Subcycle dynamics of high-harmonic generation in valence-shell and virtual states of Ar atoms: A self-interaction-free time-dependent density-functional-theory approach

We perform an ab initio all-electron study of the subcycle structure, dynamics, and spectra of high harmonic generation (HHG) processes of Ar atoms in the presence of extreme ultraviolet (XUV) attosecond pulses and near-infrared (NIR) laser fields by means of the self-interaction-free time-dependent density functional theory (TDDFT). The TDDFT equations are solved accurately and efficiently via the time-dependent generalized pseudospectral (TDGPS) method. We focus on the subcycle (with respect to NIR field) temporal behavior of the level shift of the excited energy levels and related dynamics of harmonic photon emission. We observe and identify the subcycle shifts in the harmonic emission spectrum as a function of the time delay between the XUV and NIR pulses. In the region where the two pulses overlap, the photon emission peaks have an oscillatory structure with a period of $\sim 1.3$ fs, which is half of the NIR laser optical cycle. We present and analyze the harmonic emission spectra from $3sn{p}_0,3p_{0}ns,3p_{1}n{d}_1,3p_{1}n{p}_1,3p_{0}n{d}_0,3p_{0}n{p}_0$, and $3p_{0}ns$ excited states and the $3p_{0}4p_0^{-}$ virtual state as functions of the time delay. In addition, we explore the subcycle a.c. Stark shift phenomenon in NIR fields and its influence on the harmonic emission process. Our analysis reveals several features of the subcycle HHG dynamics and spectra as well as a temporal energy level shift.

Figure 1

Photon emission energy spectrum of the $3p_{0}4s$ excited state and the $3p_{0}4p_0^{-}$ virtual state as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP. One-NIR laser optical cycle is equal to 2.5 fs.

Figure 2

Photon emission energy spectrum of the $3p_{0}3d_0$ excited state as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP.

Figure 3

Photon emission energy spectrum of the $3p_{1}3d_1$ excited state as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP.

Figure 4

Photon emission energy spectrum of the $3p_{0}5s$ excited state as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP.

Figure 5

Photon emission energy spectrum of the $3p_{0}6s$ or $3p_{0}4d_0$ (near resonance) excited states as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP.

Figure 6

Photon emission energy spectrum of the $3p_{1}n{d}_1$ $\left(n=4,5,\text{and}6\right)$ excited states as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP.

Figure 7

Photon emission energy spectrum of the $3s4p_0$ excited state as a function of the time delay between the NIR pulse and the SAP. The yellow color indicates the highest energy emitted. The color bars are represented by the ${log}_{10}S\left(\omega \right)$ of the spectral density in Eq. (11). Negative delays indicate the NIR pulse arrives on target before the SAP.