Quantum critical electro-optic and piezo-electric nonlinearities

Electro-optics, the tuning of optical properties of materials with electric fields, is key to a multitude of quantum and classical photonics applications. However, a major obstacle preventing many emerging use cases is inefficient modulation in cryogenic environments, as traditional tuning mechanisms degrade at low temperatures. Guided by the connection between phase transitions and nonlinearity, we identify the quantum paraelectric perovskite SrTiO$_3$ (STO) as the strongest cryogenic electro-optic photonic material. As a result of the unique quantum paraelectric phase of STO, we demonstrate a dynamically tunable linear Pockels coefficient ($r_{33}$) exceeding 500 pm/V at $T=5$ K, and study its full temperature and bias dependence. We also measure an enhanced piezo-electric coefficient ($d_{33}$) above 90 pC/N. Both of these coefficients exceed all previously reported values for cryogenic materials, including lithium niobate ($r_{33}\approx24$ pm/V) and barium titanate ($r_{42}\approx170$ pm/V). Furthermore, by tuning STO towards \textit{quantum criticality} with oxygen isotope substitution we more than double the optical and piezo-electric nonlinearities, demonstrating a linear Pockels coefficient above 1100 pm/V. Our results probe the link between quantum phase transitions, dielectric susceptibility, and optical nonlinearities, unlocking opportunities in cryogenic optical and mechanical systems, and provide a framework for discovering new nonlinear materials.