Disentangling Intertwined Quantum States in a Prototypical Cuprate Superconductor

Spontaneous symmetry breaking constitutes a paradigmatic classification scheme of matter. However, broken symmetry also entails domain degeneracy that often impedes identification of novel low symmetry states. In quantum matter, this is additionally complicated by competing intertwined symmetry breaking orders. A prime example is that of unconventional superconductivity and density-wave orders in doped cuprates in which their respective symmetry relation remains a key question. Using uniaxial pressure as a domain-selective stimulus in combination with x-ray diffraction, we unambiguously reveal that the fundamental symmetry of the charge order in the prototypical cuprate La$_{1.88}$Sr$_{0.12}$CuO$_4$ is characterized by uniaxial stripes. We further demonstrate the direct competition of this stripe order with unconventional superconductivity via magnetic field tuning. The stripy nature of the charge-density-wave state established by our study is a prerequisite for the existence of a superconducting pair-density-wave -- a theoretical proposal that clarifies the interrelation of intertwined quantum phases in unconventional superconductors -- and paves the way for its high-temperature realization.