We measure nuclear and electron spin-polarized H and D densities of at least 10^{19} cm^{-3} with ∼10 ns lifetimes, from the photodissociation of HBr and DI with circularly polarized UV light pulses. This density is ∼6 orders of magnitude higher than that produced by conventional continuous-production methods and, surprisingly, at least 100 times higher than expected densities for this photodissociation method. We observe the hyperfine quantum beating of the H and D magnetization with a pickup coil, i.e., the respective 0.7 and 3 ns periodic transfer of polarization from the electrons to the nuclei and back. The 10^{19} cm^{-3} spin-polarized H and D density is sufficient for laser-driven ion acceleration of spin-polarized electrons, protons, or deuterons, the preparation of nuclear-spin-polarized molecules, and the demonstration of spin-polarized D-T or D-^{3}He laser fusion, for which a reactivity enhancement of ∼50% is expected.