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cal frequency ω$_{c}$ and teeth separated by ν$_{R}$ whose in- dividual widths scale like ∼ ν$_{R}$/N . The Raman res- onance condition will be satisfied when a harmonic of the repetition rate is equal to the hyperfine qubit split- ting ω$_{0}$ , implying that the parameter q ≡ ω$_{0}$/ 2 πν$_{R}$ , is an integer. To demonstrate coherent control with a pulse train, $^{171}$Yb + ions confined in a linear Paul trap are used to encode qubits in the $^{2}$S$_{1}$$_{/}$$_{2}$ hyperfine clock states | F = 0 , m$_{F}$ = 0 〉 ≡ |↓〉 and | F = 1 , m$_{F}$ = 0 〉 ≡ |↑〉 , having hyperfine splitting ω$_{0}$/ 2 π = 12 . 6428 GHz. For state preparation and detection we use standard Doppler cooling, optical pumping, and state-dependent fluores- cence methods on the 811 THz $^{2}$S$_{1}$$_{/}$$_{2}$ ↔ $^{2}$P$_{1}$$_{/}$$_{2}$ electronic transition [19]. The frequency comb is produced by a frequency-doubled mode-locked Ti:Sapphire laser at a carrier frequency of 802 THz, detuned by Δ / 2 π = 9 THz from the electronic transition. The repetition rate of the laser is ν$_{R}$ = 80 . 78 MHz, with each pulse having a du- ration of τ ≈ 1 psec. The repetition rate is phase-locked to a stable microwave oscillator as shown in Fig. 2, pro- viding a ratio of hyperfine splitting to comb spacing of q = 156 . 5. An EO pulse picker is used to allow the pas- sage of one out of every n pulses, decreasing the comb spacing by a factor of n and permitting integral values 

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of q . As shown in Fig. 3, when n = 2 ( q = 313 and ν$_{R}$ = 40 . 39 MHz), application of the pulse train drives oscillations between the qubit states of a single ion. How- ever, when n = 3 ( q = 469 . 5 and ν$_{R}$ = 26 . 93 MHz), the qubit does not evolve. 

The Rabi frequency of these oscillations can be esti- mated by considering the Hamiltonian resulting from an infinite train of pulses. After adiabatically eliminating 

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