nanodevices. One example of a successful superconductor-semiconductor device is the gatemon qubit [3]. This device incorporates a superconductor-semiconductor-superconductor junction that acts as a nonlinear inductor, and its behavior can be fully controlled by gate-defined potential offsets acting on the semiconductor.

Nonlinear capacitive elements can as well have many applications in quantum computation and quantum information processing, provided that the capacitance and its nonlinearity can be externally controlled by e.g., a gate-defined potential offset. A possible implementation of a nonlinear capacitor can be achieved by placing a semiconductor-based quantum well within a superconducting capacitor. Fluctuations in the electric potential in the superconductor will change the electric landscape within the quantum well, and that, in turn, will change the charge distribution of the electrons in the well and their energy levels. This can result in a capacitance that depends on the potential across the capacitor, that is, a nonlinear capacitance.

This quantum well capacitor has some similarities with the superconductor-semiconductor-superconductor junction in a gatemon qubit. It is therefore a reasonable device that can be fabricated with state-of-the-art technology.

For this project, the candidate will design a superconductor-semiconductor nanodevice that displays a nonlinear capacitance. She/he will then model this device and study its properties.

Requirements

This proposal involves relatively simple systems, but the combination of them can bring up very interesting dynamics. In order to tackle this problem, the candidate should have a good knowledge of quantum mechanics and some basic programming skills. ​

References

1. L. M. K. Vandersypen et al, Quantum computing with semiconductor spins. Physics Today, 72, 38–45 (2019).
2. F. Arute et al, Quantum supremacy using a programmable superconducting processor. Nature, 574, 505–510 (2019). See also J. Martins et al, Quantum supremacy using a programmable superconducting processor, Google AI Blog (2019).
3. S. J. Weber, Gatemons get serious. Nature Nanotechnology 13, 877 (2018).