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.
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.
Abstract Quantum simulations of electronic structure and strongly correlated quantum phases are among the most promising applications of quantum computing. These computations benefit from native fermionic encodings 1,2 , enforcing fermionic statistics and conservation laws such as particle number and magnetization 3 independent of gate errors. While ultracold atoms in optical lattices have become established as powerful analogue simulators of strongly correlated fermionic matter 4–7 , neutral-atom platforms have concurrently emerged as versatile, scalable architectures for spin-based digital quantum computation 8 . Unifying these capabilities requires high-fidelity motionally coherent gates for fermionic atoms 9–11 , similar to collisional gates in bosonic systems 12,13 , paving the way for programmable fermionic quantum processors. Here we demonstrate collisional entangling gates with fidelities up to 99.75(6)% and Bell-state lifetimes exceeding 10 s, realized by means of controlled interactions of fermionic atoms in an optical superlattice. Using quantum gas microscopy 14 , we microscopically characterize spin-exchange and pair-tunnelling gates and realize a robust composite pair-exchange gate, a key building block for quantum chemistry simulations 3,15 . Our results establish controlled collisions in optical lattices as a competitive and complementary route to high entangling gate fidelities in neutral-atom quantum computers. Operating intrinsically with fermions, this capability naturally extends to many-qubit architectures, in which fermionic statistics become relevant, enabling complex state preparation and advanced readout 16–19 in scalable analogue–digital hybrid quantum simulators. Combined with local addressing 20,21 , these gates mark a crucial step towards a fully digital fermionic quantum computer based on controlled motion and entanglement of neutral atoms.
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.
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.
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.
Ultracold neutral atoms in optical lattices have become a powerful platform for the simulation of complex quantum systems. With our quantum gas microscope, we measure snapshots of the quantum many-body wavefunction by fully resolving the position and spin of each atom. I will present the application of this method to two quantum phases: The Haldane spin-1 phase is the prototype of a symmetry-protected topological phase, whose spin order is hidden in conventional two-point correlation functions. On our images, we can evaluate the characteristic string-correlator of this state and directly see the associated edge states of the system. In an antiferromagnetic background, holes get dressed by a surrounding cloud of ferromagnetic correlations. We study these magnetic polarons, which are a building block of the intricate physics of cuprates, by mapping out the spatial structure of the spin environment of individual holes. Upon increased doping, we observe the transition from this unusual polaronic metal to a Fermi Liquid and provide quantum-simulated results of the Fermi-Hubbard model as a benchmark for different theoretical approaches.
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.