The majority of quantum simulators treat simplified one-band strongly correlated models, whereas multiple bands are needed to describe materials with intermediate correlation. We investigate the sensitivity of multiband quantum simulators to: (1) the form of optical lattices, (2) the interactions between electron analogs. Since the kinetic-energy terms of electron analogs in a quantum simulator and electrons in a solid are identical, by examining both periodic potential and interaction we explore the full problem of many-band quantum simulators within the Born--Oppenheimer approximation. Density functional calculations show that band structure is highly sensitive to the form of optical lattice, and it is necessary to go beyond sinusoidal potentials to ensure that the bands closest to the Fermi surface are similar to those in real materials. Analysis of several electron analog types finds that dressed Rydberg atoms (DRAs) have promising interactions for multiband quantum simulation. DRA properties can be chosen so that interaction matrices approximate those in real systems and decoherence effects are controlled, albeit with parameters at the edge of currently available technology. We conclude that multiband quantum simulators implemented by using the principles established here could provide insight into the complex processes in real materials.
The majority of quantum simulators treat simplified one-band strongly correlated models, whereas multiple bands are needed to describe materials with intermediate correlation. We investigate the sensitivity of multiband quantum simulators to: (1) the form of optical lattices, (2) the interactions between electron analogs. Since the kinetic-energy terms of electron analogs in a quantum simulator and electrons in a solid are identical, by examining both periodic potential and interaction we explore the full problem of many-band quantum simulators within the Born--Oppenheimer approximation. Density functional calculations show that band structure is highly sensitive to the form of optical lattice, and it is necessary to go beyond sinusoidal potentials to ensure that the bands closest to the Fermi surface are similar to those in real materials. Analysis of several electron analog types finds that dressed Rydberg atoms (DRAs) have promising interactions for multiband quantum simulation. DRA properties can be chosen so that interaction matrices approximate those in real systems and decoherence effects are controlled, albeit with parameters at the edge of currently available technology. We conclude that multiband quantum simulators implemented by using the principles established here could provide insight into the complex processes in real materials.
The majority of quantum simulators treat simplified one-band strongly correlated models, whereas multiple bands are needed to describe materials with intermediate correlation. We consider two aspects of multiband quantum simulators: (1) resolution effects that limit the shape and form of optical lattices (2) interaction limitations between electron analogues such as dressed Rydberg atoms (DRAs) and cold ions. Resolution effects are examined with density functional calculations of electron analogues moving in an approximation to the full lattice potential generated with e.g. painted potentials. The ratio of beam waist, w, to interatomic spacing, ann, is key. The energy of core bands increases with w/ann, eventually leading to rearrangement of core and valence bands. For sufficiently small w/ann, the bands closest to the Fermi surface are similar to those in real materials. DRA properties can be chosen so that interaction matrices approximate those in real systems and decoherence effects are controlled, with parameters at the edge of currently available technology. Since interaction matrices are approximate, materials simulations would not be predictive. Nonetheless, there could be sufficient similarities between such simulators and real systems to gain insight into complex multiband effects in intermediate correlation materials.
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.
Relative to single-band models, multiband models of strongly interacting electron systems are of growing interest because of their wider range of novel phenomena and their closer match to the electronic structure of real materials. In this brief review we discuss the physics of three multiband models (the three-band Hubbard, the periodic Anderson, and the Falicov-Kimball models) that was obtained by numerical simulations at zero temperature. We first give heuristic descriptions of the three principal numerical methods (the Lanczos, the density matrix renormalization group, and the constrained-path Monte Carlo methods). We then present generalized versions of the models and discuss the measurables most often associated with them. Finally, we summarize the results of their ground state numerical studies. While each model was developed to study specific phenomena, unexpected phenomena, usually of a subtle quantum mechanical nature, are often exhibited. Just as often, the predictions of the numerical simulations differ from those of mean-field theories.
