Abstract
Recently, we presented (Berrada K, Abdel-Khalek S and Raymond Ooi C H 2012 Phys. Rev. A 86 033823) an improved phase estimation scheme employing entangled spin coherent states (ESCSs) using the Holstein-Primakoff realization of angular momentum algebra. Here, we study the nonlinear phase enhancement from a generalized nonlinearity on ESCSs under perfect and lossy conditions with the same mean photon number and nonlinearity order. The results show that an increase in the spin number gives the smallest variance in the phase parameter in comparison to N00N states for different orders of nonlinearity. Finally, we study the physical properties of the input optical field and explore a connection between this quantity and the output state phase uncertainty. In particular, we show that the Mandel parameter may be used as an indicator of the phase estimation behavior in this interferometric setting.