Accessing new regimes in quantum simulation requires the development of new techniques for quantum state preparation. We demonstrate the quantum state engineering of a strongly correlated many-body state of the two-component repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an ultralow entropy doublon band insulator created through entropy redistribution. After isolating the band insulator, we change the underlying potential to expand it into a half-filled system. The final many-body state realized shows strong antiferromagnetic correlations and a temperature below the exchange energy. We observe an increase in entropy, which we find is likely caused by the many-body physics in the last step of the scheme. This technique is promising for low-temperature studies of cold-atom-based lattice models.
Accessing new regimes in quantum simulation requires the development of new techniques for quantum state preparation. We demonstrate the quantum state engineering of a strongly correlated many-body state of the two-component repulsive Fermi-Hubbard model on a square lattice. Our scheme makes use of an ultralow entropy doublon band insulator created through entropy redistribution. After isolating the band insulator, we change the underlying potential to expand it into a half-filled system. The final many-body state realized shows strong antiferromagnetic correlations and a temperature below the exchange energy. We observe an increase in entropy, which we find is likely caused by the many-body physics in the last step of the scheme. This technique is promising for low-temperature studies of cold-atom-based lattice models.
Strongly correlated systems have rich and intriguing behaviors that have been at the focal point of modern condensed-matter physics. One promising research direction is the study of the Fermi-Hubbard model, which is thought to describe the essential physics of the cuprates and is naturally realized with ultracold atoms in optical lattices. The development of single-site control and readout on this platform has allowed for new methods in creating and studying states in the Fermi-Hubbard model. In this thesis, we discuss the engineering of low-entropy correlated states using a novel technique. By preparing a gapped band-insulator in the presence of an entropy reservoir, we create states with an entropy per particle of 0.016(3) k_B. We then demonstrate that the low-entropy band insulator can be used as a resource for creating strongly correlated states; by dynamically manipulating the on-site potentials we are able to convert the uncorrelated band insulator into a correlated Mott insulator. We also investigate if heating is responsible for the increase in entropy when creating the correlated phase and determine that it does not play a dominant role. In a separate experiment, we leverage the single-site manipulation capabilities in a different way by creating a single localized hole dopant in an antiferromagnetic state. We then allow the hole to delocalize by suddenly removing its pinning potential and study the resulting density and spin correlation evolution. As the hole delocalizes, we find that it displaces the surrounding spin correlations in a trajectory that is initially controlled by quantum interference. At later times, the hole delocalizes at a rate that scales with the spin exchange energy, revealing that the presence of magnetism fundamentally alters charge transport. These developments demonstrate continued progress in optical lattice quantum simulators and how they can play a role in unraveling the mysteries of the Fermi-Hubbard model.
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.
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.
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.
An advanced cooling scheme, incorporating entropy engineering, is vital for isolated artificial quantum systems designed to emulate the low-temperature physics of strongly correlated electron systems. This study theoretically demonstrates a cooling method employing multicomponent Fermi gases with SU(N)-symmetric interactions, focusing on the case of ^{173}Yb atoms in a two-dimensional optical lattice. Adiabatically introducing a nonuniform state-selective laser gives rise to two distinct subsystems: a central low-entropy region, exclusively composed of two specific spin components, acts as a quantum simulator for strongly correlated electron systems, while the surrounding N-component mixture retains a significant portion of the entropy of the system. The total particle numbers for each component are good quantum numbers, creating a sharp boundary for the two-component region. The cooling efficiency is assessed through extensive finite-temperature Lanczos calculations. The results lay the foundation for quantum simulations of two-dimensional systems of Hubbard or Heisenberg type, offering crucial insights into intriguing low-temperature phenomena in condensed-matter physics.
Understanding quantum many-body states of correlated electrons is one main theme in modern condensed-matter physics. Given that the Fermi-Hubbard model, the prototype of correlated electrons, was recently realized in ultracold optical lattices, it is highly desirable to have controlled numerical methodology to provide precise finite-temperature results upon doping to directly compare with experiments. Here, we demonstrate the exponential tensor renormalization group (XTRG) algorithm [Chen et al., Phys. Rev. X 8, 031082 (2018)], complemented by independent determinant quantum Monte Carlo, offers a powerful combination of tools for this purpose. XTRG provides full and accurate access to the density matrix and thus various spin and charge correlations, down to an unprecedented low temperature of a few percent of the tunneling energy. We observe excellent agreement with ultracold fermion measurements at both half filling and finite doping, including the sign-reversal behavior in spin correlations due to formation of magnetic polarons, and the attractive hole-doublon and repulsive hole-hole pairs that are responsible for the peculiar bunching and antibunching behaviors of the antimoments.