Large-scale analogue quantum simulation using atom dot arrays
M. B. Donnelly, Yousun Chung, Rebekka Garreis, Stephan Plugge, D. Pye, M. Kiczynski, J. Támara-Isaza, Mushita M. Munia, S. Sutherland, B. Voisin, Ludwik Kranz, Yu‐Ling Hsueh, A. M. Saffat‐Ee Huq, Casey R. Myers, Rajib Rahman, Joris Gerhard Keizer, Samuel Keith Gorman, Michelle Yvonne Simmons
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.
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.
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 : 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.
Ultracold atoms in optical lattices can provide faithful analog realizations of the Hubbard model and many of its variants. Recently, these simulators have been augmented with improved programmable controls that enable new routes to state preparation, new kinds of dynamics, and, by extension, access to new observables. I will discuss two examples where such tools have enabled simulations that challenge classical numerical techniques: first, a sampling problem involving non-interacting bosons on a lattice that is closely related to boson sampling; and second, the preparation of low temperature equilibrium states of interacting spinful fermions on a lattice. These simulations have the potential to enhance our understanding of quantum many body physics, including practical problems of interest in material design relating to strongly correlated quantum materials. However, fully harnessing their capabilities in the regime where exact classical numerical simulations are absent requires new, precision probes of the relevant microscopic or thermodynamic quantities.
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.
Ultracold fermionic atoms in optical lattices offer pristine realizations of Hubbard models1, which are fundamental to modern condensed-matter physics2,3. Despite notable advancements4–6, the accessible temperatures in these optical lattice material analogues are still too high to address many open problems7–10. Here we demonstrate a several-fold reduction in temperature6,11–13, bringing large-scale quantum simulations of the Hubbard model into an entirely new regime. This is accomplished by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters14,15, which is extremely challenging to simulate classically10. At half-filling, the long-range antiferromagnetic order is close to saturation, leading to a temperature of T/t=0.05−0.05+0.06 based on comparisons with numerically exact simulations. Doped away from half-filling, it is exceedingly challenging to realize systematically accurate and predictive numerical simulations9. Importantly, we are able to use quantum simulation to identify a new pathway for achieving similarly low temperatures with doping. This is confirmed by comparing short-range spin correlations to state-of-the-art, but approximate, constrained-path auxiliary-field quantum Monte Carlo simulations16–18. Compared with the cuprates2,19,20, the reported temperatures correspond to a reduction from far above to below room temperature, at which physics such as the pseudogap and stripe phases may be expected3,19,21–24. Our work opens the door to quantum simulations that solve open questions in material science, develop synergies with numerical methods and theoretical studies, and lead to discoveries of new physics8,10. A several-fold reduction in temperature is accomplished using a neutral-atom Hubbard quantum simulator by transforming a low-entropy product state into strongly correlated states of interest via dynamic control of the model parameters.