  The Kerr effect in optical microresonators plays an important role for
integrated photonic devices and enables third harmonic generation, four-wave
mixing, and the generation of microresonator-based frequency combs. Here we
experimentally demonstrate that the Kerr nonlinearity can split ultra-high-Q
microresonator resonances for two continuous-wave lasers. The resonance
splitting is induced by self- and cross-phase modulation and
counter-intuitively enables two lasers at different wavelengths to be
simultaneously resonant in the same microresonator mode. We develop a
pump-probe spectroscopy scheme that allows us to measure power dependent
resonance splittings of up to 35 cavity linewidths (corresponding to 52 MHz) at
10 mW of pump power. The required power to split the resonance by one cavity
linewidth is only 286${\mu}$W. In addition, we demonstrate threefold resonance
splitting when taking into account four-wave mixing and two counterpropagating
probe lasers. These Kerr splittings are of interest for applications that
require two resonances at optically controlled offsets, eg. for opto-mechanical
coupling to phonon modes, optical memories, and precisely adjustable spectral
filters.
