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arXiv:2609.27742

Order-Dependent Modification of High-Harmonic Generation by Quantum Dissipation and Lamb Shift

Xiangyu Zhang, Tong Wu, Xiang Li, Jianshi Lu, Zhe Yang, Chao Yu, Shicheng Jiang, Ruifeng Lu

Published Sep 23, 2026• 0 citations
arXivHTMLPDF

Abstract

Many-body environments are conventionally incorporated into quantum dynamics as heat baths, which induce a Lamb shift and quantum dissipation. In the traditional picture, such environmental coupling is expected to induce suppression and broadening of spectral signals. In this letter, we investigate high-order harmonic generation (HHG) in a two-level system coupled to a heat bath via dipole-dipole interactions using the Lindblad master equation. It is found that the environmental effect does not simply suppress the harmonic efficiency. Instead, when the cutoff frequency of the coupling spectral density exceeds the energy-level spacing, the environment can actually enhance the harmonic yield. Further analysis reveals that this enhancement originates from intense level fluctuations induced by the Lamb shift. Meanwhile, the environmental influence exhibits a distinct dependence on harmonic order, manifesting clearly different behaviors for lower and higher harmonics. Our results challenge the common relaxation-time picture of uniform damping and establish a microscopic, order-dependent mechanism for environmental control of HHG, with direct implications for solid-state attosecond spectroscopy and quantum material engineering.

