Photonic realization of an electromagnetic cavity field with uniform mirror motion

We perform a detailed mathematical study of the effective Hamiltonian describing a non-stationary electromagnetic cavity field, introduced by C. K. Law, in the presence of uniform linear motion. We find that the corresponding dynamical equations admit a unitary diagonalization and that the normalized velocity of motion satisfies the two-sided bound v/c 10.1716. Although this result is mathematically consistent, the interval obtained is an order of magnitude larger than the physically admissible range v/c < 1. To address this limitation, we propose a reinterpretation of bosonic coupling terms as generators of the symplectic algebra Sp(4, R), identifying them with transformations that can be implemented through linear optical elements. Within this photonic approach, the coupling parameters are not restricted to small values, allowing us to explore regimes of strong effective interactions. In this case, we demonstrate the generation of two-mode squeezed states and derive analytical expressions for the average photon number in each mode. Furthermore, we analyze statistical properties that characterize mixedness and entanglement, including intermode correlations, the Mandel parameter, and the linear entropy. The corresponding Wigner function provides a phase-space visualization of the system's behavior, illustrating the connection between cavity motion, mode coupling, and nonclassical field correlations via the underlying symplectic algebra.