Suggestive, but indirect evidence of the existence of pair-density wave (PDW)
order in several high-Tcβ cuprates has been reported. As this
constitutes a new quantum phase of matter, it is important to {\it establish}
its existence at least somewhere in the phase diagram. However, a direct
correspondence between experiment and theory has remained elusive. Here, we
report the observation of a theoretically predicted PDW {\it bulk} signature in
two La-based cuprates, Sr-doped La1.875βBa0.125βCuO4β and Fe-doped
La1.87βSr0.13βCuO4β, through a comprehensive study that incorporates
zero-magnetic field x-ray scattering, neutron scattering, and transport
measurements. Specifically, we observe the emergence of so-called "1Q" order,
which is to say subharmonic order associated with the charge-density wave (CDW)
stripes, in a range of temperatures in which independent evidence suggests the
co-existence of PDW long-range order and fluctuating uniform superconducting
order. The subharmonic order is most pronounced around a half-integer
l-vector, where the CDW diffraction peak is also strongest. This is
consistent with the theoretical proposal that the cancellation of the Josephson
coupling ("layer-decoupling"), is a signature of PDW order and that it is
commensurately locked to the density wave stripes that are known to alternate
orientation between adjacent layers. Even if the PDW is not the "mother of all
state", it is at least a close relative -- possibly a second cousin