Quantum Dots Coupled to Andreev Bound States

Abstract

Andreev bound states arise in low-dimensional confined systems, coupled to superconductors. They show great similarity to the highly sought-after Majorana bound states, yet they lack the desirable non-Abelian statistics or topological protection. Except for these, Andreev bound states possess a multitude of unique and interesting properties. This thesis explores several of these properties, using semiconductor quantum dots as a measurement tool. In addition, quantum dots are hybridized with Andreev bound states to form novel systems, including Andreev molecules, and Kitaev chains.

In the theory section, we introduce several basic concepts, followed by a discussion of the properties of Andreev bound states and similar Yu-Shiba-Rusinov states. We then extend the concept of Andreev bound states to Kitaev chains in various implementations. In the first chapter, we use a quantum dot as both a spin and energy filter to probe an Andreev bound state. We observe pure spin states despite the strong spin-orbit interaction in the host semiconductor. Utilizing a three-terminal measurement setup, we can change the spin-relaxation process of the Andreev bound state by changing tunnel barrier strengths. Next, we configure a quantum dot as a charge sensor to study Andreev bound states. We observe smooth changes in ground state charge due to hybridization of the even-occupation states. We additionally detect abrupt loading of electrons during the singlet-doublet transition, which agrees with a change of ground state parity. Having used quantum dots as a measurement tool, we then hybridize them with Andreev bound states to form an Andreev molecule. We demonstrate readout of the ground state parity of the combined system using the charge sensor. We argue that parity-to-charge conversion in semiconductorsuperconductor systems is a viable scheme for reading out Kitaev chains and associated qubits.

We proceed by strongly coupling two quantum dots to a single Andreev bound state. This coupling mediates tunneling and Cooper pair splitting processes between the quantum dots, effectively constituting a Kitaev chain. For each Andreev bound state, we can find two gate voltages at which the rates of these processes are equal and non-zero. Spectroscopic measurements reveal localized Majorana zero modes on the quantum dots that are robust against local electrostatic changes.

Engineering Kitaev chain-based qubits requires consistently finding Majorana zero modes. In the final experimental chapter of this thesis, we present an algorithm that tunes gate voltages until Majorana zero modes emerge in Kitaev chains. We employ a neural network to estimate the relative Cooper pair splitting and tunneling rates from spectroscopic measurements. These estimates are then input into a gradient descent algorithm until the rates are balanced, and Majorana zero modes emerge. We present statistics on the algorithm’s performance and conclude that it is a vital tool in elevating Kitaev chains from the realm of fundamental study to quantum information.

We then propose a series of future experiments, based on our current findings. Notably, we explore the possibility of storing quantum information in the spin degree of freedom of a superconductor using Yu-Shiba-Rusinov states.