  We demonstrate theoretically and experimentally that linear coupling due to
the backscattering between two counterpropagating modes in a Kerr
microresonator leads to extreme sensitivity of the intensity asymmetry of
nonlinear light states to the relative phase between the bidirectional pumps of
equal power. In the absence of linear coupling, the relative pump phase does
not affect counterpropagating intraresonator intensities, and two asymmetric
states arise due to spontaneous symmetry breaking. Contrariwise, in the
presence of weak linear intermode coupling, the asymmetry of the states is
deterministically controlled via changes in phase (for all phases except 0 and
$\pi$). Spontaneous symmetry breaking at zero phase is suppressed when the
linear intermode coupling is increased, while for the $\pi$ phase it can be
enhanced, so that the overall threshold for the spontaneous symmetry breaking
can be significantly lower for nonzero linear coupling. These results are
important for fundamental understanding of the processes in Kerr resonators and
other systems with Kerr-like nonlinearities and linear intermode coupling and
have high prospects for the development of photonic devices such as
ultrasensitive sensors.
