Application of the polaron-transport theory to σ(ω) in ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Gd}}_{\mathit{x}}$${\mathrm{Cu}}_2$${\mathrm{O}}_8$, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, and ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_4$

We analyze the frequency-dependent photoinduced infrared conductivity, ${\mathrm{\sigma }}_{\mathit{P}}$(ω), obtained from photoinduced absorption measurements of the insulators ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{Ca}}_{0.98}$${\mathrm{Gd}}_{0.02}$${\mathrm{Cu}}_2$${\mathrm{O}}_8$, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.3}$, and ${\mathrm{La}}_2$${\mathrm{CuO}}_4$ in terms of ${\mathrm{\sigma }}_{\mathrm{PT}}$(ω) calculated from nonadiabatic polaron-transport theory. The calculated ${\mathrm{\sigma }}_{\mathrm{PT}}$(ω) is in good agreement with the experimental ${\mathrm{\sigma }}_{\mathit{P}}$(ω) in the midinfrared. We also compare ${\mathrm{\sigma }}_{\mathit{P}}$(ω) with the infrared conductivity, σ(ω), of the high-${\mathit{T}}_{\mathit{c}}$ superconductors ${\mathrm{Tl}}_2$${\mathrm{Ba}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, and ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_4$. The similar spectral shape and systematic trends in both ${\mathrm{\sigma }}_{\mathit{P}}$(ω) and σ(ω) indicate that the carriers in the concentrated (metallic) regime retain much of the character of the carriers in the dilute (photoexcited) regime. Together, these results imply that in the superconducting cuprates and in their ‘‘parent’’ insulators, the carriers are polarons dressed with a phonon polarization cloud.