Studying the low-temperature phases of doped Hubbard models, including the emergence of collective order and exotic normal phases, is at the heart of strongly correlated physics. This thesis offers new theoretical insights into the low-energy physics of doped Hubbard models, with a particular emphasis on leveraging quantum simulation as a powerful investigative tool. We explore the emergence of collective order driven by many-body interactions, by predicting and observing stripe-like structures in quantum gas microscopes of engineered Hamiltonians. These fluctuating stripe patterns are developed into a theoretical framework for the pseudogap— a highly enigmatic phase in hole-doped cuprates—where we show how fluctuating domain walls yield effective toric code descriptions. Ultracold atoms in optical lattices provide a unique platform for directly probing and testing this theory. We further investigate unconventional bilayer nickelate superconductors, predicting an exceptionally stable superfluid state in a single-band Hubbard model at experimentally accessible temperatures. By proposing schemes to observe coherent pair-pair correlations, this advances the long-standing goal of realizing and observing long-range superconducting order in ultracold atomic systems in optical lattices. On non-bipartite lattices, we examine kinetic magnetism in Hubbard models and moiré heterostructures. Additionally, the low-temperature regime of doped Hubbard models with enhanced symmetries is analyzed, revealing exotic phenomena such as sub-dimensional polaronic particles. We develop machine learning techniques to extract key physical insights from many-body snapshots, offering a new avenue for understanding intricate quantum phases. Finally, we go beyond the Fermi-Hubbard paradigm and show how non-local strongly correlated models can be leveraged to address classical optimization problems through quantum annealing.
Studying the low-temperature phases of doped Hubbard models, including the emergence of collective order and exotic normal phases, is at the heart of strongly correlated physics. This thesis offers new theoretical insights into the low-energy physics of doped Hubbard models, with a particular emphasis on leveraging quantum simulation as a powerful investigative tool. We explore the emergence of collective order driven by many-body interactions, by predicting and observing stripe-like structures in quantum gas microscopes of engineered Hamiltonians. These fluctuating stripe patterns are developed into a theoretical framework for the pseudogap— a highly enigmatic phase in hole-doped cuprates—where we show how fluctuating domain walls yield effective toric code descriptions. Ultracold atoms in optical lattices provide a unique platform for directly probing and testing this theory. We further investigate unconventional bilayer nickelate superconductors, predicting an exceptionally stable superfluid state in a single-band Hubbard model at experimentally accessible temperatures. By proposing schemes to observe coherent pair-pair correlations, this advances the long-standing goal of realizing and observing long-range superconducting order in ultracold atomic systems in optical lattices. On non-bipartite lattices, we examine kinetic magnetism in Hubbard models and moiré heterostructures. Additionally, the low-temperature regime of doped Hubbard models with enhanced symmetries is analyzed, revealing exotic phenomena such as sub-dimensional polaronic particles. We develop machine learning techniques to extract key physical insights from many-body snapshots, offering a new avenue for understanding intricate quantum phases. Finally, we go beyond the Fermi-Hubbard paradigm and show how non-local strongly correlated models can be leveraged to address classical optimization problems through quantum annealing.
Analog quantum simulation provides a unique toolkit to investigate quantum many-body problems of whose solutions may be incredibly challenging. In particular, using ultracold fermionic atoms in optical lattices it realizes the Fermi Hubbard model, which is a fundamental model in condensed matter physics exhibiting properties relevant to many intriguing strongly-correlated systems. However, most quantum simulators of the Hubbard model have so far restricted to the square geometries. In addition, access to low temperatures where the exotic quantum phases are predicted to develop has still remained elusive. In this thesis, we engineer a novel optical lattice with dynamically tunable geometries and significantly reduced technical noises. We extend for the first time the study of quantum magnetism into the exotic phases in a Fermi Hubbard system with tunable geometric frustration. As we continuously tune our system from a square to a triangular lattice geometry, we observe a transition from a Néel antiferromagnet to a 120-degree spin spiral state. We then study, again for the first time, how doping affects a frustrated quantum magnet. To our surprise, we found an emergent ferromagnetic state with strong particle doping, which is absent on the hole-doped side and is in stark contrast with the particle-hole symmetric doping dependence in a square lattice. To shed light on the role of itinerant dopants in the emergence of these new magnetic properties, we furthermore leverage the unique single-particle resolution capabilities of our platform to probe higher-order density and spin correlations. These measurements hint at a new type of magnetism induced by kinetic frustration, which manifests as local antiferromagnetic correlations around hole dopants and and ferromagnetic correlations around particle dopants. Unlike magnetism induced by exchange or superexchange interactions, the energy associated with this mechanism is the kinetic energy, closely related to the famous rigorous results by Nagaoka. Furthermore, the dynamical tunability of the lattice allows adibatic engineering of quantum states in optical lattices. We discuss the preliminery efforts to prepare strongly-correlated states with significantly reduced temperatures, which may pave the way towards low temperature states in the Hubbard model.
