Abstract
We investigate the phase sensitivity of a Mach-Zehnder interferometer using a special class of generalized coherent states constructed from generalized Heisenberg and deformed su(1,1) algebras. These states, derived from a perturbed harmonic oscillator with a four parameter deformed spectrum, provide enhanced tunability and nonclassical features. The quantum Fisher information and its associated quantum Cramer-Rao bound are computed to define the fundamental precision limits in phase estimation. We analyze the phase sensitivity under three realistic detection methods: difference intensity detection, single mode intensity detection, and balanced homodyne detection. The performance of each method is compared with the quantum Cramer Rao bound to evaluate their optimality. Our results demonstrate that, for suitable parameter regimes, these generalized coherent states enable phase sensitivities approaching the quantum limit. This offers a flexible framework for precision quantum metrology and potential applications in quantum enhanced sensing.