Abstract : The authors use electrostatically defined quantum dot arrays to study quantum simulation, examining both large arrays to explore the ground state and excitations of the Fermi-Hubbard model, and to examine very small arrays of 3-4 quantum dots as the basis for simulating superexchange, frustration, magnetism, etc. The large arrays were created by defining a grid-shaped gate on a semiconductor, forcing the electrons to see a periodic potential and be confined in a lattice of sites, where the low temperature reachable by the system in a dilution refrigerator allows examining the phase diagram of the model in a regime where spin correlations have an important influence. Initial plans to perform transport measurement were unsuccessful as the clean room realization of contacts to the two layers of the bilayered heterostructure had very low yield, so the authors performed capacitance spectroscopy measurement instead. This provides direct measurement of density of states, and the lithography process involved allowed grids with 150-200nm periods to be successfully written. The small array examination analyzed how a system of four quantum dots on a square and filled with three electrons allowed the authors to study magnetism of few-body systems, examining whether the Nagaoka theorem could be realizable with quantum dots (conclusion: the ferromagnetic-paramagnetic state is in reach experimentally) and examining the experimental techniques to test the spin-structure of the ground state and induce the transition (finding: application of magnetic field can break the ferromagnetic ground state, in contrast to the usual). The authors also studied a linear array of three dots, resulting in publications in Nature Nanotechnology, Applied Physics Letters, and Annalen Der Physik.
Abstract : The authors use electrostatically defined quantum dot arrays to study quantum simulation, examining both large arrays to explore the ground state and excitations of the Fermi-Hubbard model, and to examine very small arrays of 3-4 quantum dots as the basis for simulating superexchange, frustration, magnetism, etc. The large arrays were created by defining a grid-shaped gate on a semiconductor, forcing the electrons to see a periodic potential and be confined in a lattice of sites, where the low temperature reachable by the system in a dilution refrigerator allows examining the phase diagram of the model in a regime where spin correlations have an important influence. Initial plans to perform transport measurement were unsuccessful as the clean room realization of contacts to the two layers of the bilayered heterostructure had very low yield, so the authors performed capacitance spectroscopy measurement instead. This provides direct measurement of density of states, and the lithography process involved allowed grids with 150-200nm periods to be successfully written. The small array examination analyzed how a system of four quantum dots on a square and filled with three electrons allowed the authors to study magnetism of few-body systems, examining whether the Nagaoka theorem could be realizable with quantum dots (conclusion: the ferromagnetic-paramagnetic state is in reach experimentally) and examining the experimental techniques to test the spin-structure of the ground state and induce the transition (finding: application of magnetic field can break the ferromagnetic ground state, in contrast to the usual). The authors also studied a linear array of three dots, resulting in publications in Nature Nanotechnology, Applied Physics Letters, and Annalen Der Physik.
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.
It has been demonstrated that small plaquettes of quantum dot spin qubits are capable of simulating condensed matter phenomena that arise from the Hubbard model, such as the collective Coulomb blockade and Nagaoka ferromagnetism. Motivated by recent materials developments, we investigate a bilayer arrangement of quantum dots with four dots in each layer which exhibits a complex ground state behavior. We find using a generalized Hubbard model with long-range Coulomb interactions, several distinct magnetic configurations occur as the Coulomb interaction strength is varied, with possible ground states that are ferromagnetic, antiferromagnetic, or having both one antiferromagnetic and one ferromagnetic layer. We map out the full phase diagram of the system as it depends on the inter- and intralayer Coulomb interaction strengths, and find that for a single layer, a similar but simpler effect occurs. We also predict interesting contrasts among electron, hole, and electron-hole bilayer systems arising from complex correlation physics. Observing the predicted magnetic configuration in already-existing few-dot semiconductor bilayer structures could prove to be an important assessment of current experimental quantum dot devices, particularly in the context of spin-qubit-based analog quantum simulations.
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.
Quantum dots can confine single electrons or holes to define spin qubits that can be operated with high fidelity. Experimental work has progressed from linear to two-dimensional arrays of quantum dots, enabling qubit interactions that are essential for quantum simulation and computation. Here, we explore architectures beyond planar geometries by constructing quantum dot arrays in three dimensions. We realize an eight-quantum dot system in a silicon-germanium heterostructure comprising two stacked germanium quantum wells, where quantum dots are positioned at the vertices of a cuboid. Using electrostatic gate control, we load a single hole into any of the eight quantum dots. To demonstrate the potential of multilayer quantum dot systems, we show coherent spin control and hopping-induced spin rotations by shuttling between the quantum wells. The ability to extend quantum dot arrays in three dimensions provides opportunities for novel quantum hardware and high-connectivity quantum circuits.
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 singlettriplet 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.
Recent progress of quantum simulators provides insight into the fundamental problems of strongly correlated systems. To adequately assess the accuracy of these simulators, the precise modeling of the many-body physics, with accurate model parameters, is crucially important. In this paper, we employed an ab initio exact diagonalization framework to compute the correlated physics of a few electrons in artificial potentials. We apply this approach to a quantum-dot system and study the magnetism of the correlated electrons, obtaining good agreement with recent experimental measurements in a plaquette. Through control of dot potentials and separation, including geometric manipulation of tunneling, we examine the Nagaoka transition and determine the robustness of the ferromagnetic state. While the Nagaoka theorem considers only a single-band Hubbard model, in this work we perform extensive ab initio calculations that include realistic multiorbital conditions in which the level splitting is smaller than the interactions. This simulation complements the experiments and provides insight into the formation of ferromagnetism in correlated systems. More generally, our calculation sets the stage for further theoretical analysis of analog quantum simulators at a quantitative level.