Decoherence-free subspaces for quantum simulation and quantum information with ultracold RbCs molecules

Ultracold polar molecules possess a rich network of rotational and hyperfine states that can be precisely coupled in experiments with resonant microwave fields. Engineering long-lived quantum coherences between rotational states is the crucial next step towards realising the full potential of ultracold molecules in current experiments. For molecules confined to optical traps, the rotational coherence time is typically limited by to the presence of large differential light shifts between the rotational states as a result of the anisotropic molecular polarizability. Here we present the successful development of a rotationally-magic optical trap that enables long rotational coherence times in a bulk gas of ultracold RbCs molecules. The trap is based around light at 1146nm detuned 168 GHz from a nominally forbidden X¹Σ→b³Π vibronic transition, which allows tuning of the anisotropic component of the polarisability to zero. The trap is compatible with long molecule lifetimes, and the achievable coherence time is currently limited by the frequency stability of the trap laser; we estimate coherence times greater than 1s should be achievable for a laser frequency stabilised to less than 1 MHz. Using precision microwave spectroscopy over multiple rotational transitions, we show that the trap is near-magic for multiple rotational states at the same time. Motivated by this, we identify closed networks of quantum states in RbCs spanning multiple rotational levels that can be used to realise proposed schemes for quantum computing or novel synthetic dimensions for quantum simulation. Our approach for state selection is generally applicable to any bialkali molecule and is based upon the Python-based open source Diatomic-Py code developed by our group.