Enhanced coherent oscillations in the superconducting state of underdoped $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$ induced via ultrafast terahertz excitation

We utilize intense, single-cycle terahertz pulses to induce collective excitations in the charge-density-wave-ordered underdoped cuprate $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$. These excitations manifest themselves as pronounced coherent oscillations of the optical reflectivity in the transient state, accompanied by minimal incoherent quasiparticle relaxation dynamics. The oscillations occur at frequencies consistent with soft phonon energies associated with the charge-density-wave, but vanish above the superconducting transition temperature rather than that at the charge-density-wave transition. These results indicate an intimate relationship of the terahertz excitation with the underlying charge-density-wave and the superconducting condensate itself.

Figure 1

(a) An illustration of the experimental setup (not drawn to scale). (b) A cartoon of the band structure of a $d$-wave superconductor exhibited in YBCO. An 800 nm pump pulse, with a photon energy of ∼1.5 eV, excites a large number of “hot” electrons well above the Fermi energy and can in principle excite quasiparticles over the entire Brillouin zone. A THz frequency pump pulse, which has a much lower energy (∼4 meV) and which is on the same scale as the electron states near the nodal point ($\phi =\pi /4$), can couple to these near-node states directly. (c) The time evolution of the 800 nm reflectivity change after an optical excitation of 800 nm at 15 K (adapted from Hinton et al. [10] with permission). (d) The time trace of the 800 nm reflectivity change due to a THz excitation at 10 K. The optical excitation [(c), red curve] used a fluence of $\sim 1.5\mu \mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ and results in a large number of photoinduced quasiparticles as seen as a large background in the figure. The THz data [(d), blue curve] uses a fluence of $\sim 44\mu \mathrm{J}/\mathrm{c}{\mathrm{m}}^2$ and shows the large oscillation with minimal quasiparticle generation.

Figure 2

THz-induced reflectivity change with the probe polarization (a) parallel to the YBCO $b$ axis at 10 K and (b) parallel to the $a$ axis at 25 K. The black dotted lines show the square of the THz field for comparison. The THz $E$ field is parallel to the $b$ axis in both cases. (c), (d) Oscillatory contribution to the signal after subtracting an exponential fit to the data, shown as a red curve in (a) and (b), respectively. The solid lines are damped sine fits with (c) one frequency and (d) three frequency components, for the two different polarizations. (e) and (f) show the Fourier transforms of the background subtracted oscillations in (c) and (d), respectively. The error bars in the Fourier transform were obtained by error propagation of the time domain uncertainty into the frequency domain. The dotted line shows the Fourier amplitude spectrum of the THz pump pulse in both geometries. The red curve in (f) is the result of a fit to three separate Gaussian functions to each of the three modes, displaying the central frequency of each.

Figure 3

(a) Temperature-dependent traces of the THz-induced reflectivity change $\mathrm{\Delta }R/R$ with probe polarization parallel to the $b$ axis. The evidence of the increase of the relaxation time near $T_c$, as well as the oscillations below $T_c$, are both clearly evident in the raw data. (b) Incoherent background $\left|B\left(t\right)\right|$ plotted with temperature for $t=1.5\mathrm{ps}$, representing the photoinduced quasiparticle number. Inset: The single-exponential relaxation time τ($T$). A similar peak observed in the plot of the relaxation time on approaching $T_c$ was previously observed in YBCO [27] and has been attributed to the “phonon bottleneck” effect. (c) The amplitude of the Fourier mode at 1.8 THz as a function of temperature. The amplitude was calculated by fitting a damped harmonic oscillator response function to the Fourier transform of the oscillatory signal after normalizing by the reflectivity.