DOI
10.48550/arxiv.2609.27742

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Many-body environments are conventionally incorporated into quantum dynamics as heat baths, which induce a Lamb shift and quantum dissipation. In the traditional picture, such environmental coupling is expected to induce suppression and broadening of spectral signals. In this letter, we investigate high-order harmonic generation (HHG) in a two-level system coupled to a heat bath via dipole-dipole interactions using the Lindblad master equation. It is found that the environmental effect does not simply suppress the harmonic efficiency. Instead, when the cutoff frequency of the coupling spectral density exceeds the energy-level spacing, the environment can actually enhance the harmonic yield. Further analysis reveals that this enhancement originates from intense level fluctuations induced by the Lamb shift. Meanwhile, the environmental influence exhibits a distinct dependence on harmonic order, manifesting clearly different behaviors for lower and higher harmonics. Our results challenge the common relaxation-time picture of uniform damping and establish a microscopic, order-dependent mechanism for environmental control of HHG, with direct implications for solid-state attosecond spectroscopy and quantum material engineering.
High-order harmonic generation (HHG) is one of the most commonly studied nonlinear optical phenomena, originating in the ultrafast dynamics of electrons in atomic gases and semiconductors. It has attracted much attention because of its nonperturbative nature and potential for future attosecond laser pulse sources. On the theory side, a semiclassical picture based on tunneling ionization of electrons is successfully used in explaining key characteristics of the HHG. This model assumes that electric fields nonperturbatively excite electrons beyond the ionization potential or the band gap. Thus, intuitively, a larger gap should lead to an exponentially smaller HHG emission. Despite this intuition, the HHG in the Mott insulator Ca2RuO4{\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}Ca2​RuO4​ has shown an unconventional exponential increase with respect to the gap width. This experiment implies effects beyond the semiclassical theory. However, most theoretical works have focused on the dependence of the HHG on external control parameters, and the gap dependence of the HHG is poorly understood even in noninteracting systems. Thus, it is essential to clarify the gap dependence of the HHG in a fully quantum mechanical approach. Here, we analyze numerically exactly the gap dependence of the HHG in two-level systems. We find an increase in the strength of the HHG when the Rabi frequency is large compared to the gap width. Furthermore, the relaxation and scattering of electrons increase the visibility of this gap dependence. Finally, we find that the enhancement rate follows a universal scaling law regardless of the driving frequency. The existence of this gap dependence in two-level systems suggests that this unconventional gap dependence is a universal behavior that can be found not only in Mott insulators but also in atomic gases and semiconductors.
This paper presents an analytical study of high-order harmonic generation (HHG) by quantum systems possessing permanent dipole moments (PDMs), such as atoms/molecules placed in a static electric field or polar molecules. HHG by conventional, non-PDM systems typically demonstrated a plateau in the envelope of harmonics followed by a steep fall in harmonic intensities when the harmonic number exceeds a certain threshold. This paper shows that the HHG by PDM systems results in a significant extension of the plateau to higher frequencies and a slower decline of intensities at frequencies higher than the end of the plateau . Moreover, there occurs a substantial growth of the total, summed intensity of all components of the scattering spectrum . Other physically interesting distinctive features of the HHG by PDM systems are: the presence of both odd and even harmonics of the laser frequency in the scattering spectrum; a triplet structure of both odd and even harmonics; and the appearance of a component at the doubled Rabi frequency (i.e. at a frequency much lower than the laser frequency). The results are obtained by using the adiabatic basis for the analysis of a multi-quantum resonance in a two-level system possessing PDMs.
We present a theoretical study of the high-order-harmonic generation (HHG) from coherent superposition states of a three-level system driven by monochromatic cw laser fields. The HHG spectrum can be enhanced by about 105{10}^{5}105 times via tuning the relative phase between the states which are initially prepared. Even if the ionization effects are taken into account, the enhancement factors are still up to about 102{10}^{2}102 times. The enhancement is interpreted as the quantum constructive interference of different dipole transitions between quasienergy states. To realize the interference, the intensity of the driving laser field is chosen such that frequencies of the harmonics generated from the different dipole-transition paths, which are dependent on the ac Stark shifted energy separation of quasienergy states, are equal to each other. Moreover, the case studies of HHG spectra from a coherent superposition state of a three-level system show that the enhancement of harmonics is closely related to the harmonic strengths of the dipole transitions, as well as the parity of quasienergy states which are involved in the dipole-transition paths. The reduction of enhancement factors due to ionization effects is also qualitatively analyzed.
High harmonic generation (HHG) has emerged as a powerful probe of ultrafast electron dynamics in solids. However, in strongly correlated materials, where electronic excitations arise from many-body interactions rather than single-particle band dispersion, the field remains in its infancy. Here, we report HHG up to the 23rd^{rd}rd order in the prototypical Mott insulator La2_22​CuO4_44​. We observe a robust 4 eV cutoff that is independent of driving field strength, revealing an intrinsic energy scale defined by the Hubbard bands. Using time-resolved high harmonic spectroscopy, we disentangle the distinct contributions of carrier creation, intraband acceleration, and interband recombination to the nonequilibrium radiation spectrum. We demonstrate that photo-doping triggers a fundamental reorganization of the many-body manifolds above a critical excitation density, a process that renormalizes the band curvature and suppresses nonlinear intraband currents, thereby directly imprinting the signature of many-body band reconstruction onto the harmonic emission. These results establish HHG as a sensitive probe of subtle correlation-driven electronic reconstructions and highlight that many-body interactions enable extreme nonlinear optical responses that are highly tunable in nonequilibrium states.
Open quantum batteries (QBs) operate under unavoidable system--environment interactions, where both dissipation and coherent frequency renormalization can affect their dynamics. While dissipative effects have been extensively studied, the role of environment-induced frequency shifts, such as the Lamb shift, remains less explored. Here, we investigate a driven open QB consisting of two coherently coupled quantum harmonic oscillators representing the charger and the battery. By incorporating dissipation and Lamb-shift corrections within a Lindblad master equation, we show that the Lamb shift renormalizes the system eigenfrequencies and modifies the resonance condition with the external drive. We further demonstrate that the resulting frequency renormalization leads to a mode-selective energy-transfer process, producing a redistribution of energy between the charger and the battery. This behavior is characterized through a supermode decomposition of the coupled system, which reveals how the environment-induced frequency shift alters the dominant energy-transfer channel. Our results clarify the role of coherent environmental effects in open quantum batteries and provide a physical framework for understanding work-extraction dynamics beyond purely dissipative descriptions.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a nonideal two level subspace, identified as the qubit, and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model that we use is an rf-SQUID under macroscopic quantum coherence and coupled inductively to a flux noise characterized by an environmental spectrum. The model interaction can generate dipole couplings which can be appreciable between the qubit and the high levels. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We calculate the relaxation and dephasing times as the spectral parameters of the environment are varied. We observe that, these calculated time scales receive contribution from all available frequencies in the noise spectrum (even well above the system's resonant frequency scales) stressing the dominant role played by the nonresonant transitions. The relaxation and dephasing and the leakage times thus calculated, strongly depend on the appreciably interacting levels determined by the strength of the dipole coupling. Under the influence of these nonresonant and multilevel effects, the validity of the two level approximation is dictated not by the low temperature as conveniently believed, but by these multilevel dipole couplings as well as the availability of the environmental modes.