  Number state filtered coherent states are a class of nonclassical states
obtained by removing one or more number states from a coherent state. Phase
sensitivity of an interferometer is enhanced if these nonclassical states are
used as input states. The optimal phase sensitivity, which is related to the
quantum Cramer-Rao bound (QCRB) for the input state, improves beyond the
standard quantum limit. It is argued that removal of more than one suitable
number state leads to better phase sensitivity. As an important limiting case
in this context, the even and odd coherent states, where the odd and even
number states are filtered from coherent state respectively, are considered.
The optimal phase sensitivity for these limiting cases equals that of the
squeezed vacuum. It is observed that the improvement in phase sensitivity is
not in direct proportion to the nonclassicality of the input states.
