Quantum Optics Parity Effect on Generalized NOON States and Its Implications for Quantum Metrology

NOON states are entangled states of great interest in the development of quantum technologies, because they enable high-precision phase measurements in interferometric schemes relevant to quantum metrology and sensing. This study shows that two degenerate modes of a cavity field coupled to an atom or molecule that can be modeled as a two-level system through two-photon interactions, initially prepared in a (generalized) NOON state, experience a dynamical evolution that distinctly depends on the parity of the photon number. When the total photon number is even, the system dynamics is characterized by a time range in which the state of the system evolves near maximally entangled states that may be fed to an optical interferometer to make phase measurements essentially at the Heisenberg limit. Such entangled states cannot be achieved for odd photon numbers instead. The parity effect thus emerges as a potential control factor in quantum metrology, sensing, and lithography.