Long-lived multilevel coherences and spin-1 dynamics encoded in the rotational states of ultracold molecules

Rotational states of ultracold polar molecules possess long radiative lifetimes, microwave-domain coupling, and tunable dipolar interactions. The availability of numerous rotational states has inspired many proposed applications, including simulations of quantum magnetism, encodings of information in high-dimensional qudits, and synthetic dimensions with many synthetic lattice sites. Many of these applications are yet to be realised, primarily because engineering long-lived coherent superpositions of multiple rotational states is highly challenging. Here, we investigate how multilevel coherences between rotational states can be engineered by using optical tweezer traps operating close to a magic wavelength for a given pair of states. By performing precision Ramsey spectroscopy we find the exact magic wavelengths and sensitivities to detuning errors for multiple rotational state superpositions. We find that, for a trap polarised parallel to the quantisation axis, the magic wavelengths are closely clustered enabling long-lived coherence across multiple rotational states simultaneously. As an example, we demonstrate simultaneous second-scale coherence between three rotational states. Utilising this extended coherence, we perform multiparameter estimation using a generalised Ramsey sequence and demonstrate coherent spin-1 dynamics encoded in the rotational states. With modest experimental improvements, we predict that second-scale coherent dynamics of ten rotational states should be readily achievable.