We propose an approach for quantum simulation of electron–phonon interactions using Rydberg states of cold atoms and ions. We show how systems of cold atoms and ions can be mapped onto electron–phonon systems of the Su–Schrieffer–Heeger type. We discuss how properties of the simulated Hamiltonian can be tuned and how to read physically relevant properties from the simulator. In particular, use of painted spot potentials offers a high level of tunability, enabling all physically relevant regimes of the electron–phonon Hamiltonian to be accessed.
We propose an approach for quantum simulation of electron–phonon interactions using Rydberg states of cold atoms and ions. We show how systems of cold atoms and ions can be mapped onto electron–phonon systems of the Su–Schrieffer–Heeger type. We discuss how properties of the simulated Hamiltonian can be tuned and how to read physically relevant properties from the simulator. In particular, use of painted spot potentials offers a high level of tunability, enabling all physically relevant regimes of the electron–phonon Hamiltonian to be accessed.
In condensed matter, it is often difficult to untangle the effects of competing interactions, and this is especially problematic for superconductors. Quantum simulators may help: here we show how exploiting the properties of highly excited Rydberg states of cold fermionic atoms in a bilayer lattice can simulate electron-phonon interactions in the presence of strong correlation--a scenario found in many unconventional superconductors. We discuss the core features of the simulator, and use numerics to compare with condensed matter analogues. Finally, we illustrate how to achieve a practical, tunable implementation of the simulation using "painted spot" potentials.
We describe a quantum simulator for the Hubbard-Holstein model (HHM), comprising two dressed Rydberg atom species held in a monolayer by independent painted potentials, predicting that boson-mediated preformed pairing and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures are experimentally accessible. The HHM is important for modeling the essential physics of unconventional superconductors. Experimentally realizable quantum simulators for HHMs are needed (1) since HHMs are difficult to solve numerically and analytically, (2) to explore how competition between electron-phonon interactions and strong repulsion affects pairing in unconventional superconductors, and (3) to understand the role of boson-mediated local pairing in pseudogaps and fermion condensates. We propose and study a quantum simulator for the HHM, using optical lattices, painted using zeros in the ac Stark shift, to control two Rydberg atom species independently within a monolayer. We predict that interactions are sufficiently tunable to probe (1) both HHMs and highly unconventional phonon-mediated repulsions, (2) the competition between intermediate-strength phonon- and Coulomb-mediated interactions, and (3) BKT transitions and preformed pairing that could be used to examine key hypotheses related to the pseudogap. We discuss how the quantum simulator can be used to investigate boson-mediated pairing and condensation of fermions in unconventional superconductors.
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.
Physics
Quantum simulation can map challenging problems in complex materials onto better defined ones in simpler, easier-to-manipulate systems. Physical implementations range from trapped ions to superconducting qubits, each having distinct strengths and weaknesses. Nguyen et al. propose a quantum simulator that seems to combine many of the best features of the existing simulators in one system, while being within current experimental reach. The simulator is based on circular Rydberg atoms—with a highly excited electron orbiting the nucleus along a roughly circular path—where the atoms can be trapped by laser light, can be read out one by one, and have very long lifetimes. The interactions between such atoms would make it possible to simulate some of the most challenging problems in many-body physics.
Phys. Rev. X 8 , 011032 (2018).
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.
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.