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We demonstrate coherent control of both the rotational and hyperfine state ofultracold, chemically stable $^{87}$Rb$^{133}$Cs molecules with externalmicrowave fields. We create a sample of ~2000 molecules in the lowest hyperfinelevel of the rovibronic ground state N = 0. We measure the transitionfrequencies to 8 different hyperfine levels of the N = 1 state at two magneticfields ~23 G apart. We determine accurate values of rotational and hyperfinecoupling constants that agree well with previous calculations. We observe Rabioscillations on each transition, allowing complete population transfer to aselected hyperfine level of N = 1. Subsequent application of a second microwavepulse allows transfer of molecules back to a different hyperfine level of N =0.

Controlling the Rotational and Hyperfine State of Ultracold $^{87}$Rb$^{133}$Cs Molecules