Interacting electrons on material lattices can build up strong quantum correlations, which in turn can lead to the emergence of a wide range of novel and potentially useful magnetic and electronic material properties. Our understanding of this physics, however, is severely limited by the exponential growth in complexity with system size, which leads all classical methods to fall fundamentally short. In this thesis, I show how artificial lattices of conduction band electrons in semiconductors, so-called quantum dot arrays, can be used to directly emulate and therefore elucidate such Fermi-Hubbard physics. To this end, I focus on two approaches. A top-down approach allows to scale easily, but lacks to ability to control or measure individual sites. A bottom-up approach on the other hand utilizes the small devices employed by the community for qubit experiments, in which the control of individual sites is both a blessing and a curse. We address the issue of control to the point where mapping to relevant models is possible and efficiently calibrating larger devices becomes feasible. These results open up the inherently well-suited and scalable platform of quantum dots to emulate novel quantum states of matter.
Interacting electrons on material lattices can build up strong quantum correlations, which in turn can lead to the emergence of a wide range of novel and potentially useful magnetic and electronic material properties. Our understanding of this physics, however, is severely limited by the exponential growth in complexity with system size, which leads all classical methods to fall fundamentally short. In this thesis, I show how artificial lattices of conduction band electrons in semiconductors, so-called quantum dot arrays, can be used to directly emulate and therefore elucidate such Fermi-Hubbard physics. To this end, I focus on two approaches. A top-down approach allows to scale easily, but lacks to ability to control or measure individual sites. A bottom-up approach on the other hand utilizes the small devices employed by the community for qubit experiments, in which the control of individual sites is both a blessing and a curse. We address the issue of control to the point where mapping to relevant models is possible and efficiently calibrating larger devices becomes feasible. These results open up the inherently well-suited and scalable platform of quantum dots to emulate novel quantum states of matter.
The Hubbard model is an essential tool for understanding many-body physics in condensed matter systems. Artificial lattices of dopants in silicon are a promising method for the analog quantum simulation of extended Fermi-Hubbard Hamiltonians in the strong interaction regime. However, complex atom-based device fabrication requirements have meant emulating a tunable two-dimensional Fermi-Hubbard Hamiltonian in silicon has not been achieved. Here, we fabricate 3 × 3 arrays of single/few-dopant quantum dots with finite disorder and demonstrate tuning of the electron ensemble using gates and probe the many-body states using quantum transport measurements. By controlling the lattice constants, we tune the hopping amplitude and long-range interactions and observe the finite-size analogue of a transition from metallic to Mott insulating behavior. We simulate thermally activated hopping and Hubbard band formation using increased temperatures. As atomically precise fabrication continues to improve, these results enable a new class of engineered artificial lattices to simulate interactive fermionic models.
We are entering the era of the second quantum revolution, where we aim to harness the power of quantum mechanics to create new technologies. Quantum technologies have the potential to revolutionize the fields of simulation, computation, communication, sensing, metrology, and many others. Here we discuss analog quantum simulation, which has attracted a lot of attention in the last few years from several platforms. Although arrays of gate-defined quantum dots exhibit significant potential for analog simulation, example experiments have been few and far between. This thesis focuses on simulating the Fermi-Hubbard model using two dimensional (2d) arrays of quantum dots. The first experiment describes the creation and measurement of a 2x2 quantum dot array. Historically, most experiments with quantum dots have been performed with linear arrays due to the relative ease of fabrication. We introduce a bi-layer gate structure, facilitated by the lift-off of sputtered silicon nitride, to create the 2x2 dot array. This gate design enables us to achieve unprecedented tunability of the tunnel coupling between all nearest-neighbor pairs of dots in 2d arrays. We also demonstrate individual control over the chemical potential and the electron occupation of each dot along with accurate measurement of the on-site and inter-site interaction terms. The use of virtual gates significantly aids in the tuning of tunnel coupling and chemical potential. The demonstrated high degree of control of the system along with fast single-shot spin-readout achieved through Pauli spin blockade establish this dot array as a promising simulator of the Fermi-Hubbard model. The 2x2 dot array is used to simulate Nagaoka ferromagnetism in the next experiment. This form of itinerant ferromagnetism arises from the Fermi-Hubbard model, and was first shown analytically in the limit of infinite interaction strengths and infinite lattices by Nagaoka in 1966. Nagaoka ferromagnetism has been a topic of rigorous theoretical studies ever since, but its experimental signature has eluded us for more than five decades. In this experiment, we load the four dot plaquette with three electrons and demonstrate the emergence of spontaneous ferromagnetism by measuring the spin correlation of two out of the three electrons. Changing the topology of the array to an open chain is shown to destroy the ferromagnetic signature, consistent with the Lieb-Mattis theorem. We also show indications that this ferromagnetic ground state can be destroyed by applying a perpendicular magnetic field, unlike most other forms of ferromagnetism. However, this ground state shows striking robustness to the offset in the local potential of any dot. This is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantumdot arrays. The final experiment takes a different approach to simulate the Fermi-Hubbardmodel with a large 2d array of quantum dots. The dot array is created using only three gates in a top-down approach. This allows for only global control over the electron filling and tunnel coupling of the dots, contrary to the previous experiments. The readout is performed with capacitance spectroscopy, which allows us to directly probe the density of states of the two-dimensional electron systems. We measure the disorder levels and optimize both substrates and gating strategies to induce periodic potential, sufficiently stronger than the disorder level, at the 2d electron gas. Although we demonstrate a novel platformfor the realization of artificial lattices of interacting particles, this effort is currently limited by the substrate inhomogeneity.
