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Journal of the Optical Society of America B

Extracting correlation length in Mott insulators by strong-field driving

Abdallah AlShafey, Xu-Yan Jia, Yuan-Ming Lu, Shou-Shu Gong, Gerard McCaul, Denys I. Bondar, Mohit Randeria, Takashi Oka, Alexandra S. Landsman

Published Apr 2, 2024• 1 citation
Publisher

Abstract

The breakdown of a Mott-insulator when subjected to intense laser fields is characterized by the formation of doublon-hole pairs. This breakdown is furthermore evidenced by the production of high harmonics that can be experimentally measured. Here, we present an approach for extracting the doublon-hole correlation length of a Mott insulator. The method is based on a dynamical calculation of the Mott insulator’s rate of charge production in response to an applied strong-field laser pulse. We find that coupling the Mott insulator to a metal drastically increases the correlation length, in support of our recent hypothesis [ Phys. Rev. B 108 , 144434 ( 2023 ) 2469-9950 10.1103/PhysRevB.108.144434 ] that coupling to a metal enhances the charge fluctuations in the insulator. We confirm our conclusions using density matrix renormalization group (DMRG) calculations. The proposed method can be applied to experimentally measured observables, such as differential reflectivity or the high harmonic generation (HHG) spectrum to extract doublon-hole correlation length.

DOI
10.1364/josab.515940

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The breakdown of a Mott-insulator when subjected to intense laser fields is characterized by the formation of doublon-hole pairs. This breakdown is furthermore evidenced by the production of high harmonics that can be experimentally measured. Here, we present an approach for extracting the doublon-hole correlation length of a Mott insulator. The method is based on a dynamical calculation of the Mott insulator’s rate of charge production in response to an applied strong-field laser pulse. We find that coupling the Mott insulator to a metal drastically increases the correlation length, in support of our recent hypothesis [ Phys. Rev. B 108 , 144434 ( 2023 ) 2469-9950 10.1103/PhysRevB.108.144434 ] that coupling to a metal enhances the charge fluctuations in the insulator. We confirm our conclusions using density matrix renormalization group (DMRG) calculations. The proposed method can be applied to experimentally measured observables, such as differential reflectivity or the high harmonic generation (HHG) spectrum to extract doublon-hole correlation length.
High-harmonic generation (HHG) in strongly correlated Mott insulators is investigated using exact diagonalization and time-dependent density-matrix propagation of a laser-driven one-dimensional Hubbard chain. By projecting onto equilibrium Hubbard bands, we use the doublon population and its dynamics as a diagnostic to analyze intraband (spin-wave-like) and interband (doublon-holon creation) excitation channels. A filling-dependent crossover emerges: Bloch-like intraband response at dilute filling, mixed dynamics at intermediate filling, and interband-dominated HHG with plateau and cutoff near half filling. In the considered parameter range, increasing interaction strength UUU strongly suppresses interband contributions through the enlarged Mott gap and correlation-induced localization. Intra- and interband current decomposition reveals opposing flows below the Mott gap (Δ_{\mathrm{Mott}}) and selective dephasing suppression of interband coherence, enhancing net doublon accumulation. Time-frequency analysis uncovers the filling-dependent features of quantum trajectories, manifesting in distinct below-Δ_{\mathrm{Mott}} emission. This doublon-based analysis provides a transparent link between equilibrium spin-charge separation and nonequilibrium strong-field response, and clarifies how dephasing modifies interband coherence and doublon accumulation.
Doublon-hole pair production, which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field, is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multiphoton absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy are changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution, and the results are compared with those of the time-dependent density matrix renormalization group. Using this method, we calculate the distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory are proposed, such as angle-resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relationship of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics, known as the Schwinger mechanism.
Doublon-hole pair production which takes place during dielectric breakdown in a Mott insulator subject to a strong laser or a static electric field is studied in the one-dimensional Hubbard model. Two nonlinear effects cause the excitation, i.e., multi-photon absorption and quantum tunneling. Keldysh crossover between the two mechanisms occurs as the field strength and photon energy is changed. The calculation is done analytically by the Landau-Dykhne method in combination with the Bethe ansatz solution and the results are compared with those of the time dependent density matrix renormalization group. Using this method, we calculate distribution function of the generated doublon-hole pairs and show that it drastically changes as we cross the Keldysh crossover line. After calculating the tunneling threshold for several representative one-dimensional Mott insulators, possible experimental tests of the theory is proposed such as angle resolved photoemission spectroscopy of the upper Hubbard band in the quantum tunneling regime. We also discuss the relation of the present theory with a many-body extension of electron-positron pair production in nonlinear quantum electrodynamics known as the Schwinger mechanism.
We study the high harmonic generation (HHG) in Mott insulators using Floquet dynamical mean-field theory (DMFT). We show that the main origin of the HHG in Mott insulators is the doublon-holon recombination, and that the character of the HHG spectrum differs depending on the field strength. In the weaker-field regime, the HHG spectrum shows a single plateau as in the HHG from gases, and its cut-off energy εcutε_{\rm cut}εcut​ scales linearly with the field strength E0E_0E0​ as εcut=Δgap+αE0ε_{\rm cut}=Δ_{\rm gap} + αE_0εcut​=Δgap​+αE0​, where ΔgapΔ_{\rm gap}Δgap​ is the Mott gap. On the other hand, in the stronger-field regime, multiple plateaus emerge and the mmm-th cut-off scales as εcut,m=U+mE0ε_{\rm cut,m}=U + m E_0εcut,m​=U+mE0​. We show that this difference originates from the different dynamics of the doublons and holons in the weak- and strong-field regimes. We also comment on the similarities and differences between HHG from Mott insulators and from semiconductors. This proceedings paper complements our recent work, Phys. Rev. Lett. 121, 057405 (2018), with additional results and analyses.
Charge creation via quantum tunneling, i.e. dielectric breakdown, is one of the most fundamental and significant phenomena arising from strong light(field)-matter coupling. In this work, we conduct a systematic numerical analysis of quantum tunneling in one-dimensional Mott insulators described by the extended (UUU-VVV) Hubbard model. We discuss the applicability of the analytical formula for doublon-holon (DH) pair production, previously derived for the one-dimensional Hubbard model, which highlights the relationship between the tunneling threshold, the charge gap, and the correlation length. We test the formulas ability to predict both DH pair production and energy increase rate. Using tensor-network-based approaches, we demonstrate that the formula provides accurate predictions in the absence of excitonic states facilitated by the nearest-neighbor interaction VVV. However, when excitonic states emerge, the formula more accurately describes the rate of energy increase than the DH pair creation rate and in both cases gets improved by incorporating the exciton energy as the effective gap.
Using dynamical mean-field theory and the non-crossing approximation as impurity solver, we study the response of a Mott insulator to strong dc electric fields. The breakdown of the Mott insulating state is triggered by field-induced creation of doublon-hole pairs. In a previous investigation, Ref. [1], it was found that the system approaches a long-lived quasi-steady state in which the current is time-independent although the number of carriers constantly increases. Here we investigate and clarify the nature of this state, which exists only because thermalization is slow in the Hubbard model at strong coupling. The current is time-independent because doublons and holes have an infinite temperature distribution. Evidence for this fact is obtained from spectral functions and by comparing the electric current with the field-induced doublon-hole creation rate. Implications to real experiments, in systems with energy dissipation, are discussed.