  Because of their nonlinearity, vibrational modes of resonantly driven
nanomechanical systems have coexisting stable states of forced vibrations in a
certain range of the amplitude of the driving force. Depending on its phase,
which encodes binary information, a signal at the same frequency increases or
decreases the force amplitude. The resulting force amplitude can be outside the
range of bistability. The values of the mode amplitude differ significantly on
the opposite sides of the bistability region. Therefore the mode amplitude is
very sensitive to the signal phase. This suggests using a driven mode as a
bi-directional bifurcation amplifier, which switches in the opposite directions
depending on the signal phase and provides an essentially digital output. We
study the operation of the amplifier near the critical point where the width of
the bistability region goes to zero and thus the threshold of the signal
amplitude is low. We also develop an analytical technique and study the error
rate near the threshold. The results apply to a broad range of currently
studied systems and extend to micromechanical systems and nonlinear
electromagnetic cavities.
