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 La$_3$Ni$_2$O$_7$ 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.
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.
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.
Rapid advancements in the experimental capabilities with ultracold alkaline-earth-like atoms (AEAs) bring to a surprisingly near term the prospect of performing quantum simulations of spin models and lattice field theories exhibiting SU( N ) symmetry. Motivated in particular by recent experiments preparing high density samples of strongly interacting 87 Sr atoms in a three-dimensional optical lattice, we develop a low-energy effective theory of fermionic AEAs which exhibits emergent multi-body SU( N )-symmetric interactions, where N is the number of atomic nuclear spin levels. Our theory is limited to the experimental regime of (i) a deep lattice, with (ii) at most one atom occupying each nuclear spin state on any lattice site. The latter restriction is a consequence of initial ground-state preparation. We fully characterize the low-lying excitations in our effective theory, and compare predictions of many-body interaction energies with direct measurements of many-body excitation spectra in an optical lattice clock. Our work makes the first step in enabling a controlled, bottom-up experimental investigation of multi-body SU( N ) physics.
Real materials are extremely complicated, and any attempt to understand their bulk properties must begin with the appropriate choice of an idealized model, or Hamiltonian. There are many situations where such models have furnished a decisive understanding of complex quantum phenomena, such as BCS superconductivity and quantum magnetism. There are also cases, for instance the unconventional superconductivity of doped cuprates or heavy-fermion metals, where even the simplest conceivable models are intractable to current theoretical techniques. A promising route toward understanding the physics of such models is to simulate them directly with a highly controlled quantum system. Ultracold neutral atoms, polar molecules, and ions are in many ways ideally suited to this task.\nIn this thesis, we emphasize how the unique features of particular atomic and molecular sys- tems can be leveraged to access interesting physics in experimentally feasible temperature regimes. In chapter 3, we consider prospects for simulation of the Kondo lattice model using alkaline- earth atoms. In particular, we show how groundstate properties--for instance anomalous mass enhancement--can be probed by looking at far-from equilibrium dynamics, which are a standard diagnostic tool in ultracold atom experiments. Chapter 4 describes a realistic implementation of a bosonic version of the Kondo lattice model, and we show how the Kondo interaction qualitatively changes the superfluid to Mott insulator phase transition. Chapters 5, 6, and 7 are unified through an attempt to understand the effects of dissipation in many-body quantum systems. In chapter 5, our goal is mainly to understand the detrimental effects of two-body reactive collisions on dipolar molecules in a 3D optical lattice. Chapter 6 takes a rather different perspective, and shows that this type of loss naturally induces quantum correlations in the steady state of reactive fermionic molecules or alkaline earth atoms. In chapter 7, we develop an exact analytic solution for the non-equilibrium dynamics of long-ranged Ising models with Markovian decoherence. We apply our solution to the benchmarking of dynamics in an existing trapped-ion quantum simulator, which due to its large size and long-ranged, frustrated, interactions is well beyond the reach of a brute force numerical description.
We introduce a method for quantum simulation of U(1) lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices.The proposal enables the study of both gauge and fermionic matter fields without integrating out one of them in one and two dimensions.We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species.Starting from an ab initio modeling of the experimental setting, we systematically carry out a derivation of the target U(1) gauge theory.This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that-while pivotal for a successful implementation-have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics.We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope 173 Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one-and two-dimensional settings.
Over the past few decades, quantum simulation with ultracold atoms in optical lattices has proven to be a useful tool for understanding many-body Hamiltonians.One of its primary directions is the experimental study of the Fermi Hubbard Model (FHM), which aims to capture the fundamental properties of cuprate superconductors and has produced a wide range of intriguing phenomena, including the metal-to-Mott insulator transition, antiferromagnetism, strange metallicity, pseudogap physics, and is frequently used in the study of superconductivity. In recent years, new kinds of quantum simulators have emerged, and in particular we focus on two of them: 1) quantum simulators that study high symmetry fermions in optical lattices, and 2) optical tweezer arrays which provide a bottom-up approach to engineering the FHM. The first class of emerging quantum simulators utilizes alkaline-earth-like atoms (AEA’s) – which have large nuclear spin I (such as 173Yb and 87Sr) – to engineer the SU(N = 2I +1) symmetric FHM, where N = 2,..., 10. The second class corresponds to quantum simulators based on optical tweezer arrays which combine deterministic single tweezer ground state loading and tunneling coupled sites. Both classes of quantum simulators are interesting on their own. For example, the SU(N) FHM is generating a lot of interest due to its connections to multiorbital solid state systems and theoretical predictions of rich phase diagrams which exhibit exotic phases of matter, including unusual ones like spin liquids. On the other hand, optical tweezer arrays have gained a lot of attention since they can be used to study arbitrary geometries and access very low-entropy samples. This thesis reports on the numerical study of both quantum simulation architectures. Results of the SU(N) FHM at finite temperature, for different fillings and interaction strengths that span the non-interacting to the strongly interacting limit are obtained using Determinant Quantum Monte Carlo, Exact Diagonalization, and Numerical Linked Cluster Expansion. In particular, we focus on how thermodynamic and magnetic observables, such as the number of on-site pairs, energy, entropy, spin correlations, and structure factors depend on N, the interaction strength U/t, temperature T/t, and the anisotropy of tunneling rates. Our results demonstrate that in a homogeneous square lattice with one particle per site on average, thermodynamic observables as a function of temperature obey a universal scaling with N, and that short-range antiferromagnetic correlations are stronger for larger N and in lower dimensions. In addition, we present theory-experiment comparisons where possible, where we perform thermometry and provide a precise characterization of the equation of state of the SU(N) FHM. Our results emerge as a tool to perform thermometry in experiments from theory-experiment comparison and also provide guidance for future experiments with AEAs in optical lattices. Additionally, we present calculations using numerically precise discrete variable representation methods for two-dimensional stroboscopic tweezer arrays and compare the outcomes with experimental data. We quantify the effects of stroboscopic potentials on Hubbard parameters like the interaction strength U and the tunneling t in optical tweezer arrays and illustrate how heating from the stroboscopic potential relies on strobe frequency. Our calculations enable evaluation and optimization of two-dimensional tweezer array experiments. An important milestone of the results of this thesis corresponds to the record temperatures and entropies achieved with these quantum simulation architectures: 1) the coldest fermions ever created in nature in absolute temperature and in cold atoms, and 2) the lowest entropy per particle fermions ever created, albeit in a so-far small system.
Abstract Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU( N ) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU( N ) symmetry in conventional quantum materials for large N . Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU( N )-symmetric many-body models, where N is tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear as N increases. We then discuss the properties of the SU( N ) Fermi–Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU( N ) lattice models and a discussion of some exciting directions for future research.