Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields

High harmonic generation (HHG) spectroscopy has opened up a new frontier in ultrafast science, where electronic dynamics can be measured on an attosecond time scale. The strong laser field that triggers the high harmonic response also opens multiple quantum pathways for multielectron dynamics in molecules, resulting in a complex process of multielectron rearrangement during ionization. Using combined experimental and theoretical approaches, we show how multi-dimensional HHG spectroscopy can be used to detect and follow electronic dynamics of core rearrangement on sub-laser cycle time scales. We detect the signatures of laser-driven hole dynamics upon ionization and reconstruct the relative phases and amplitudes for relevant ionization channels in a CO2 molecule on a sub-cycle time scale. Reconstruction of channel-resolved complex ionization amplitudes on attosecond time scales has been a long-standing goal of high harmonic spectroscopy. Our study brings us one step closer to fulfilling this initial promise and developing robust schemes for sub-femtosecond imaging of multielectron rearrangement in complex molecular systems

(a) Schematic representation of the fundamental and control fields in multi-dimensional high harmonic spectroscopy

<p><strong>Figure 1.</strong> (a) Schematic representation of the fundamental and control fields in multi-dimensional high harmonic spectroscopy. (b) Schematic representation of the evolution in complex time <em>t_s</em> = <em>t_i</em> + iτ. Quantum orbit enters the barrier at the complex time <em>t_s</em>, appears in the continuum at ionization time <em>t_i</em> and returns to the core at time <em>t</em>.</p> <p><strong>Abstract</strong></p> <p>High harmonic spectroscopy has the potential to combine attosecond temporal with sub-Angstrom spatial resolution of the early nuclear and multielectron dynamics in molecules. It involves strong-field ionization of the molecule by an infrared (IR) laser field followed by time-delayed recombination of the removed electron with the molecular ion. The time-delay is controlled on the attosecond time scale by the oscillation of the IR field and is mapped into the harmonic number, providing a movie of molecular dynamics between ionization and recombination. One of the challenges in the analysis of a high harmonic signal stems from the fact that the complex dynamics of both ionization and recombination with their multiple observables are entangled in the harmonic signal. Disentangling this information requires a multidimensional approach, capable of mapping ionization and recombination dynamics into different independent parameters. We suggest multidimensional high harmonic spectroscopy as a tool for characterizing ionization and recombination processes separately allowing for simultaneous detection of both the ionization delays and sub-cycle ionization rates. Our method extends the capability of the two-dimensional set-up suggested recently by Shafir <em>et al</em> on reconstructing ionization delays, while keeping the reconstruction procedure as simple as in the original proposal. The scheme is based on the optimization of the high harmonic signal in orthogonally polarized strong fundamental and relatively weak multicolour control fields.</p

Slice-by-slice reconstruction of the 3D HHG data: <em>I_p</em> = 24.59 eV, ₂ = 0.07, ₃ = 0.05, <em>I</em> = 1.36 <b>×</b> 10¹⁴ W cm⁻², λ = 1600 nm

<p><strong>Figure 3.</strong> Slice-by-slice reconstruction of the 3D HHG data: <em>I_p</em> = 24.59 eV, ₂ = 0.07, ₃ = 0.05, <em>I</em> = 1.36 <b>×</b> 10¹⁴ W cm⁻², λ = 1600 nm. (a) Optimal delay \phi _2^{{\rm opt},1}(N) in the degenerate case ₃ = 0 corresponding to the maximum of the quantum gate Q^{q}_2 (black dots); corresponding to the maximum of classical gate Q^{c}_2 (red); corresponding to zero of the vector potential of the control field at time <em>t_i</em> (green); corresponding to zero of the vector potential of 2ω field at time <em>t_i</em> (magenta); corresponding to zero of the vector potential of 3ω field at time <em>t_i</em> (blue). (b) Optimal delay \phi _2^{{\rm opt},2}(N) for non-degenerate case ₃ = 2.1 rad. The same notations are used. (c) Reconstruction of ionization time. The red curve represents theoretical values of <em>t_i</em>, red dots—reconstructed values of ionization time <em>t_i</em>. The blue curve represents theoretical values of τ, blue dots—reconstructed values of imaginary ionization time τ.</p> <p><strong>Abstract</strong></p> <p>High harmonic spectroscopy has the potential to combine attosecond temporal with sub-Angstrom spatial resolution of the early nuclear and multielectron dynamics in molecules. It involves strong-field ionization of the molecule by an infrared (IR) laser field followed by time-delayed recombination of the removed electron with the molecular ion. The time-delay is controlled on the attosecond time scale by the oscillation of the IR field and is mapped into the harmonic number, providing a movie of molecular dynamics between ionization and recombination. One of the challenges in the analysis of a high harmonic signal stems from the fact that the complex dynamics of both ionization and recombination with their multiple observables are entangled in the harmonic signal. Disentangling this information requires a multidimensional approach, capable of mapping ionization and recombination dynamics into different independent parameters. We suggest multidimensional high harmonic spectroscopy as a tool for characterizing ionization and recombination processes separately allowing for simultaneous detection of both the ionization delays and sub-cycle ionization rates. Our method extends the capability of the two-dimensional set-up suggested recently by Shafir <em>et al</em> on reconstructing ionization delays, while keeping the reconstruction procedure as simple as in the original proposal. The scheme is based on the optimization of the high harmonic signal in orthogonally polarized strong fundamental and relatively weak multicolour control fields.</p

Shaping polarization of attosecond pulses via laser control of electron and hole dynamics

We show how laser control over both electronic and hole dynamics in aligned molecules can be used to shape polarization of attosecond pulses produced via high harmonic generation driven by two-color, linearly polarized laser fields.Peer reviewed: YesNRC publication: Ye

Multidimensional high harmonic spectroscopy of polyatomic molecules: detecting sub-cycle laser-driven hole dynamics upon ionization in strong mid-IR laser fields

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