Analog Quantum Simulation of Spin and Charge Quasiparticles on a Quantum Dot Ladder

Abstract

The field of quantum simulations promises to tackle formidable problems which are inaccessible to classical computers due to their complexity. These questions range from the simulation of many-body effects in materials and fundamental questions of physics, to the exact calculation of chemical and biological processes. A possible way to tackle these problems is through the use of analog quantum simulators, a class of controllable quantum systems in which the underlying Hamiltonian is directly mappable to the problem of interest. Combined with a high degree of control and tunability over individual parameters, analog quantum simulators promise to reach practicality already at intermediate device scales, without the need for scaling up to the hundreds of thousands of sites necessary for their digital counterparts.

In this thesis,we study gate-defined semiconductor quantum dot arrays as a possible candidate for analog quantum simulators. Semiconductor quantum dots have become an attractive system for quantum technologies given their small footprint, fast operation, long coherence times and individual and in-situ tunability of couplings and on-site energies. Additionally, the system is natively described by the Fermi-Hubbard Hamiltonian, a complex many-body Hamiltonian which is predicted to give rise to a variety of interesting phases of matter. This makes quantum dot arrays a promising platform for many-body quantum simulations. However, scaling beyond a few quantum dots while maintaining a high degree of controllability has remained a long-standing challenge for the field.

In this thesis, we study a 2×4 quantum dot array of Ge/SiGe quantum dots as an analog quantum simulator, exploring the emergence of correlated spin and charge phenomena. With the quantum dots arranged in a ladder geometry, this device constitutes one of the first two-dimensional realizations of quantum dot arrays. After introducing the relevant theoretical and experimental concepts, we showcase the experimental simulation of two different types of quasiparticles and their dynamics, each emerging in a different parameter regime of the Fermi-Hubbard model. First, we look at the creation and transport of electron-hole pairs or excitons. Here, we crucially exploit the existence of strong Coulomb repulsion between both legs of the quantum dot ladder. Subsequently, we explore the dynamics of single-spin and two-spin excitations as they evolve through the array. These so-called magnon and triplon excitations propagate thanks to nearest-neighbor exchange interactions which we can locally and independently tune over a large range of parameters. This is achieved thanks to a novel scheme of crosstalk compensation which we develop and showcase in this thesis. In the last chapter, we summarize our findings, discuss challenges going forward and provide a variety of possible experiments which could be attainable with current state-of-the-art quantum dot quantum simulators.