# Slice-by-slice reconstruction of the 3D HHG data: *I*_{p} = 24.59 eV, _{2} = 0.07, _{3} = 0.05, *I* = 1.36 **×** 10^{14} W cm^{−2}, λ = 1600 nm

_{p}

**Figure 3.** Slice-by-slice reconstruction of the 3D HHG data: *I _{p}* = 24.59 eV,

_{2}= 0.07,

_{3}= 0.05,

*I*= 1.36

**×**10

^{14}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

*t*(green); corresponding to zero of the vector potential of 2ω field at time

_{i}*t*(magenta); corresponding to zero of the vector potential of 3ω field at time

_{i}*t*(blue). (b) Optimal delay \phi _2^{{\rm opt},2}(N) for non-degenerate case

_{i}_{3}= 2.1 rad. The same notations are used. (c) Reconstruction of ionization time. The red curve represents theoretical values of

*t*, red dots—reconstructed values of ionization time

_{i}*t*. The blue curve represents theoretical values of τ, blue dots—reconstructed values of imaginary ionization time τ.

_{i}**Abstract**

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 *et al* 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.