April 13, 2024

Raman time delay in strong-field attosecond transient absorption created krypton vacancy

Theoric model

To uncover the dynamics involved, the physics behind the delay of the two resonant transitions is investigated by adopting the density matrix approach.31 (see Methods and SM note 5) with the relevant states included:

$$\frac{d{\rho }^{+}}{{dt}}=-\frac{i}{\hslash}\left[{H}^{+},\,{\rho }^{+}\right]+{\left[\dot{{\rho }^{+}}\right]}_{{ion}}+{\left[\dot{{\rho }^{+}}\right]}_{{decay}}$$

(1)

where ρ+ denotes the ion density matrix, and the second (third) term on the right represents the injection (decay) of the ion. This model has been successfully applied to the study of coherent emission of nitrogen ions32, here is developed to take transient absorption into account. The following processes are considered as illustrated in Fig. 1b: (i) the ionization of the neutral under strong field approximation (SFA)24; (ii) the coupling of the two 4p ionic states3/2−1 and 4 hours1/2−1 (only mj = −1/2 considered) with the neighboring 4 s configurations of the ion due to the NIR pulse; (iii) transitions from 4p orbitals to 3d orbitals induced by the IAP polarized in parallel with the NIR pulse; (iv) the decay of 3d hole states with a lifetime of 7.5 fs due to Auger processes. All states are evolving under the NIR and IAP pulses with the time-dependent Hamiltonian H+

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