Obtaining a microscopic understanding of the dynamics in strongly correlated electronic systems has remained a challenge for many decades. The interplay between the spin and charge degrees of freedom in these materials at different temperatures and dopant concentrations is not well understood and is still an area of intense scientific research. Recently, quantum simulators based on ultracold atoms in optical lattices have emerged as a promising platform to probe strongly correlated fermionic systems. This thesis reports on the work carried out with a quantum gas microscope of ultracold fermionic Li-6, where Fermi-Hubbard systems are prepared and imaged with single site spin and density resolution. The main results of the thesis explore the microscopic dynamics underlying one-dimensional materials, where individual constituents such as the electron with charge e and spin-1/2 are not relevant to the description of the system anymore and are instead replaced by spin and charge excitations that can propagate independent of one another - a phenomenon called spin-charge separation. In our quantum simulator, we use analogous one-dimensional Fermi-Hubbard chains of Li-6, to perform time- and space-resolved microscopy of the spin and charge excitations following a local quench. By extracting their strikingly different velocities and showing an absence of binding between the excitations, we demonstrate spin-charge separation. Our microscopic technique also allows us to quantitatively extract the excess spin carried by the spin excitiation, connecting our results to the phenomenon of fractionalization. In another set of experiments, Fermi-Hubbard chains are probed at equilibrium and incommensurate spin correlations arising in the presence of both density doping and spin polarization are observed. The wavevector of these incommensurate correlations are found to have a linear dependence on doping and polarization. Finally, the effect of the spin-charge interplay is probed in the crossover from one to two dimensions. The spin correlations across dopants are seen to be dramatically different in two dimensions, and the strong antiferromagnetic correlations across dopants present in one dimension disappear. For a single dopant in a fully two dimensional system, the spin-charge interplay manifests as a distorted spin cloud surrounding the dopant, indicating the formation of a magnetic polaron. The experiments reported here demonstrate the power of a quantum simulator; by probing the physics of strongly correlated systems in real space with unprecedented resolution, we can zoom into emergent phenomena, validate theories and access regimes that are not possible in other experimental settings.
Obtaining a microscopic understanding of the dynamics in strongly correlated electronic systems has remained a challenge for many decades. The interplay between the spin and charge degrees of freedom in these materials at different temperatures and dopant concentrations is not well understood and is still an area of intense scientific research. Recently, quantum simulators based on ultracold atoms in optical lattices have emerged as a promising platform to probe strongly correlated fermionic systems. This thesis reports on the work carried out with a quantum gas microscope of ultracold fermionic Li-6, where Fermi-Hubbard systems are prepared and imaged with single site spin and density resolution. The main results of the thesis explore the microscopic dynamics underlying one-dimensional materials, where individual constituents such as the electron with charge e and spin-1/2 are not relevant to the description of the system anymore and are instead replaced by spin and charge excitations that can propagate independent of one another - a phenomenon called spin-charge separation. In our quantum simulator, we use analogous one-dimensional Fermi-Hubbard chains of Li-6, to perform time- and space-resolved microscopy of the spin and charge excitations following a local quench. By extracting their strikingly different velocities and showing an absence of binding between the excitations, we demonstrate spin-charge separation. Our microscopic technique also allows us to quantitatively extract the excess spin carried by the spin excitiation, connecting our results to the phenomenon of fractionalization. In another set of experiments, Fermi-Hubbard chains are probed at equilibrium and incommensurate spin correlations arising in the presence of both density doping and spin polarization are observed. The wavevector of these incommensurate correlations are found to have a linear dependence on doping and polarization. Finally, the effect of the spin-charge interplay is probed in the crossover from one to two dimensions. The spin correlations across dopants are seen to be dramatically different in two dimensions, and the strong antiferromagnetic correlations across dopants present in one dimension disappear. For a single dopant in a fully two dimensional system, the spin-charge interplay manifests as a distorted spin cloud surrounding the dopant, indicating the formation of a magnetic polaron. The experiments reported here demonstrate the power of a quantum simulator; by probing the physics of strongly correlated systems in real space with unprecedented resolution, we can zoom into emergent phenomena, validate theories and access regimes that are not possible in other experimental settings.
