Attosecond Pulses from a Solid Driven by a Synthesized Two-Color Field at Megahertz Repetition Rate

Abstract

Probing coherent quantum dynamics in light-matter interactions at the microscopic level requires high-repetition-rate isolated attosecond pulses (IAPs) in pump-probe experiments. To date, the generation of IAPs has been mainly limited to the kilohertz regime. In this work, we experimentally achieve attosecond control of extreme-ultraviolet (XUV) high harmonics in the wide-bandgap dielectric MgO, driven by a synthesized field of two femtosecond pulses at 800 and 2000 nm with relative phase stability. The resulting quasi-continuous harmonic plateau with ∼9 eV spectral width centered around 16.5 eV photon energy can be tuned by the two-color phase and supports the generation of an IAP (∼700 attoseconds), confirmed by numerical simulations based on the three-band semiconductor Bloch equations. Leveraging the high-repetition-rate driver laser, the moderate intensity requirements of solid-state high-harmonic generation, and band-structure-induced spectral enhancement, we achieve IAP production at an unprecedented megahertz repetition rate, paving the way for compact all-solid-state XUV sources for IAP generation.

Keywords: attosecond pulses; extreme nonlinear optics; high-harmonic generation in condensed matter; semiconductor Bloch equations; subcycle optical field synthesis.

1

Experimental setup and synthesized two-color field distribution. (a) Experimental setup for attosecond control of high-harmonic generation and isolated attosecond pulse generation from MgO with synthesized two-color light fields. (b) The field profile (solid blue with shading) shows a dominant field peak in the center. Red solid (with shading) and green dashed curves (with shading) depict the 800 and 2000 nm field, respectively. The peak intensity of the 2000 nm field is 2% of the 800 nm peak intensity. The red and green circles in the insets indicate where the 2000 nm field enhances and suppresses the corresponding half-cycle, respectively. (c) Band structure of MgO along the Γ–X direction, with the shaded region indicating the spectral range where harmonic yields are enhanced by the Van Hove singularity. VB, CB1, and CB2 denote the valence band, the first conduction band, and the second conduction band, respectively.

2

Attosecond-controlled harmonic spectra. (a) Experimentally measured harmonic intensity as a function of two-color delay from –120 to 120 fs. The white dashed line has a slope of 6.5 fs eV^–1. (b) Experimentally measured harmonic intensity for the 800 nm pulse pump (orange) and for the synthesized two-color field (blue) with 0.5 fs delay. (c) Spectral intensity at 15.5 eV as a function of two-color delay shows a period of 6.6 fs. (d) Harmonic intensity in the Fourier time domain as a function of delay, corresponding to (a).

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Comparison of experimental results with SBEs simulation results. (a, b) Harmonic intensity as a function of two-color delay for SBE simulation and experiment (logarithmic scale), respectively. For both cases, the peak intensity for the 800 nm pulse is 15 TW cm^–2. The black dashed circle curves show three local maxima for each 6.6 fs period for both experiment and simulation. The white dashed line for both cases has a slope of 6.5 fs eV^–1. The white arrow in (a) indicates zero delay. (c) Attosecond pulse intensity as a function of two-color delay in real time. The white arrow indicates zero delay where a high-contrast IAP is produced. (d) Comparison of the formation of attosecond pulse trains and IAPs at time delay −165 fs (orange) and 0 fs (blue), respectively. (e) Field strength square distribution |E(t)|² of the synthesized pulse as a function of the two-color delay. The white arrow indicates zero delay. (f) The synthetic field strength square distribution with a two-color delay equal to 0 fs.

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(a) Spectral intensity and emission time distribution of the simulated high-harmonic spectrum, obtained under the same conditions as in Figure (d) The emission times are obtained from a time–frequency analysis of the simulation results. (b) The corresponding temporal intensity profile, with a pulse duration of approximately 600 as (blue solid curve), obtained via Fourier transform of the spectral intensity and emission times shown in (a) For comparison, the red dashed-dotted curve represents the transform-limited pulse with a duration of 580 as.