Superconductivity Reinforces Charge-Density-Wave Phase Coherence across Cuprates

For decades, superconductivity in high-T_{c} cuprates has been viewed as a competitor that suppresses charge-density-wave (CDW) order by reducing its amplitude and spatial extent. Here, we show that this picture is incomplete, as superconductivity is accompanied by a systematic enhancement of CDW phase coherence across multiple cuprate families. Using resonant soft x-ray scattering combined with a coherence-sensitive momentum-profile analysis, we uncover a BCS-like growth of phase coherence below T_{c}, which phenomenologically manifests as the absence of CDW peak broadening and near-perfect wave-vector locking. This enhancement remains visible even in a disorder-dominated regime created by long-term crystal aging and follows a common trend when compared with published data on Bi-, Hg-, Y-, and Nd-based cuprates. These results indicate that superconductivity reshapes CDW order in two distinct ways, suppressing its amplitude while strengthening its phase coherence, and reveal an additional phase-level interplay with lattice coupling in high-T_{c} cuprates.