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

Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase