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arXiv:2610.21712

Size-Dependent High-Order Harmonic Generation from Linear Carbon-Chain Molecules in Linearly Polarized Laser Fields

Yifan Kang, Yang Yang, Yingtan Li, Shuwen Pang, Huiwen Yang, Yingdan Zhang, Shushan Zhou

quant-phSubmitted Oct 15, 2026• Announced Oct 16, 2026
arXivHTMLPDF

Abstract

High-order harmonic generation from molecules is highly sensitive to molecular geometry and strong-field electron dynamics, providing a powerful route for probing and controlling ultrafast processes in extended systems. In this work, we systematically investigate the influence of molecular chain length on HHG from linear carbon-chain molecules C$_2$H$_2$, C$_6$H$_2$, and C$_{10}$H$_2$ driven by an 800 nm linearly polarized laser field. To isolate the molecular-size effect from the influence of different ionization potentials, the laser intensities are adjusted to maintain the same Keldysh parameter for different molecules. Real-time time-dependent density functional theory simulations are performed with the molecular axis aligned parallel to the laser polarization direction. The results show that increasing the molecular chain length significantly enhances the harmonic yield and tends to extend the cutoff region. In particular, C$_{10}$H$_2$ exhibits much stronger plateau harmonics than C$_2$H$_2$, while the intermediate molecule C$_6$H$_2$ shows harmonic intensities between those of C$_2$H$_2$ and C$_{10}$H$_2$. Time-frequency analysis and charge-density evolution reveal that the enhanced HHG emission in longer chains originates from the enlarged electron acceleration distance and increased probability of multi-center recollision, especially near the terminal carbon atoms. These findings demonstrate that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems.

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The generation of high harmonics is a strongly nonlinear effect that allows to probe properties of the target and to study electron dynamics in matter. It has been investigated in many different kinds of targets, including molecular gases, liquids and solids. Recently, high-harmonic generation was studied in organic molecular crystals by Wiechmann et al. [Nat. Commun. 16, 9890 (2025)]. It was found that the laser-polarization-dependent harmonic yield is sensitive to the weak couplings between nearest- and next-nearest-neighbor molecules. In this paper, the impact of the laser polarization angle and the intermolecular interaction on the harmonic yield is examined in detail using a simple but insightful two-dimensional tight-binding system that models a molecular dimer, i.e. two weakly coupled molecules. We find that the intensities of lower harmonic orders tend to maximize for a laser polarization direction aligning with the molecular axes, whereas higher harmonic orders rather show the strongest yield for a polarization direction along the intermolecular axis. We further demonstrate that the harmonic order at which the maximum flips from the molecular to the intermolecular direction strongly depends on the intermolecular coupling strength. To gain a deeper insight into the origins of the findings, we include a detailed adiabatic analysis, showing that the flipping of the maximum yield towards the intermolecular direction is already contained qualitatively in the adiabatically following states.

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Unconventional gap dependence of high-order harmonic generation in the extremely strong light-matter-coupling regime

Akira Kofuji, Robert Peters

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 ${\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}$ 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.

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In the realm of open quantum systems, steady states and high-harmonic generation (HHG) existing far from equilibrium have become core pillars of ultrafast science. Most solid-state research explores charge HHG with limited investigations into spin degrees of freedom. In this study, we theoretically address spin HHG in the steady state resulting from the terahertz laser-driven spin-phonon coupling in a dissipative dimerized spin-1/2 chain. Instead of directly driving spins using time-dependent magnetic fields, we employ the magnetophononic mechanism, where the laser first drives the lattice, and then the excited lattice subsequently drives the spins. We investigate the role of various model parameters for optimizing HHG. Increasing the laser amplitude amplifies spin HHG beyond the perturbative regime, enhancing both harmonic amplitudes and orders. We find that configuring the drive frequency far below the spin band yields the highest harmonic order. Additionally, we provide a theory matching the numerical results under weak spin-phonon coupling and propose an experimental procedure to probe the emission spectrum of spin HHG.

arXiv:2404.05830•Physical review. B./Physical review. B•Aug 19, 2024•16 citations
High-order harmonic generation from molecules is highly sensitive to molecular geometry and strong-field electron dynamics, providing a powerful route for probing and controlling ultrafast processes in extended systems. In this work, we systematically investigate the influence of molecular chain length on HHG from linear carbon-chain molecules C2_22​H2_22​, C6_66​H2_22​, and C10_{10}10​H2_22​ driven by an 800 nm linearly polarized laser field. To isolate the molecular-size effect from the influence of different ionization potentials, the laser intensities are adjusted to maintain the same Keldysh parameter for different molecules. Real-time time-dependent density functional theory simulations are performed with the molecular axis aligned parallel to the laser polarization direction. The results show that increasing the molecular chain length significantly enhances the harmonic yield and tends to extend the cutoff region. In particular, C10_{10}10​H2_22​ exhibits much stronger plateau harmonics than C2_22​H2_22​, while the intermediate molecule C6_66​H2_22​ shows harmonic intensities between those of C2_22​H2_22​ and C10_{10}10​H2_22​. Time-frequency analysis and charge-density evolution reveal that the enhanced HHG emission in longer chains originates from the enlarged electron acceleration distance and increased probability of multi-center recollision, especially near the terminal carbon atoms. These findings demonstrate that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems.
The generation of high harmonics is a strongly nonlinear effect that allows to probe properties of the target and to study electron dynamics in matter. It has been investigated in many different kinds of targets, including molecular gases, liquids and solids. Recently, high-harmonic generation was studied in organic molecular crystals by Wiechmann et al. [Nat. Commun. 16, 9890 (2025)]. It was found that the laser-polarization-dependent harmonic yield is sensitive to the weak couplings between nearest- and next-nearest-neighbor molecules. In this paper, the impact of the laser polarization angle and the intermolecular interaction on the harmonic yield is examined in detail using a simple but insightful two-dimensional tight-binding system that models a molecular dimer, i.e. two weakly coupled molecules. We find that the intensities of lower harmonic orders tend to maximize for a laser polarization direction aligning with the molecular axes, whereas higher harmonic orders rather show the strongest yield for a polarization direction along the intermolecular axis. We further demonstrate that the harmonic order at which the maximum flips from the molecular to the intermolecular direction strongly depends on the intermolecular coupling strength. To gain a deeper insight into the origins of the findings, we include a detailed adiabatic analysis, showing that the flipping of the maximum yield towards the intermolecular direction is already contained qualitatively in the adiabatically following states.
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.
We extend our recently developed semiclassical strong-field Herman-Kluk (SFHK) propagator method to calculate high-order harmonic generation (HHG) in diatomic molecules driven by few-cycle intense laser fields. On the example of applications to H2 and N2, we show that our method, based on a combination of the Herman-Kluk propagator and the strong-field approximation, can provide very accurate results for both HHG yield and phase, nearly identical to those from the exact numerical solutions of the time-dependent Schrodinger equation. To compare with experimental measurements, averaging over molecular orientations must be performed. Here we demonstrate a distinct and powerful advantage of the SFHK, as its Monte Carlo sampling for the integration over the alignment distribution can be efficiently combined with the integration over the initial momentum distributions of electron wave-packet right after the tunnel exit. Therefore, the total number of trajectories used for the alignment-averaged HHG spectrum does not increase much compared to that for a single fixed alignment. Similar to atomic targets, the main computational task in the SFHK is to solve the classical Hamiltonian equations for the active electron in the combined electron-target ion potential and electron-laser interaction. The motion of the center of each electron wave packet in the continuum, represented by a coherent state, is governed by an independent classical trajectory so that the computation can be parallelized very efficiently.
Tailoring optical Schrödinger cat states via orientation-dependent high-harmonic generation in H2+\rm{H}_2^+H2+​
We theoretically demonstrate that the molecular orientation angle θθθ provides a structurally intrinsic, continuously tunable control parameter for engineering optical Schrödinger cat states via high-harmonic generation (HHG) in H2+_2^+2+​. Coupling time-dependent Schrödinger equation simulations to the fully quantized HHG framework, we evaluate the Wigner functions of the post-selected harmonic-mode states under two complementary conditioning strategies. Conditioning on resonance-enhanced low-order harmonics exploits the complementary dipole selection rules of the 1σg→1σu1σ_g\to1σ_u1σg​→1σu​ and 1σg→1πu1σ_g\to1π_u1σg​→1πu​ transitions, driving a kitten-cat crossover whose direction is opposite in the two channels as θθθ is varied. Conditioning on plateau harmonics instead exploits two-center destructive interference, producing a reentrant cat→\to→kitten→\to→cat transition controlled by the order-dependent interference angle θ∗(q)θ^*(q)θ∗(q). In both cases the crossover is decoupled from the laser intensity, focal geometry, and molecular density, offering a degree of control with no counterpart in atomic targets.
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.
In the realm of open quantum systems, steady states and high-harmonic generation (HHG) existing far from equilibrium have become core pillars of ultrafast science. Most solid-state research explores charge HHG with limited investigations into spin degrees of freedom. In this study, we theoretically address spin HHG in the steady state resulting from the terahertz laser-driven spin-phonon coupling in a dissipative dimerized spin-1/2 chain. Instead of directly driving spins using time-dependent magnetic fields, we employ the magnetophononic mechanism, where the laser first drives the lattice, and then the excited lattice subsequently drives the spins. We investigate the role of various model parameters for optimizing HHG. Increasing the laser amplitude amplifies spin HHG beyond the perturbative regime, enhancing both harmonic amplitudes and orders. We find that configuring the drive frequency far below the spin band yields the highest harmonic order. Additionally, we provide a theory matching the numerical results under weak spin-phonon coupling and propose an experimental procedure to probe the emission spectrum of spin HHG.