Quantum systems with engineered Hamiltonians can be used to study many-body physics problems to provide insights beyond the capabilities of classical computers. Semiconductor gate-defined quantum dot arrays have emerged as a versatile platform for realizing generalized Fermi-Hubbard physics, one of the richest playgrounds in condensed matter physics. In this work, we employ a germanium 4×2 quantum dot array and show that the naturally occurring long-range Coulomb interaction can lead to exciton formation and transport. We tune the quantum dot ladder into two capacitively coupled channels and exploit Coulomb drag to probe the binding of electrons and holes. Specifically, we shuttle an electron through one leg of the ladder and observe that a hole is dragged along in the second leg under the right conditions. This corresponds to a transition from single-electron transport in one leg to exciton transport along the ladder. Our work paves the way for the study of excitonic states of matter in quantum dot arrays.

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Long-range interactions play a key role in several phenomena of quantum physics and chemistry. To study these phenomena, analog quantum simulators provide an appealing alternative to classical numerical methods. Gate-defined quantum dots have been established as a platform for quantum simulation, but for those experiments the effect of long-range interactions between the electrons did not play a crucial role. Here we present a detailed experimental characterization of long-range electron-electron interactions in an array of gate-defined semiconductor quantum dots. We demonstrate significant interaction strength among electrons that are separated by up to four sites, and show that our theoretical prediction of the screening effects matches well the experimental results. Based on these findings, we investigate how long-range interactions in quantum dot arrays may be utilized for analog simulations of artificial quantum matter. We numerically show that about ten quantum dots are sufficient to observe binding for a one-dimensional H2-like molecule. These combined experimental and theoretical results pave the way for future quantum simulations with quantum dot arrays and benchmarks of numerical methods in quantum chemistry.

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Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases. Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains. In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted. Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers. To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required. Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array. We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met. Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian. Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlet-triplet measurements on each nearest-neighbor pair and the correlations therein. The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

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More is more applies in particular to systems with interacting parts. These interactions enable the emergence of collective behaviour. Examples can be found among the behaviour of animals, such as the V-shaped formation of migrating geese and the flight of a flock of starlings. More examples are found among the electromagnetic properties of materials. For properties that rely on quantum-mechanical correlations it quickly becomes infeasible for classical numerical simulations to provide accurate results. An appealing alternative is to study these properties with quantum simulators, which mimic the material properties themselves. Besides being of scientific interest for the field of condensed matter physics, insights obtained from quantum simulations could in the future serve as input for the synthesis of novel materials. Developing quantum simulators requires the engineering of quantum systems. One such quantum system is that of electrons in gate-defined quantum dots, which are formed by three-dimensional confinement at the nano-scale. Experiments with quantum dots have already demonstrated measurement and coherent control of both individual charges and spins, and their operation as quantum bits. The first quantum simulation experiments with quantum dots have been performed in the last couple of years. Further development of quantum dots as platform for quantum simulations forms the overarching motivation for this thesis. The first experiment in this thesis describes the automated tuning of the tunnel coupling between quantum dots. This automation builds on previously developed automated tuning of double quantum dots. The automated tuning relies on image processing to extract parameters from measurement results. This step is part of a feedback loop in which the voltages on the gates are iteratively adjusted. This loop repeats until the target tunnel coupling is achieved. The second experiment further studies the tuning of tunnel couplings. For operation of gate-defined quantum dots it is common practice to independently control chemical potentials with so-called virtual gates. These virtual gates compensate for crosstalk effects due to cross-capacitances of the physical gates. The control of multiple tunnel couplings similarly suffers from crosstalk, but efficient compensation techniques were lacking. This chapter reports an efficient calibration scheme for such crosstalk, and demonstrates independent control of tunnel couplings with enhanced virtual gates. The third experiment demonstrates a method to measure charge and spin in large quantum dot arrays. The charge configuration of a quantum dot array is typically measured with a charge sensor, which is usually another quantum dot. To measure the spin configuration it is first mapped onto a charge configuration, which for singlet-triplet measurements is based on the Pauli exclusion principle. The charge measurement relies on Coulomb repulsion, which decays with distance, thus only charge and spin close to the sensor can be reliably measured. This chapter presents how, inspired by the effect of toppling dominoes, a cascade of hopping electrons induced by Coulomb repulsion can effectively convert the information about motion of a distant charge to the motion of a charge close to the sensor. The benefit of cascade-based readout is demonstrated by comparing singlet-triplet measurements with or without the cascade activated. The most involved experiment described in this thesis is a proof-of-principle quantum simulation of Heisenberg magnetism, which is one of the most famous models in condensed-matter physics. Specifically, this experiment demonstrates how a linear array of quantum dots can be operated as a Heisenberg spin chain. The first part of the experiment shows the characterization of the energy spectrum, which is based on degeneracies between spin states with different magnetization. From the energy spectroscopy the conditions are identified for which the exchange couplings are homogeneous. Next, the coherence is studied by inducing global exchange oscillations, and evolution in different subspaces of the Heisenberg Hamiltonian is demonstrated. The final step of the experiment consists of the adiabatic preparation of the low-energy global singlet state for a homogeneous chain, and its characterization with pairwise singlet-triplet measurements for each of the nearest-neighbours and correlations therein. These techniques and results form the basis for the operation of quantum dots to simulate larger spin systems and different lattice structures. The final experiment, shifts the focus from spin-spin interactions to electron-electron interactions. For gate-defined quantum dots, the Coulomb repulsion results in both on-site and inter-site interactions between electrons. The interaction is experimentally characterized with a linear array of six dots in which the tunnel couplings are tuned to be homogeneous. The decay of the interaction as a function of distance is modelled with both the method of image charges, where the gate metal acts as screening layer, and with a Yukawa type potential as a heuristic model. The latter provides an intuitive interpretation for the decay of the interaction in terms of a screening length. The characterization of the long-range electron-electron interaction is relevant for the operation of quantum dot arrays as hosts of spin qubits, but also for quantum simulations in which the charge degree of freedom and electron-electron interactions play an important role. Some examples of many-body physics for which long-range interactions are essential, are quantum chemistry, Wigner crystallization, and high-temperature superconductivity. Summarizing, this thesis reports novel techniques for the control and measurement of larger quantum dot arrays, the operation of such an array as quantum simulator of Heisenberg magnetism with control over the spin-spin interactions, and characterization of the electron-electron interactions. These results pave the way for future quantum simulations with quantum dots. @en

