Quantum simulations of Hubbard models with ultracold atoms rely on the exceptional control of coherent motion provided by optical lattices. Here we demonstrate enhanced tunability using an optical superlattice in a fermionic quantum gas microscope, evidenced by long-lived coherent double-well oscillations, next-nearest-neighbor quantum walks in a staggered configuration, and correlated quantum walks of two particles initiated through a resonant pair-breaking mechanism. We furthermore demonstrate tunable spin couplings through local offsets and engineer a spin ladder with ferromagnetic and antiferromagnetic couplings along the rungs and legs, respectively. Our Letter underscores the high potential of optical superlattices for engineering, simulating, and detecting strongly correlated many-body quantum states, with direct applications ranging from the study of mixed-dimensional systems to fermionic quantum computing.
Quantum simulations of Hubbard models with ultracold atoms rely on the exceptional control of coherent motion provided by optical lattices. Here we demonstrate enhanced tunability using an optical superlattice in a fermionic quantum gas microscope, evidenced by long-lived coherent double-well oscillations, next-nearest-neighbor quantum walks in a staggered configuration, and correlated quantum walks of two particles initiated through a resonant pair-breaking mechanism. We furthermore demonstrate tunable spin couplings through local offsets and engineer a spin ladder with ferromagnetic and antiferromagnetic couplings along the rungs and legs, respectively. Our Letter underscores the high potential of optical superlattices for engineering, simulating, and detecting strongly correlated many-body quantum states, with direct applications ranging from the study of mixed-dimensional systems to fermionic quantum computing.
This thesis presents quantum simulation of strongly-correlated systems beyond standard Hubbard models, using ultracold fermionic potassium atoms in both static and periodically-driven optical superlattices. For this study, we utilize a three-dimensional optical lattice setup, controlling particle interactions via magnetic Feshbach resonances and tunneling between lattice sites through optical lattice intensity. High-resolution absorption imaging combined with radio-frequency spectroscopy distinguishes between singly and doubly occupied sites. To enhance our systems capabilities beyond the standard Hubbard model, we extend the apparatus with an in-plane optical superlattice, creating a bi-chromatic structure by superposition of two optical lattices with commensurate lattice spacings. Using a phase locked loop with an environmental feed forward, we create an excellent phase stability of the superlattice exceeding 3 mrad. This precision allows us to explore both static and periodically-driven one-dimensional tight-binding models with strong interactions. We characterize the static superlattice through radio-frequency spectroscopy and Rabi oscillations, and validate the experimental data against theoretical calculations. In a tilted superlattice configuration, we successfully prepare and detect repulsively bound atom pairs, representing a highly excited eigenstate of the system. Furthermore, we demonstrate control over pair tunneling dynamics in a double-well potential using Floquet engineering, employing a low-noise periodic modulation of the optical superlattice tilt. Using an adiabatic band mapping technique, we directly observe the tunneling dynamics in the driven superlattice. We realize dynamic localization in quarter-filled wells and density-assisted tunneling up to the third harmonic order in half-filled wells. We observe a crossover from density-assited tunneling to dominant pair tunneling by tuning the effective interactions. Remarkably, the pair tunneling is not only enhanced relative to the suppressed single-particle tunneling but also exceeds the superexchange rate of a static double-well by more than a factor of two. This opens the possibility to study many-body systems with dominant pair tunneling, that extend beyond the standard Hubbard model.
Ultracold atoms in optical lattices provide a versatile platform for studying many-body physics in a defect-free system with tunable parameters. For the analog quantum simulation of the Fermi-Hubbard model, fermionic atoms take on the role of the valence electrons and optical lattices provide the periodic potential in place of the solid-state crystal. The dynamics in the system are described by the tunneling amplitude t between neighboring lattice sites and the interaction energy U of two particles occupying the same lattice site. With the depth of the optical lattices and an external magnetic field, both parameters can be tuned to access a wide range of regimes. Two superimposed lattices with different lattice periods form an optical superlattice, where the most common configuration is a bichromatic superlattice with lattice periods different by a factor of two. Depending on the lattice depths and the relative phase of the lattices, the bichromatic superlattice potential ranges from an array of weakly-coupled double wells to a continuous lattice potential with a staggered energy offset. We developed a calibration technique for measuring the depth of an optical lattice with local resolution. The band structure of the optical lattice is probed by modulating the lattice depth and exciting the atoms to higher bands. However, compared to resolving the band occupations in a time-of-flight measurement, we further excite the atoms to an untrapped band to deplete the optical lattice along equipotential lines where the modulation frequency is resonant with the local band transitions. From the profile of the lattice depth, we obtain the calibration factor for the power regulation, the waist of the underlying lattice beams and the position of the lattice axis. This technique combines several calibration measurements, thereby reducing the measurement time and enabling an automation of the lattice alignment. For the bichromatic superlattice we realized an active stabilization of the superlattice phase that enables long-term measurements with a precise control over the superlattice phase. The instability of the superlattice phase is a result of the different refractive indices for the two lattices in air and the optical elements along the optical path. Using environmental sensors, we monitor the temperature, the pressure, and the relative humidity to apply the expected correction to the superlattice phase. The stabilized superlattice phase enabled the investigation of Floquet-driven double wells by modulating the energy offset through the superlattice phase. We used a near-resonant driving frequency with respect to the interaction energy to enhance the pair-tunneling amplitude in doubly-occupied double wells compared to static double wells and compared to the tunneling amplitude in singly-occupied double wells.
