Ultracold molecules for quantum simulation: rotational coherences in CaF and RbCs

We explore the uses of ultracold molecules as a platform for future experiments in the field of quantum simulation, focusing on two molecular species, $^{40}$Ca$^{19}$F and $^{87}$Rb$^{133}$Cs. We report the development of coherent quantum state control using microwave fields in both molecular species; this is a crucial ingredient for many quantum simulation applications. We demonstrate proof-of-principle Ramsey interferometry measurements with fringe spacings of $\sim 1~\rm kHz$ and investigate the dephasing time of a superposition of $N=0$ and $N=1$ rotational states when the molecules are confined. For both molecules, we show that a judicious choice of molecular hyperfine states minimises the impact of spatially varying transition-frequency shifts across the trap. For magnetically trapped $^{40}$Ca$^{19}$F we use a magnetically insensitive transition and observe a coherence time of 0.61(3) ms. For optically trapped $^{87}$Rb$^{133}$Cs we exploit an avoided crossing in the AC Stark shift and observe a maximum coherence time of 0.75(6) ms.