A long-term goal of quantum simulation is to faithfully reproduce the low-energy Hamiltonians of correlated quantum materials, establishing a direct connection between solid-state experiment, electronic-structure theory, and programmable many-body systems. Here, we introduce an integrated quantum-simulation architecture based on fermionic alkaline-earth atoms that enables programmable control over the key ingredients of multi-orbital material Hamiltonians. Long-lived clock states encode synthetic orbitals, their differential polarizabilities generate orbital-selective tunneling, and contact interactions provide multi-orbital Hubbard and Hund couplings. Spatially structured coherent driving on the ultra-narrow clock transition further realizes symmetry-selective inter-orbital hybridization, while the clock detuning independently controls orbital energy offsets. In this way, the spatial symmetries of solid-state orbitals can be encoded directly into the effective Hamiltonian, even though the atoms themselves remain in conventional s-wave Wannier orbitals of the lowest optical-lattice bands. We demonstrate the resulting integrated control using the four-band low-energy Hamiltonian of the bilayer nickelate La3Ni2O7 as a demanding benchmark. Self-consistent calculations show that the microscopic parameters obtained from first-principles modeling can be reproduced within a single experimentally accessible lattice configuration and independently programmed over substantial parameter ranges. Our results establish a general route for translating material-derived multi-orbital Hamiltonians into programmable ultracold-atom quantum simulators.
Most experiments with ultracold atoms in optical lattices have contact interactions and therefore operate at high densities of around one atom per site to observe the effect of strong interactions.Strong ranged interactions can be generated via Rydberg dressing, which opens up the path to exploring the physics of few interacting particles.Rather than the unit cells of a crystal, the sites of the optical lattice can now be interpreted as discretized space.This allows the study of completely new types of problems in a familiar architecture.We investigate the possibility of realizing problems akin to those found in quantum chemistry, although with a different scaling law in the interactions.Through numerical simulation, we show that simple pseudoatoms and pseudomolecules could be prepared with high fidelity in state-of-the-art experiments.
Many outstanding problems in quantum physics, such as high-Tc superconductivity or quark confinement, are still - after decades of research - awaiting commonly accepted explanations. One reason is that such systems are often difficult to control, show an intermingling of several effects, or are not easily accessible to measurement. To arrive at a deeper understanding of the physics at work, researchers typically derive simplified models designed to capture the most striking phenomena of the system under consideration. However, due to the exponential complexity of Hilbert space, even some of the simplest of such models pose formidable challenges to analytical and numerical calculations. In 1982, Feynman proposed to solve such quantum models with experimental simulation on a physically distinct, specifically engineered quantum system [Int. J. Theor.Phys. 21, 467]. Designed to be governed by the same underlying equations as the original model, it is hoped that direct measurements on these so called quantum simulators (QSs) will allow to gather deep insights into outstanding problems of physics and beyond. In this thesis, we identify four requirements that a useful QS has to fulfill, relevance, control, reliability, and efficiency. Focusing on these, we review the state of the art of two popular approaches, digital QSs (i.e., special purpose quantum computers) and analog QSs (devices with always-on interactions). Further, focusing on possibilities to increase control over QSs, we discuss a scheme to engineer quantum correlations between mesoscopic numbers of spinful particles in optical lattices. This technique, based on quantum polarization spectroscopy, may be useful for state preparation and quantum information protocols. Additionally, employing several analytical and numerical methods for the calculation of many-body ground states, we demonstrate the variety of condensed-matter problems that can be attacked with QSs consisting of ultracold ions or neutral atoms in optical lattices. The chosen examples, some of which have already been realized in experiment, include such diverse settings as frustrated antiferromagnetism, quantum phase transitions in exotic lattice geometries, topological insulators, non-Abelian gauge-fields, orbital order of ultracold Fermions, and systems with long-range interactions. The experimental realization of all of these models requires techniques which go beyond standard optical lattices, e.g., time-periodic driving of lattices with exotic geometry, loading ultracold atoms into higher bands, or immersing trapped ions into an optical lattice. The chosen models, motivated by important open questions of quantum physics, pose difficult problems for classical computers, but they may be amenable in the near future to quantum simulation with ultracold atoms or ions. While the experimental control over relevant models has increased dramatically in the last years, the reliability and efficiency of QSs has received considerably less attention. As a second important part of this thesis, we emphasize the need to consider these aspects under realistic experimental conditions. We discuss specific situations where terms that have typically been neglected in the description of the QS introduce systematic errors and even lead to novel physics. Further, we characterize in a generic example the influence of quenched disorder on an analog QS. Its performance for simulating universal behavior near a quantum phase transition seems satisfactory for low disorder. Moreover, our results suggest a connection between the reliability and efficiency of a QS: it works less reliable exactly in those interesting regimes where classical calculations are less efficient. If QSs fulfill all of our four requirements, they may revolutionize our approach to quantum-mechanical problems, allowing to solve the behavior of complex Hamiltonians, and to design nano-scale materials and chemical compounds from the ground up.