Quantum interferometric protocol using spin-dependent displacements

We propose a quantum interferometric protocol that leverages spin-dependent spatial displacements to enable high-precision parameter estimation beyond classical limits. By inducing a unitary coupling between a particle's spin degree of freedom and its momentum, the protocol generates entanglement between spin states and spatial positions, resulting in coherent spatial superpositions. Interferometric reconstruction of the resulting phase differences enables Heisenberg-limited sensitivity for parameters encoded in the spin Hamiltonian. As a concrete application, we demonstrate the protocol's effectiveness in magnetic field sensing, where the field is transduced into spatial interference fringes. Quantum Fisher information analysis confirms sub-shot-noise scaling, and the protocol's feasibility is discussed for physical platforms including ultracold atoms and nitrogen-vacancy centers. Our framework provides a versatile approach to quantum metrology with potential extensions to multiparameter sensing and gravitational wave detection.