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The phase diagram of cuprate high-temperature superconductors features anenigmatic pseudogap region that is characterized by a partial suppression oflow energy electronic excitations. Polarized neutron diffraction, Nernsteffect, THz polarimetery and ultrasound measurements on YBa$_2$Cu$_3$O$_y$suggest that the pseudogap onset below a temperature T* coincides with a bonafide thermodynamic phase transition that breaks time-reversal, four-foldrotation and mirror symmetries respectively. However, the full point groupabove and below T* has not been resolved and the fate of this transition as T*approaches the superconducting critical temperature T$_c$ is poorly understood.Here we reveal the point group of YBa$_2$Cu$_3$O$_y$ inside its pseudogap andneighboring regions using high sensitivity linear and second harmonic opticalanisotropy measurements. We show that spatial inversion and two-fold rotationalsymmetries are broken below T* while mirror symmetries perpendicular to theCu-O plane are absent at all temperatures. This transition occurs over a widedoping range and persists inside the superconducting dome, with no detectablecoupling to either charge ordering or superconductivity. These results suggestthat the pseudogap region coincides with an odd-parity order that does notarise from a competing Fermi surface instability and exhibits a quantum phasetransition inside the superconducting dome.

A global inversion-symmetry-broken phase inside the pseudogap region of YBa$_2$Cu$_3$O$_y$