  An unidentified quantum fluid designated as the pseudogap (PG) phase is
produced by electron-density depletion in the CuO$_2$ antiferromagnetic
insulator. Current theories suggest that the PG phase may be a pair density
wave (PDW) state characterized by a spatially modulating density of electron
pairs. Such a state should exhibit a periodically modulating energy gap
$\Delta_P(\pmb r)$ in real-space, and a characteristic quasiparticle scattering
interference (QPI) signature $\Lambda_P(\pmb q)$ in wavevector space. By
studying strongly underdoped Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ at hole-density ~0.08
in the superconductive phase, we detect the $8a_0$-periodic $\Delta_P(\pmb r)$
modulations signifying a PDW coexisting with superconductivity. Then, by
visualizing the temperature dependence of this electronic structure from the
superconducting into the pseudogap phase, we find evolution of the scattering
interference signature $\Lambda(\pmb q)$ that is predicted specifically for the
temperature dependence of an $8a_0$-periodic PDW. These observations are
consistent with theory for the transition from a PDW state coexisting with
d-wave superconductivity to a pure PDW state in the Bi$_2$Sr$_2$CaDyCu$_2$O$_8$
pseudogap phase.
