Thomas–Reiche–Kuhn correction for truncated configuration-interaction spaces: Case of laser-assisted dynamical interference

The Thomas–Reiche–Kuhn sum rule is used to form an effective potential that is added to the time-dependent configuration-interaction singles (TDCIS) equations of motion in velocity gauge. The purpose of the effective potential is to include virtual coupling from singles to doubles, which is required for size-consistent velocity-gauge TDCIS results. The proposed method is compared to length-gauge TDCIS results for laser-assisted photoionization. Finally, a dynamical interference effect controlled by two-color fields is predicted for atomic targets.

Figure 1

Goldstone diagrams of the energy contributions within CIS [panels (a)–(d)] and CID [panels (e)–(g)]. The diagram in panel (a) describes the energy shift of the core, while the diagrams in panels (b)–(g) describe the energy shift of an excited CIS state. The background shading color indicates the CI space where the atom resides. Time flows upwards in these Goldstone diagrams.

Figure 2

Calculated polarization of the HF ground state of neon with an applied static vector potential in the velocity gauge with truncated space and full CIS space. Perturbation theory results are included as guiding lines.

Figure 3

Normalized photoionization spectra using velocity-gauge TDCIS in neon with the $2p$ orbitals active [panels (a)–(c)] and with the $2s$ and $2p$ orbitals active [panels (d)–(f)]. The solid lines show the measured peak position and the dashed lines show the expected peak position given by $\mathrm{\Delta }{E}_{\mathrm{kin}}=-U_p$. The middle column [panels (b) and (e)] displays the velocity-gauge TDCIS-TRK with the effective potential ${\widehat{V}}_{\mathrm{TRK}}^{\left(\mathrm{S}\right)}$ and the rightmost column [panels (c) and (f)] displays the velocity-gauge TDCIS-TRK with the substitution $\tilde{N}-1\to \tilde{N}$.

Figure 4

One-photon peak of laser-assisted photoionization with a truncated Gaussian envelope using both TDCIS-TRK velocity gauge and length gauge. The expected classical energy shift for a Gaussian envelope is shown with an arrow labeled $U_p/\sqrt{2}$.

Figure 5

Numerical demonstration of laser-assisted dynamical interference. (a) Single XUV pulse and IR pulse using truncated Gaussian envelopes. (b) Mixing flat-top and truncated Gaussian envelopes of the XUV and IR fields with $I_{\omega }=5\times {10}^{12}\mathrm{W}/{\mathrm{cm}}^2$. The expected classical energy shift is shown with an arrow and labeled $U_p$ and $U_p/\sqrt{2}$ for a flat-top envelope and a Gaussian envelope, respectively.