  Both the group velocity and phase velocity of two solitons can be
synchronized by a Kerr-effect mediated interaction, causing what is known as
soliton trapping. Trapping can occur when solitons travel through single-pass
optical fibers or when circulating in optical resonators. Here, we demonstrate
and theoretically explain a new manifestation of soliton trapping that occurs
between counter-propagating solitons in microresonators. When counter-pumping a
microresonator using slightly detuned pump frequencies and in the presence of
backscattering, the group velocities of clockwise and counter-clockwise
solitons undergo periodic modulation instead of being locked to a constant
velocity. Upon emission from the microcavity, the solitons feature a relative
oscillatory motion having an amplitude that can be larger than the soliton
pulse width. This relative motion introduces a sideband fine structure into the
optical spectrum of the counter-propagating solitons. Our results highlight the
significance of coherent pumping in determining soliton dynamics within
microresonators and add a new dimension to the physics of soliton trapping.
