Controlling the rotational and hyperfine state of ultracoldRb87Cs133molecules

We demonstrate coherent control of the rotational and hyperfine state of ultracold, chemically stable $^{87}\mathrm{Rb}^{133}\mathrm{Cs}$ molecules with external microwave fields. We create a sample of $\ensuremath{\sim}2000$ molecules in the lowest hyperfine level of the rovibronic ground state $N=0$. We measure the transition frequencies to eight different hyperfine levels of the $N=1$ state at two magnetic fields $\ensuremath{\sim}23$ G apart. We determine accurate values of rotational and hyperfine coupling constants that agree well with previous calculations. We observe Rabi oscillations on each transition, allowing complete population transfer to a selected hyperfine level of $N=1$. Subsequent application of a second microwave pulse allows the transfer of molecules back to a different hyperfine level of $N=0$.