  With demonstrated applications ranging from metrology to telecommunications,
soliton microresonator frequency combs have emerged over the past decade as a
remarkable new technology. However, standard implementations only allow for the
generation of combs whose repetition rate is tied close to the fundamental
resonator free-spectral range (FSR), offering little or no dynamic control over
the comb line spacing. Here we propose and experimentally demonstrate harmonic
and rational harmonic driving as novel techniques that allow for the robust
generation of soliton frequency combs with discretely adjustable frequency
spacing. By driving an integrated Kerr microresonator with a periodic train of
picosecond pulses whose repetition rate is set close to an integer harmonic of
the 3.23 GHz cavity FSR, we deterministically generate soliton frequency combs
with frequency spacings discretely adjustable between 3.23 GHz and 19.38 GHz.
More remarkably, we also demonstrate that driving the resonator at rational
fractions of the FSR allows for the generation of combs whose frequency spacing
corresponds to an integer harmonic of the pump repetition rate. By measuring
the combs' radio-frequency spectrum, we confirm operation in the low-noise
soliton regime with no supermode noise. The novel techniques demonstrated in
our work provide new degrees of freedom for the design of synchronously pumped
soliton frequency combs.