Abstract In pursuit of a practical quantum advantage 1 , analogue quantum systems provide an invaluable way to simulate the physics of quantum materials 2–4 , quantum systems out of equilibrium 5,6 or interaction-induced localization 7 . Notable recent progress to realize such systems has been achieved in ultracold atoms 8–12 , superconducting circuits 13–15 and twisted van der Waals materials 16–19 . However, so far, these platforms have struggled to simulate large-scale strongly interacting fermionic systems at low temperatures, at which electronic correlations dominate materials properties and numerical simulations remain restricted in accuracy and scope 20,21 . Here we demonstrate the realization of a new platform consisting of large-scale 2D arrays of sub-nanometre precision-engineered atom-based quantum dots (15,000 sites) to simulate strongly interacting, low-temperature physics. By observing a metal–insulator (MI) transition on a 2D square lattice of atom-based quantum dots, we demonstrate independent and precise control of the on-site interaction U and tunnelling t . Magneto-transport measurements further indicate the formation of an insulating state driven by Mott–Hubbard/Anderson physics and promising signatures of correlated electron physics. These precision-engineered analogue quantum simulators provide a unique platform to simulate quantum materials on arbitrary 2D lattices and to explore many unanswered questions in the formation of quantum magnetism, interacting topological quantum matter and unconventional superconductivity.
Strongly correlated materials exhibit complex emergent phenomena -- such as unconventional high-temperature superconductivity -- that cannot be explained within a single or weakly-interacting particle description, making understanding their physics a central challenge in condensed matter physics. This thesis develops and applies novel approaches to strongly correlated electron systems, focusing on neural quantum states (NQS) and quantum simulation with cold atoms in optical lattices or Rydberg tweezer arrays. A key contribution of this work is the advancement of neural-network-based representations of quantum many-body states. By employing state-of-the-art network architectures like Transformers and combining them with physical constructions such as determinants, Pfaffians and Gutzwiller-projection, NQS are extended to simulate large two-dimensional fermionic single- and multi-band systems with high accuracy and beyond the capabilities of conventional methods. In addition, the thesis explores how quantum simulators based on ultracold atoms in optical lattices can be leveraged to study models directly relevant to strongly correlated materials -- e.g. the multi-band model of cuprate superconductors -- as well as proposes strategies to probe superconductivity in this setting. Furthermore, hybrid approaches that combine NQS with data from quantum simulators are developed. This synergy allows for improved optimization and direct comparison between theory and experiment. These methodological developments are applied to investigate two fundamental questions in high-temperature superconductivity: On the one hand, the work proposes a microscopic mechanism based on Feshbach resonances and tests this hypothesis extensively in a model system relevant to cuprates, nickelates and heavy fermion materials. On the other hand, it develops systematic approaches to derive effective low-energy models from more complex systems like multi-band models or electron-phonon coupled systems, shining light on the timely question which single-band models capture the physics of high-temperature superconductors like cuprate or nickelate materials. Overall, the thesis demonstrates how combining machine learning and quantum simulation provides powerful tools for understanding strongly correlated quantum matter.
Cutting-edge technology needs small, ultrafast devices, operational in a wide range of regimes. This calls for solids with novel, unconventional and tailorable properties. Great progress is expected from materials in which electron-electron and electron-phonon correlations strongly affect the dynamics ( i.e. "unforeseen" useful properties are expected to be most likely found in systems with complex behavior). In spite of the potentially huge technological pay-off, our understanding of these systems is rather incomplete, especially in non-equilibrium. Often, with knowledge of systems or phenomena at an early stage, it is rewarding to resort to model, simplified descriptions. This strategy is used in this thesis, where we study several models lattice systems via density-functional theory. The latter is a well established approach (in fact, it is the current method of choice) for investigations of real materials. In our research, we focussed on little understood properties of interacting many-particle systems, such as the time-dependent conduction properties of electronic devices in the presence of interactions, disorder, and lattice vibrations, or the expansion of ultracold fermion clouds in 3D optical lattices. All these systems were described in terms of Hubbard-type interactions for the electrons, and Holstein-type electron-phonon interactions. Our results show interesting features due to the interactions which depend on dimensionality; they also show a dynamical crossover for several properties, due to the competition between disorder and interaction. Finally, when lattice vibrations are included, we showed how it is possible to manipulate in a controlled way the nuclear dynamics of molecular device via fast electronic external fields, of potential interest for technologies employing nanomolecular motors.
We propose a device for studying the Fermi-Hubbard model with long-range Coulomb interactions using an array of coupled quantum dots defined in a semiconductor two-dimensional electron-gas system. Bands above the lowest energy band are used to form the Hubbard model, so that a high average electron density may be used to implement the device. We find that depending on the average electron density, the system is well described by a one- or two-band Hubbard model. Our device design enables the control of the ratio of the Coulomb interaction to the kinetic energy of the electrons independently to the filling of the quantum dots, such that a large portion of the Hubbard phase diagram may be probed. Estimates of the Hubbard parameters suggest that a metal-Mott insulator quantum phase transition and a d-wave superconducting phase should be observable using current technologies.