  It is shown that the maximal phase sensitivity of a two-path interferometer
with high-intensity coherent light and squeezed vacuum in the input ports can
be achieved by photon-number-resolving detection of only a small number of
photons in a dark output port. It is then possible to achieve the quantum
Cram\'{e}r-Rao bound of the two-path interferometer using only the field
displacement dependence of the photon number statistics in the single mode
output of the dark port represented by a field-displaced squeezed vacuum state.
We find that, at small field displacements, it is not sufficient to use the
average photon number as the estimator, indicating that an optimal phase
estimation depends critically on measurements of the precise photon number. We
therefore analyze the effect of detection efficiency on the Fisher information
and show that there is a transition from low robustness against photon losses
associated with quantum interference effects at low field displacements to high
robustness against photon losses at high field displacements. The transition
between the two regimes occurs at field shifts proportional to the third power
of the squeezing factor, indicating that squeezing greatly enhances the phase
interval in which quantum effects are relevant in optimal phase estimations
using photon resolving detectors. The case under study could thus be understood
as a `missing link' between genuine multiphoton interference and the
straightforward suppression of noise usually associated with squeezed light.
