  A Michelson-type interferometer with two-mode squeezed coherent state input
is considered. Such an interferometer has a better phase sensitivity over the
shot-noise limit by a factor of $e^{2r}$, where $r$ is the squeezing parameter
[Phys. Rev. A 102,022614 (2020)]. We show that when photon loss and noise in
the two arms is asymmetric an optimal choice of the squeezing angle can allow
improvement in phase sensitivity without any increase in input or pump power.
In particular, when loss occurs only in one arm of the interferometer, we can
have improvement in phase sensitivity for photon loss up to 80\%. Hence, a
significant improvement can be made in several applications such as LiDAR,
gyroscopes and measuring refractive indices of highly absorptive/reflective
materials.
