Femtosecond Response of Quasiparticles and Phonons in Superconducting ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathbf{O}}_{7-\delta }$ Studied by Wideband Terahertz Spectroscopy

We measure the anisotropic midinfrared response of electrons and phonons in bulk ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ after femtosecond photoexcitation. A line shape analysis of specific lattice modes reveals their transient occupation and coupling to the superconducting condensate. The apex oxygen vibration is strongly excited within 150 fs, demonstrating that the lattice absorbs a major portion of the pump energy before the quasiparticles are thermalized. Our results attest to substantial electron-phonon scattering and introduce a powerful concept probing electron-lattice interactions in a variety of complex materials.

Figure 1

Optical conductivity ${\sigma }_1(\omega )$ of YBCO in the SC ($T=10\mathrm{K}$, solid curve) and normal ($T=100\mathrm{K}$, broken curve) states for (a) $\mathbf{E}\perp c$ and (b) $\mathbf{E}\parallel c$. Insets: Unit cell of YBCO and directions of the probe electric field. The oxygen ions involved in the observed vibrations are shown in red. The modes centered at 39 and 71 meV in (b) correspond to the bond-bending and apex oxygen vibrations, respectively.

Figure 2

2D optical pump-THz probe data: (a) Pump-induced changes $\Delta {\sigma }_1(\omega ,\tau )$ as a function of the photon energy and the pump delay time $\tau$, for $\mathbf{E}\perp c$. (b) Corresponding changes of $\Delta \alpha (\omega ,\tau )$, for $\mathbf{E}\parallel c$. Both experiments are performed at $T=20\mathrm{K}$ with $\Phi =0.3\mathrm{mJ}/{\mathrm{cm}}^2$. (c) Conductivity difference between normal and SC states (solid curve) for $\mathbf{E}\perp c$ and pump-induced $\Delta {\sigma }_1(\omega ,\tau )$ at delay time $\tau =1\mathrm{ps}$ after photoexcitation (broken curve). (d) Dynamics of the photoinduced QP spectral weight as a function the delay time $\tau$. Dashed curve: Spectral weight for $\mathbf{E}\perp c$ integrated between 40 and 130 meV. Blue line: Spectral weight (scaled by factor 170) for $\mathbf{E}\parallel c$ between 45 and 60 meV. The experimental time resolution is indicated by the hatched area.

Figure 3

Spectra of the optical conductivity ${\sigma }_1(\omega )$ and ${\sigma }_2(\omega )$ of YBCO for $\mathbf{E}\parallel c$: (a),(b) Equilibrium spectra at selected temperatures; (c),(d) transient spectra at selected pump-probe delay times $\tau$ measured at $T=20\mathrm{K}$ with $\Phi =0.3\mathrm{mJ}/{\mathrm{cm}}^2$. The solid lines show the fitting curves according to Eq. (1).

Figure 4

(a) Asymmetry factor and (b) eigenfrequency of the apex mode as functions of temperature. (c),(d) The corresponding quantities as functions of the pump-probe delay time $\tau$. The blue dots and red diamonds denote excitations of the SC ($T=20\mathrm{K}$) and normal state ($T=100\mathrm{K}$), respectively. The error bars indicate 95% confidence intervals for the fitting parameters.