Standard-quantum-limit-surpassing vector polarimetry using Rydberg atoms in an SU(1,1) interferometer

Vector polarimetry is an important application frontier for Rydberg-atom-based sensing. While prior research has largely concentrated on developing novel measurement schemes, high-sensitivity vector polarimetry remains an open question. Here we propose a theoretical framework for high-sensitivity detection of radio-frequency (RF) electric field polarization direction, which is particularly suitable for weak-field detection. Under a static magnetic field, the asymmetry in coupling between the Zeeman sublevels of the Rydberg atom and the RF field's polarization components enables the polarization angles to be determined from the atomic absorption index, which is retrieved via homodyne detection by incorporating the Rydberg atom system into an SU(1,1) interferometer. We derive the sensitivity of the polarization angles along with the corresponding standard quantum limit (SQL) and quantum Cram\'{e}r--Rao bound (QCRB). Our results demonstrate a sensitivity surpassing the SQL across wide angular ranges using either dual coherent states or a coherent state combined with a squeezed vacuum state as input. Significantly, the optimal sensitivity reaches below \SI{e-6}{\degree}, with sensitivities better than \SI{e-3}{\degree} maintained over most of the angular domain. This work establishes a foundation for high-precision vector polarimetry, thereby advancing the development of Rydberg-atom-based quantum sensing and contributing to a deeper understanding of light--matter interactions.