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The relation between pseudogap (PG) and superconducting (SC) gap, whether PGis a precursor of SC or they coexist or compete, is a long-standing controversyin cuprate high-temperature supercondutors. Here, we report ultrafasttime-resolved optical reflectivity investigation of the dynamic densities andrelaxations of PG and SC quasiparticles (QPs) in the underdoped$\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ ($T_c$ = 82 K) single crystals. We findevidence of two distinct PG components in the positive reflectivity changes inthe PG state, characterized by relaxation timescales of $\tau_{fast}$ $\approx$0.2 ps and $\tau_{slow}$ $\approx$ 2 ps with abrupt changes in both amplitudes$A_{fast}$ and $A_{slow}$ at the PG-opening temperature $T^*$. The formerpresents no obvious change at $T_c$ and coexists with the SC QP. The latter'samplitude starts decreasing at the SC phase fluctuation $T_p$ and vanishes at$T_c$ followed by a negative amplitude signifying the emergence of the SC QP,therefore suggesting a competition with superconductivity.

Study of pseudogap and superconducting quasiparticle dynamics in $\rm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ by time-resolved optical reflectivity