Quantum critical electro-optic and piezo-electric nonlinearities

Although electro-optic (EO) nonlinearities are essential for many quantum and classical photonics applications, a major challenge is inefficient modulation in cryogenic environments. Guided by the connection between phase transitions and nonlinearity, we identify the quantum paraelectric perovskite SrTiO₃ as a strong cryogenic EO [>500 picometers per volt (pm/V)] and piezo-electric material (>90 picocoulombs per newton) at T = 5 K, at frequencies to at least 1 megahertz. Furthermore, by tuning SrTiO₃ toward quantum criticality, we more than double the EO and piezo-electric effects, demonstrating a linear Pockels coefficient above 1000 pm/V. Our results probe the link between quantum phase transitions, dielectric susceptibility, and nonlinearity, unlocking opportunities in cryogenic optical and mechanical systems and providing a framework for discovering new nonlinear materials.