  We show theoretically and numerically that dichromatic pumping of a nonlinear
microresonator by two continuous wave coherent optical pumps creates an optical
lattice trap that results in the localization of intra-cavity Kerr solitons
with soliton positions defined by the beat frequency of the pumps. This
phenomenon corresponds to the stabilization of the Kerr frequency comb
repetition rate. The locking of the second pump, through adiabatic tuning of
its frequency, to the comb generated by the first pump allows transitioning to
single-soliton states, manipulating the position of Kerr solitons in the
cavity, and tuning the frequency comb repetition rate within the locking range.
It also explains soliton crystal formation in resonators supporting a
dispersive wave emitted as a result of higher-order group velocity dispersion
or avoided mode crossing. We show that dichromatic pumping by externally
stabilized pumps can be utilized for stabilization of microresonator-based
optical frequency combs when the comb span does not cover an octave or a
significant fraction thereof and standard self-referencing techniques cannot be
employed. Our findings have significant ramifications for high-precision
applications of optical frequency combs in spectrally pure signal generation,
metrology, and timekeeping.