This dissertation summarizes my recent work regarding systems of strongly interacting fermionic atoms in optical lattices. This work addresses the combination of two experimental techniques that have been the subject of much recent research in ultracold atom physics. One is the use of optical lattices, which provide a means to realize diverse interaction configurations within a clean, controllable system. The other is the use of magnetically tunable Feshbach resonances to control the strength of the interatomic interaction. Together, these techniques offer the possibility of an experimental realization of many important model Hamiltonians of condensed matter physics, and may also lead to the discovery of new physics. Recent study of this system has shown that strong interactions near Feshbach resonance will lead to the population of multiple lattice bands, and that collisions between atoms on neighboring sites cannot be neglected. These effects lead to a complicated Hamiltonian, but one which can be simplified to an effective single-band model equivalent to the generalized Hubbard model (GHM), which is an extension of the Hubbard model that includes correlated hopping terms. My main results concern the study of this model. The strong correlations between the particles make it difficult to definitively determine the many body physics of the GHM. As a first approach to understanding the GHM in optical lattices, I focus mainly on cases where the problem is greatly simplified by allowing interactions among only small groups of lattice sites. This restriction can be implemented in experiments using an optical superlattice potential. Our results include a proposed scheme (based on double-well superlattices) to empirically verify that the GHM describes this system and to directly measure the various parameters of this model. Other results include exact solutions on four-site square plaquettes, which demonstrate that d-wave excitations can occur in the low-energy states. By using a superlattice to give an array of weakly coupled plaquettes, one can thus produce a d-wave superfluid state. This is of relevance to the study of high-Tc superconductors, although I note certain key differences between the sort of d-wave superfluid described here and that of the superconductors.
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.
The exchange coupling between quantum mechanical spins lies at the origin of quantum magnetism. We report on the observation of nearest-neighbor magnetic spin correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy within the lattice structure. This is achieved in a tunable-geometry optical lattice, which also enables the detection of the magnetic correlations. We load a low-temperature two-component Fermi gas with repulsive interactions into either a dimerized or an anisotropic simple cubic lattice. For both systems the correlations manifest as an excess number of singlets as compared to triplets consisting of two atoms with opposite spins. For the anisotropic lattice, we determine the transverse spin correlator from the singlet-triplet imbalance and observe antiferromagnetic correlations along one spatial axis. Our work paves the way for addressing open problems in quantum magnetism using ultracold fermions in optical lattices as quantum simulators.
Strongly-correlated electrons in transition-metal oxides give rise to intriguing emergent phenomena, including high-temperature superconductivity in cuprates. While simplified one-band Hubbard models capture some aspects, explicitly describing the interplay of copper and oxygen orbitals -- as in the three-band Emery model -- is essential to capture the full phenomenology of cuprates. Quantum simulators based on ultracold atoms offer a promising route to study such systems in a controlled setting, but realizing realistic multi-orbital Hubbard models remains challenging. Here we propose an optical superlattice architecture that implements the three-band Emery model with ultracold fermions. By combining lattice beams with controllable interference, we engineer orbital degrees of freedom that reproduce key features of the cuprate band structure, while enabling independent control of orbital-dependent interactions and charge-transfer energy. We show that single-particle quantum walks can benchmark the resulting tight-binding model. Using determinant quantum Monte Carlo, we further investigate thermodynamic properties in the undoped regime and find a finite-temperature metal-insulator crossover accompanied by the onset of antiferromagnetic correlations accessible in current experiments. Finally, we apply a Hamiltonian learning protocol enabling to infer effective single-band Hubbard models from experimental realizations of Emery models. Our results provide a practical pathway to simulate multi-orbital Hubbard physics with quantum gas microscopes.