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arXiv:1907.05687 · Physical Review Letters

High Harmonic Generation in a Correlated Electron System

Shohei Imai, Atsushi Ono, Sumio Ishihara

Published Apr 16, 2020• 81 citations
arXivHTMLPDF

Abstract

High harmonic generation in crystalline solids has been examined so far on the basis of one-body energy-band structures arising from electron itineracy in a periodic potential. Here, we show the emergence of high harmonic generation signals which are attributed to the dynamics of many-body states in a low-dimensional correlated electron system. An interacting fermion model and its effective pseudospin model on a one-dimensional dimer-type lattice are analyzed. Observed high harmonic generation signals in a spontaneously symmetry-broken state, where charge densities are polarized inside of dimer units, show threshold behavior with respect to light amplitude and are interpreted in terms of tunneling and recombination of kink-antikink excitations in an electric field.

DOI
10.1103/physrevlett.124.157404

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High harmonic generation in crystalline solids has been examined so far on the basis of one-body energy-band structures arising from electron itineracy in a periodic potential. Here, we show the emergence of high harmonic generation signals which are attributed to the dynamics of many-body states in a low-dimensional correlated electron system. An interacting fermion model and its effective pseudospin model on a one-dimensional dimer-type lattice are analyzed. Observed high harmonic generation signals in a spontaneously symmetry-broken state, where charge densities are polarized inside of dimer units, show threshold behavior with respect to light amplitude and are interpreted in terms of tunneling and recombination of kink-antikink excitations in an electric field.
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The key optical and electronic functionalities in condensed materials are determined by the band filling of electrons and their Coulomb correlations. To directly capture how many-body correlations influence the correlated electron dynamics under the driving of laser pulses, the comprehensible quasiparticle picture is desired to distinguish the ultrafast creation and annihilation of doublon-holon pairs in attosecond timescale. Here, we adopt the one-dimensional non-half-filling Hubbard model to study the high-harmonic generation (HHG) in correlated electron systems. As the value of Hubbard UUU increases, the cutoff energy and spectral features in HHG spectra have been revealed and their scaling laws are explained by the characteristic energy gaps obtained from the electronic bands under the quasiparticle picture. The adjustable degree of band filling in correlated systems paves a way to enhance high-harmonic emissions by regulating the creation of doublon-holon pairs. The complex temporal profile of HHG is elucidated in this work by the light-induced evolution of quasiparticle bands in correlated materials. In addition, the dephasing of the HHG spectrum caused by the vibration-induced disorder or lattice temperature is affirmed in the correlated electron systems and this dephasing process is attributed to quasiparticle-lattice scattering during the doublons and holons propagating among the disordered lattice sites.
Using the Hubbard model we study how the process of high-order harmonic generation (HHG) is modified by electron-electron correlation for both finite and bulk systems. A finite-size enhancement of the HHG signal is found and attributed to electrons backscattering off the lattice edges. Additionally, with the increasing strength of the electron-electron correlation an enhancement of the high-frequency regime of the HHG spectrum is found. This is attributed to the on-site Coulomb repulsion between electrons giving rise to a localized correlation-induced quiver motion of the electrons. The finite-lattice enhancement dominates the HHG spectra from a few harmonic orders until a threshold from which the correlational enhancement dominates. This threshold is determined by the degree of correlation and decreases into the low-frequency regime for increasing electron-electron correlation. This infers that as the electron-electron correlation increases, the finite-size effect on the electron dynamics decreases.
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We study high-harmonic generation (HHG) in the one-dimensional Hubbard model in order to understand its relation to elementary excitations as well as the similarities and differences to semiconductors. The simulations are based on the infinite time-evolving block decimation (iTEBD) method and exact diagonalization. We clarify that the HHG originates from the doublon-holon recombination, and the scaling of the cutoff frequency is consistent with a linear dependence on the external field. We demonstrate that the subcycle features of the HHG can be reasonably described by a phenomenological three step model for a doublon-holon pair. We argue that the HHG in the one-dimensional Mott insulator is closely related to the dispersion of the doublon-holon pair with respect to its relative momentum, which is not necessarily captured by the single-particle spectrum due to the many-body nature of the elementary excitations. For the comparison to semiconductors, we introduce effective models obtained from the Schrieffer-Wolff transformation, i.e., a strong-coupling expansion, which allows us to disentangle the different processes involved in the Hubbard model: intraband dynamics of doublons and holons, interband dipole excitations, and spin exchanges. These demonstrate the formal similarity of the Mott system to the semiconductor models in the dipole gauge, and reveal that the spin dynamics, which does not directly affect the charge dynamics, can reduce the HHG intensity. We also show that the long-range component of the intraband dipole moment has a substantial effect on the HHG intensity, while the correlated hopping terms for the doublons and holons essentially determine the shape of the HHG spectrum. A new numerical method to evaluate single-particle spectra within the iTEBD method is also introduced.
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.