Dipolar molecule emulator of lattice gauge theories: experiment and theory

This project involves an interdisciplinary collaboration between quantum information science (QIS) experimentalists and computational and high energy physics (HEP) theorists. Collectively, we will develop quantum simulation protocols based on ultracold molecule-based quantum simulation hardware for the study of non-equilibrium dynamics in fundamental particle physics models. Specifically, we will develop novel simulation protocols, based on arrays of individually trapped molecules with long-ranged, dipolar interactions, for the quantum emulation of lattice gauge theories. This research effort will highlight the unique role that dipolar spin systems can play in the realistic, direct emulation of quantum link models, providing access to nontrivial quantum dynamics. This project will be of direct relevance to the field of HEP, paving the way for quantum simulations that should allow for unique insights into the dynamical properties of interacting gauge theories. The toolbox of control that we will consider and begin to develop for ultracold molecules will further be of direct relevance to the field of QIS. We expect that this project will have an impact in both areas, highlighting to these communities the key features and promises offered by ultracold polar molecules. We expect that it will motivate future protocols for quantum emulation of

lattice gauge theories based on dipolar quantum matter, and will motivate other experimental investigations into the use of cold polar molecules for QIS applications.

Theoretically, we are proposing a bold new platform for the quantum emulation of lattice gauge theories. Arrays of interacting spins (realized by ultracold molecules, or alternatively by Rydberg atoms) with multiple internal states naturally lend themselves to the study of lattice gauge theories, as gauge invariance (Gauss' law) can be directly enforced through the application of local state-dependent light shifts that restrict the spin–spin interactions. We will design and propose model systems whose dynamics can be mapped on to the physics of quantum link model realizations of lattice gauge theories. We will verify that, under realistic conditions of experimental noise and imperfections, our first proposed restricted spin model faithfully maps on to a U(1) Abelian quantum link model in (1+1)d. Employing large-scale numerical simulations based on tensor networks, we will explore how the fidelity of this emulation protocol scales with the system size. We will furthermore work to find extensions of this approach that are relevant to the quantum emulation of quantum link models in higher spatial dimensions, as well as extensions to non-Abelian lattice gauge theories. While we will pursue this approach based on cold molecules, our theoretical proposals will also be relevant to researchers utilizing trapped ions and Rydberg atoms.

Experimentally, we will work towards the realization of a novel cold molecule quantum emulator aimed, in part, at the specific study of lattice gauge theories. Under this two-year program, experimental objectives include the simultaneous laser cooling and trapping of sodium and rubidium, the evaporative cooling of sodium-rubidium mixtures to ultracold temperatures, and the coherent formation of loosely bound Feshbach molecules through magnetoassociation. Further development of the tools necessary for individual trapping

and detection of molecules, as well as their use in the quantum emulation of lattice gauge theories, will be key aspects of future investigations.