Estimation of covariance matrix for Stokes-like measurement under phase-space deformation

arXiv:2610.34176v1 Announce Type: new Abstract: We investigate the signatures of phase-space noncommutativity in an anisotropic oscillator and propose an optomechanical protocol to experimentally characterize it through Stokes-like measurements of an optical field. Starting from a deformed phase-space algebra characterized by the position-position and momentum-momentum noncommutativity parameters $\theta$ and $\eta$, we employ the Darboux transformation to construct an equivalent Hamiltonian in canonical variables. The resulting effective dynamics exhibits correlations between the oscillator degrees of freedom. We derive the corresponding covariance matrix and examine how the noncommutative parameters enter the mechanical dynamics and the optical response.