Fig. 3.

Revisited phase diagram of ${\mathrm{S}\mathrm{r}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ inside the optical cavity. (A) Effective microscopic ferroelectric frequency as a function of lattice temperature for different cavity coupling strengths. The minima of the curves, marked with red arrows, are used to identify the phase boundaries in B. (B) The microscopic phase diagram of ${\mathrm{S}\mathrm{r}\mathrm{T}\mathrm{i}\mathrm{O}}_3$ inside the cavity. Three possible scenarios are opened up by the coupling to confined light. At low temperature, increasing the coupling with the cavity leads to a transition from a quantum paraelectric (QPE) to a ferroelectric (FE); at intermediate temperatures, increasing the coupling first allows thermal fluctuations to overcome the quantum ones and eventually reach a transition from paraelectric to ferroelectric; at high temperatures, since thermal fluctuations are much larger than the quantum ones, a direct transition from normal paraelectric (PE) to ferroelectric can be expected for increasing coupling to the cavity.