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Proceedings of the National Academy of Sciences

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

Jordi Alcalà, Utso Bhattacharya, Jens Biegert, Marcelo F. Ciappina, Ugaitz Elu, Tobias Graß, Piotr T. Grochowski, Maciej Lewenstein, Anna Palau, Themistoklis P. H. Sidiropoulos, Tobias R. J. Steinle, Igor Tyulnev

Published Sep 26, 2022• 62 citations
Publisher

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.

DOI
10.1073/pnas.2207766119

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High harmonic spectroscopy of quantum phase transitions in a high-Tc_cc​ superconductor
We report on the new non--linear 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 pseudo gap phase. To reveal the underlying microscopic quantum dynamics, a novel strong-field quasi-Hubbard model was developed, which describes the measured optical response dependent on the formation of Cooper pairs. Further, the new theory provides insight into the carrier scattering dynamics and allows to differentiate between the superconducting, pseudo gap, and strange metal phases. The direct connection between non--linear optical response and microscopic dynamics provides a powerful new 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.
By employing the exact diagonalization method, we investigate the high-harmonic generation (HHG) of the correlated systems under the strong laser irradiation. For the extended Hubbard model on a periodic chain, HHG close to the quantum critical point (QCP) is more significant compared to two neighboring gapped phases (i.e., charge-density-wave and spin-density wave states), especially in low frequencies. We confirm that the systems in the vicinity of the QCP are supersensitive to the external field and more optical-transition channels via excited states are responsible for HHG. This feature holds the potential of obtaining high-efficiency harmonics by making use of materials approaching QCP. Based on the two-dimensional Haldane model, we further propose that the even- or odd-order components of generated harmonics can be promisingly regarded as spectral signals to distinguish the topologically ordered phases from locally ordered ones. Our findings in this Letter pave the way to achieve ultrafast light source from HHG in strongly correlated materials and to study quantum phase transition by nonlinear optics in strong laser fields.
By employing an unbiased numerical method, we investigate the ultrafast dynamics of the correlated systmes in one and two dimensions. For the extended Hubbard model on a periodic chain, the high-harmonic generation (HHG) of system close to the quantum critical point (QCP) is more intense than HHG in the neighboring two gapped phases, i.e., charge-density-wave and spin-density-wave states, especially in low-frequencies. The reason can be attributed to that the system in QCP is more sensitive to the external field and there are more optical-allowed excited states available to furnish photon-absorbing channels for this nonlinear processes. This feature provides a possibility of detecting the quantum phase transition by means of high-harmonic spectroscopy. We also expect to generate stronger HHG by irradiating materials with parameter settings close to QCP. In addition, we find that the even- or odd-order components of HHG can be used to distinguish the topologically ordered phases from locally ordered ones in a two-dimensional interacting Haldane model.
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