This thesis reports on the microscopic investigation of antiferromagnetic order in Hubbard chains, realized with ultracold repulsively interacting fermions in an optical lattice. Extending a quantum gas microscope on spin resolution opened the possibility to Access the full charge and spin statistics of a strongly correlated fermionic many body system. Using this technique, we measured antiferromagnetic correlations over distances up to three lattice sites. Starting with a repulsive degenerate two component mixture of 6Li atoms trapped in a single plane of a vertical lattice, we loaded the Atoms into one-dimensional tubes of a transverse optical superlattice. By adiabatically ramping up the lattice potential along the tubes, we isentropically entered the strongly correlated regime of the one-dimensional Fermi-Hubbard Hamiltonian. We spatially separated the two spin states into opposite sites of local double wells orthogonal to the direction of the lattice before single atom and site sensitive imaging. In this way we extracted the spin information of every single lattice site and were able to evaluate spin-spin correlations. The two component degenerate gases were produced with sub-Poissonian atom number fluctuations by magnetically driven evaporative cooling in vicinity of a Feshbach resonance, used to set the scattering length. The dependence of antiferromagnetic correlations on the driving superexchange coupling was experimentally investigated by varying the interparticle scattering length before loading the atoms into the optical lattice. Taking advantage of the underlying trapping potential of the optical lattice, which shaped the filling and the entropy of the gases, the influence of density excitations and different entropies on spin correlations was observed. By post-selecting the Hubbard chains based on their average filling and local atom number fluctuations, spin correlations corresponding to 58% of the zero temperature predictions in the Heisenberg regime were measured. By comparing the obtained antiferromagnetic correlations to Quantum-Monte-Carlo predictions for our System the lowest measured entropy per particle could be stated as s = 0.51(4)kB, clearly below the critical value of s = ln(2)kB, which is required to form longer ranged correlations. Below this critical entropy, in contrast to local density fluctuations, these spin correlations strongly depend on the entropy of the system. In the future, such a spin thermometer can be used to benchmark novel cooling techniques, which are required to enter the temperature regime of d-wave superconducting states. The access to the full particle and spin statistics will enable us to read out multi-point correlation functions, which characterize such exotic states of matter.
Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
Strongly-correlated electron systems generate some of the richest phenomena and most challenging theoretical problems studied in physics. One approach to understanding these systems is with ultracold fermionic atoms in optical lattices, which can provide a level of control and ways of observing strongly-correlated fermionic systems that are not accessible with conventional materials. This thesis describes the development of an experimental technique where a quantum gas of fermionic 6Li atoms is prepared in a two-dimensional optical lattice and each atom can be frozen in place and imaged with single-site resolution. Combining a vacuum-compatible large numerical aperture microscope with Raman sideband cooling enables site-resolved fluorescence imaging with high fidelity. We observe several phases of the Hubbard model, including band and Mott insulators. The observed in-situ occupation distributions of atoms in the lattice are compared to theory with unprecedented detail and are used to determine the thermodynamic properties of the system. By combining site-resolved imaging with a spin-removal technique, we observe antiferromagnetic correlations in the Hubbard model with single-site resolution. We observe, for the first time in cold atom systems, beyond-nearest-neighbor magnetic correlations, which provide a direct measurement of the correlation length. We also present detailed measurements of the formation of correlations during lattice loading.
The repulsive Hubbard Hamiltonian is one of the foundational models describing strongly correlated electrons and is believed to capture essential aspects of high-temperature superconductivity. Ultracold fermions in optical lattices allow for the simulation of the Hubbard Hamiltonian with control over kinetic energy, interactions, and doping. A great challenge is to reach the required low entropy and to observe antiferromagnetic spin correlations beyond nearest neighbors, for which quantum gas microscopes are ideal. Here, we report on the direct, single-site resolved detection of antiferromagnetic correlations extending up to three sites in spin-1/2 Hubbard chains, which requires entropies per particle well below s* = ln(2). The simultaneous detection of spin and density opens the route toward the study of the interplay between magnetic ordering and doping in various dimensions.
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.
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.