High-harmonic spectroscopy of quantum phase transitions in a high-Tc superconductor

Abstract

We report on the nonlinear optical signatures of quantum phase transitions in the high-temperature superconductor YBCO, observed through high harmonic generation. While the linear optical response of the material is largely unchanged when cooling across the phase transitions, the nonlinear optical response sensitively imprints two critical points, one at the critical temperature of the cuprate with the exponential growth of the surface harmonic yield in the superconducting phase and another critical point, which marks the transition from strange metal to pseudogap phase. To reveal the underlying microscopic quantum dynamics, a strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the theory provides insight into the carrier scattering dynamics and allows us to differentiate between the superconducting, pseudogap, and strange metal phases. The direct connection between nonlinear optical response and microscopic dynamics provides a powerful methodology to study quantum phase transitions in correlated materials. Further implications are light wave control over intricate quantum phases, light-matter hybrids, and application for optical quantum computing.

Keywords: attoscience; material science; quantum materials; spectroscopy; superconductivity.

Fig. 1.

Experimental setup and YBCO properties: (A) Orthorhombic unit cell of YBCO together with the crystallographic axes. YBCO consists of alternating planes along the crystallographic c axis with order CuO–BaO–CuO₂–Y–CuO₂–BaO. Most relevant for superconductivity are the copper oxide planes. Also indicated is the experimental arrangement with linearly polarized mid-IR laser fields whose electric field vector lies along the copper oxide planes. (B) The phase diagram for YBCO. Based on the value of $T_{\text{c}}$ from the measurement, we determine a hole concentration of p ~ 0.15. Based on this value, we mark the transition between the different phases by the red arrow. In accord with measurement and theory, $T^{*}$ marks the transition between strange metal and pseudogap phases at 173 K.

Fig. 2.

HHS of YBCO: (A) Harmonic spectra showing odd orders HH3, HH5, and HH7 for room temperature (red) and at $T_{\text{c}}=90$ K (blue) for a mid-IR field strength of 0.083 V/Å. Visible already is a blueshift of room-temperature harmonics with increasing harmonic order and relative to the harmonics measured at $T_{\text{c}}$. We observe a dramatic increase of HH7 amplitude upon cooling into the SC phase. The inlay shows the theoretical prediction of the spectrum, and the relative heights of the peaks match well the behavior of the experimental data. (B) The scaling of harmonic order with mid-IR peak intensity for measurements at room temperature and at $T_{\text{c}}$. Dark colors show data for the SC phase, whereas light colors indicate data at room temperature. (C) The reflected mid-IR field together with harmonics HH3, HH5, and HH7 as a function of temperature. These measurements are taken for a mid-IR field strength of 0.083 V/Å. Results from the strong-field quasi-Hubbard model are overlaid as solid lines. We observe a dramatic increase of HH7 amplitude upon cooling into the SC phase at 88 K. All harmonic orders show a clear turning point at the critical temperature $T_{\text{c}}$ and an exponential increase in amplitude. More subtle but still clearly discernible is another critical point $T^{*}$ at 173 K, marking the transition from strange metal to the pseudogap phase. The functional behavior is reproduced by the model. For completeness, we show the fundamental reflectivity also on a linear intensity scale in SI Appendix, Fig. S3.

Fig. 3.

Harmonic frequency and shift: (A) The center frequencies of the third, fifth, and seventh harmonic peaks are plotted vs. the intensity of the exciting light at 300 and 80 K. A frequency blueshift increasing with the driving intensity is observed. (B) The temperature dependence of the blueshift is shown. All harmonics show a rise of the blueshift for temperatures $T\mathrm{\gtrsim }{T}^{*}$. This behavior reflects the suppression of scattering processes in the superconducting phase and the pseudogap phase.

Fig. 4.

Phenomenological scattering parameters: By fitting the experimental data to the model, we extract the temperature dependence of the phenomenological scattering and dephasing times, shown in atomic units (a.u.), (A) τ₁ and (B) τ₂. Clearly visible are changes in the functional behavior of the two parameters at the two critical points. In the given temperature range from 80 to 300 K, the scattering time τ₁ decreases from 1400 to 100 a.u. (34 to 2.4 fs), and the dephasing time τ₂ decreases from 180 to 100 a.u. (4.4 to 2.4 fs).