The spin of a single electron in a semiconductor quantum dot provides a well-controlled and long-lived qubit implementation. The electron charge in turn allows control of the position of individual electrons in a quantum dot array, and enables charge sensors to probe the charge configuration. Here we show that the Coulomb repulsion allows an initial charge transition to induce subsequent charge transitions, inducing a cascade of electron hops, like toppling dominoes. A cascade can transmit information along a quantum dot array over a distance that extends by far the effect of the direct Coulomb repulsion. We demonstrate that a cascade of electrons can be combined with Pauli spin blockade to read out distant spins and show results with potential for high fidelity using a remote charge sensor in a quadruple quantum dot device. We implement and analyse several operating modes for cascades and analyse their scaling behaviour. We also discuss the application of cascade-based spin readout to densely-packed two-dimensional quantum dot arrays with charge sensors placed at the periphery. The high connectivity of such arrays greatly improves the capabilities of quantum dot systems for quantum computation and simulation.

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Electrostatically-defined semiconductor quantum dot arrays offer a promising platform for quantum computation and quantum simulation. However, crosstalk of gate voltages to dot potentials and interdot tunnel couplings complicates the tuning of the device parameters. To date, crosstalk to the dot potentials is routinely and efficiently compensated using so-called virtual gates, which are specific linear combinations of physical gate voltages. However, due to exponential dependence of tunnel couplings on gate voltages, crosstalk to the tunnel barriers is currently compensated through a slow iterative process. In this work, we show that the crosstalk on tunnel barriers can be efficiently characterized and compensated for, using the fact that the same exponential dependence applies to all gates. We demonstrate efficient calibration of crosstalk in a quadruple quantum dot array and define a set of virtual barrier gates, with which we show orthogonal control of all interdot tunnel couplings. Our method marks a key step forward in the scalability of the tuning process of large-scale quantum dot arrays.

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Electrostatically defined quantum dot arrays offer a compelling platform for quantum computation and simulation. However, tuning up such arrays with existing techniques becomes impractical when going beyond a handful of quantum dots. Here, we present a method for systematically adding quantum dots to an array one dot at a time, in such a way that the number of electrons on previously formed dots is unaffected. The method allows individual control of the number of electrons on each of the dots, as well as of the interdot tunnel rates. We use this technique to tune up a linear array of eight GaAs quantum dots such that they are occupied by one electron each. This new method overcomes a critical bottleneck in scaling up quantum-dot based qubit registers.

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Semiconductor quantum dot arrays defined electrostatically in a 2D electron gas provide a scalable platform for quantum information processing and quantum simulations. For the operation of quantum dot arrays, appropriate voltages need to be applied to the gate electrodes that define the quantum dot potential landscape. Tuning the gate voltages has proven to be a time-consuming task, because of initial electrostatic disorder and capacitive cross-talk effects. Here, we report on the automated tuning of the inter-dot tunnel coupling in gate-defined semiconductor double quantum dots. The automation of the tuning of the inter-dot tunnel coupling is the next step forward in scalable and efficient control of larger quantum dot arrays. This work greatly reduces the effort of tuning semiconductor quantum dots for quantum information processing and quantum simulation.

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Interacting fermions on a lattice can develop strong quantum correlations, which are the cause of the classical intractability of many exotic phases of matter. Current efforts are directed towards the control of artificial quantum systems that can be made to emulate the underlying Fermi-Hubbard models. Electrostatically confined conduction-band electrons define interacting quantum coherent spin and charge degrees of freedom that allow all-electrical initialization of low-entropy states and readily adhere to the Fermi-Hubbard Hamiltonian. Until now, however, the substantial electrostatic disorder of the solid state has meant that only a few attempts at emulating Fermi-Hubbard physics on solid-state platforms have been made. Here we show that for gate-defined quantum dots this disorder can be suppressed in a controlled manner. Using a semi-automated and scalable set of experimental tools, we homogeneously and independently set up the electron filling and nearest-neighbour tunnel coupling in a semiconductor quantum dot array so as to simulate a Fermi-Hubbard system. With this set-up, we realize a detailed characterization of the collective Coulomb blockade transition, which is the finite-size analogue of the interaction-driven Mott metal-to-insulator transition. As automation and device fabrication of semiconductor quantum dots continue to improve, the ideas presented here will enable the investigation of the physics of ever more complex many-body states using quantum dots.

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