Single-quasiparticle stability and quasiparticle-pair decay in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">YBa</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mrow><mml:mn>6.5</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>

We report results and analysis of time-resolved photoinduced reflectivity experiments on the cuprate superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}$. The sample, which has ${T}_{c}=45\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, was characterized by a high degree of purity and Ortho II ordering. The change in reflectivity $\ensuremath{\Delta}R$ was induced and probed using pulses of $100$ femtosecond duration and photon energy $1.55\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ from a $\mathrm{Ti}$:Sapphire laser. We provide a detailed picture of the decay rate $\ensuremath{\gamma}$ of $\ensuremath{\Delta}R$ as a function of temperature $T$ and pump intensity $I$. At low $T$, $\ensuremath{\gamma}$ decreases linearly with decreasing $I$, extrapolating to nearly zero in the limit that $I$ tends to zero. At higher temperature $\ensuremath{\gamma}$ has the same linear dependence, but with nonzero limit as $I\ensuremath{\rightarrow}0$. In the interpretation of these results we assume that $\ensuremath{\Delta}R$ is proportional to the nonequilibrium quasiparticle density created by the laser. From an analysis of the $\ensuremath{\gamma}$ vs $I$ we estimate $\ensuremath{\beta}$, the coefficient of proportionality relating the quasiparticle decay rate to the density. The intercept of $\ensuremath{\gamma}$ vs $I$ yields the thermal equilibrium quasiparticle decay rate. In a discussion section, we argue that the quasiparticles induced by the laser occupy primarily states near the antinodal regions of the Brillouin zone. We explain the divergence of the lifetime of these particles as $T$ and $I$ both tend to zero as a consequence of momentum and energy conservation in electron-electron scattering. Next, we discuss the significance of the measured value of $\ensuremath{\beta}$, which is $\ensuremath{\approx}0.1\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ . We point out that the natural unit for $\ensuremath{\beta}$ in a two-dimensional superconductor is $\ensuremath{\hbar}∕{m}^{*}$, and define a dimensionless constant $C$ such that $\ensuremath{\beta}\ensuremath{\equiv}C\ensuremath{\hbar}∕{m}^{*}$. If the decay process is one in which quasiparticles return to the condensate with emission of a phonon, then $C$ is a measure of the electron-phonon interaction. Alternatively, expressing the marginal Fermi liquid scattering in the normal state in terms of an effective $\ensuremath{\beta}$ implies $C=1∕\ensuremath{\pi}$, which is in excellent agreement with the experimentally determined value in the superconducting state.

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