Quantum Saturation of the Electro-Optic Effect

Future quantum computing architectures require electro-optic materials that maintain a strong, stable performance at cryogenic temperatures. In conventional electro-optic materials, large electro-optic coefficients are often confined to narrow temperature windows near structural phase transitions, where small changes in temperature lead to large changes in the electro-optic response. Using thermodynamic analysis, phase-field simulations, experimental growth, and cryogenic optical measurements, we show that quantum fluctuations can be harnessed to overcome this trade-off. By tuning the ferroelectric phase boundaries down to 0 K, quantum fluctuations induce a saturation regime in which a large electro-optic response becomes nearly temperature-independent below 25 K. We demonstrate that the phase boundaries can be tuned through either strain in BaTiO₃ or through chemical composition in Ba_{1- x}Ca_xTiO₃, leading to a large, temperature-insensitive, cryogenic electro-optic response, r_eff =  2850 pm V^-1 (experiment) and r₅₁ =  2900 pm V^-1 (theory) for BaTiO₃ on GdScO₃ and r₅₁ =  1898 pm V^-1 (theory) for Ba_0.77Ca_0.23TiO₃. These values exceed the room temperature performance of bulk BaTiO₃ r₅₁ =  1600 pm V^-1 and surpass the cryogenic performance of BaTiO₃-on-Si, r_eff =  200 pm V^-1, by over an order of magnitude. These findings establish a general design principle for engineering high-performance electro-optic materials for cryogenic applications.