This thesis describes experiments performed on a gas of lithium atoms in an optical lattice which are relevant to the low-temperature physics of the Hubbard model. The Hubbard model is perhaps the most intensively studied model of fermionic particles on a lattice, both because it is the simplest such model which seriously challenges modern theoretical tools, and because it is a candidate model for describing high-temperature superconductivity in cuprate materials. The challenges associated with numerical simulations of the Hubbard model have motivated “quantum simulations” of the type described in this thesis, in which a well-controlled physical system is engineered to mimic the model, allowing its properties to be determined through experiments. Historically, however, such experiments could not access the low-temperature regime of the Hubbard model most relevant to open questions on materials like cuprates, where modern computational techniques cannot yet definitively characterize the physics. We developed a novel set of cooling techniques which allowed our experiment to access this regime. These techniques are based on adiabatic conversion between a band insulator, which can be prepared with very low entropies using single-atom-resolved control and detection techniques now common in ultracold atomic physics, and various quantum fluids, including Hubbard systems. We then performed the first experiments in this new regime of the Hubbard model, focusing on the anomalous “pseudogapped” metallic state. This state is predicted to exist by computational methods, and is believed to mimic the eponymous state in cuprates which gives rise to high-temperature superconductivity upon cooling. Nevertheless, its properties and mechanisms remain poorly understood. We developed several new measurements that enabled an observation of the pseudogap and which yielded novel data on its thermodynamics, linking the pseudogap to an anomaly in the equation of state. These experiments demonstrate a new mode of operating fermionic quantum gas experiments, in which single-atom-resolved controls, rather than bulk techniques like evaporative cooling, are leveraged to access low temperatures in a sample of several hundred atoms. They also signal the arrival of quantum simulators in a regime of poorly-understood emergent low-temperature phenomena that are relevant to the electronic properties of solids, concretely demonstrating the utility of quantum simulation in addressing frontier problems in quantum many-body physics.
Among the most compelling targets for quantum simulation are strongly correlated phases and electronic-structure problems, where interactions organize electrons into collective states and produce intricate low-temperature phase diagrams. Cuprate superconductors are a canonical example: at low doping, superconductivity emerges from a metallic regime that exhibits a pseudogap above the critical temperature. Ultracold atoms in optical lattices provide a well-controlled, tunable setting to probe the microscopic mechanisms behind this behavior and, in fermion-native architectures, to implement electronic structure dynamics directly. This thesis demonstrates both large scale systematic analog quantum simulations in the most interesting regime of doped antiferromagnets and elementary high-fidelity gates as the basis for a digital or hybrid fermionic quantum processors in an optical lattice. Working with ultracold Lithium-6 in a two–dimensional optical superlattice, we first map the parameter space of the Fermi–Hubbard model over a wide range of temperatures and dopings. More than 40000 single-site spin- and density-resolved snapshots, spanning over a dense grid of doping levels and temperatures in a numerically challenging parameter space, reveal antiferromagnetic correlations extending across the system size and into the pseudogap regime. Temperatures down to T/t=0.2 are realized, determined by benchmarking the data to state-of-the-art numerical methods. By evaluating spin–charge correlators up to fifth order, we experimentally uncover a universal scaling behavior across the pseudogap crossover, governed by a single, doping-dependent temperature scale. These findings provide the first microscopic evidence of universal scaling in multi-point correlators and establish stringent benchmarks for future theoretical developments. On the same apparatus, we demonstrate that the controlled motion of fermions in double wells enables high-fidelity entanglement. Double-well potentials are used to engineer coherent pair-tunnelling and spin-exchange interactions that act as native SWAP^α operations. We demonstrate the collisional gate fidelities up to 99.8% and Bell-state lifetimes exceeding ten seconds, limited mainly by residual inhomogeneities in the optical potential. A composite pulse sequence isolates the pair-exchange channel, realizing the elementary building block required for fermionic quantum-chemistry algorithms. With the addition of site-selective addressing, our results mark a key step towards a fully digital, scalable fermionic quantum computer based on the controlled motion and entanglement of fermionic neutral atoms. The work establishes a hybrid analog-digital architecture: analog evolution under the Hubbard Hamiltonian yields thermodynamic states whose magnetic properties match and extend theoretical benchmarks, while digital collisional gates provide building blocks for error-corrected quantum computation and complex state preparation.
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.
Exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet is expected to give rise to pseudogap states and high-temperature superconductors. Quantum simulation with ultracold fermions in optical lattices offers the potential to answer open questions about the doped Hubbard Hamiltonian, and has recently been advanced by quantum gas microscopy. In order to take advantage of these possibilities, a stable, high-power, 2D square lattice system was developed and coupled with an image plane based spatial light modulator. The ability to finely tune the atomic potential has made it possible to realize an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice. At our lowest temperatures of T/t=0.25(2), antiferromagnetic long-range order (LRO) manifests through the divergence of the correlation length that reaches the size of the system, the development of a peak in the spin structure factor and a value of the staggered magnetization approaching the ground state value. Similarly, by carefully shaping the confinement, we have produced ultra-low entropy band insulators, which promise to be a perfect starting point for more advanced cooling schemes. In addition to the production of new states, Fermi gas microscopy is superbly well suited to studies of many-body dynamics. To this end I report on preliminary measurements of the propagation of holes in a Mott insualtor. These results demonstrate that Fermi gas microscopy can address open questions on the low-temperature Hubbard model.
In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual "pseudogap" metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multipoint correlation functions up to fifth order, we uncover a universal scaling behavior in magnetic and higher-order spin-charge correlations characterized by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature [Formula: see text]. Our quantitative findings reveal a qualitative behavior of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way toward the exploration of charge pairing and collective phenomena expected at lower temperatures.