First-principles nonequilibrium Green's-function approach to transient photoabsorption: Application to atoms

We put forward a first-principle nonequilibrium Green's-function (NEGF) approach to calculate the transient photoabsorption spectrum of optically thin systems. The method can deal with pump fields of arbitrary strength, frequency, and duration as well as overlapping and nonoverlapping pump and probe pulses. The electron-electron repulsion is accounted for by the correlation self-energy, and the resulting numerical scheme deals with matrices that scale quadratically with the system size. Two recent experiments, the first on helium and the second on krypton, are addressed. For the first experiment we explain the bending of the Autler-Townes absorption peaks with increasing pump-probe delay $\tau$ and relate the bending to the thickness and density of the gas. For the second experiment we find that sizable spectral structures of the pump-generated admixture of Kr ions are fingerprints of dynamical correlation effects, and hence they cannot be reproduced by time-local self-energy approximations. Remarkably, the NEGF approach also captures the retardation of the absorption onset of ${\mathrm{Kr}}^{2+}$ with respect to ${\mathrm{Kr}}^{1+}$ as a function of $\tau$.

Figure 1

Schematic illustration of a pump-probe experiment.

Figure 2

Diagrammatic representation of the 2B self-energy. Wiggly lines denote the Coulomb interaction $v$.

Figure 3

Density plot of the TPA spectrum (normalized to the maximum height) of a helium gas with ${\ell }_{\mathrm{eff}}=0.16$ mm and density $n^{\left(\mathrm{at}\right)}=2.4\times {10}^{17}$ ${\text{cm}}^{-3}$. Pump and probe pulses are given in the text. Results obtained with the CI (top left), HF (top right), 2B (bottom left), and Markovian 2B (MTB; bottom right).

Figure 4

Density plot of the TPA spectrum (normalized to the maximum height) of a helium gas with ${\ell }_{\mathrm{eff}}=1.6$ mm and density $n^{\left(\mathrm{at}\right)}=2.4\times {10}^{17} {\mathrm{cm}}^{-3}$. Pump and probe pulses are given in the text. Results obtained with the CI (top left), HF (top right), 2B (bottom left), and Markovian 2B (M2B; bottom right).

Figure 5

Density plot of $-\omega \mathrm{Im}\left[{\tilde{d}}_p\left(\omega \right)\right]/d_0$, with ${\tilde{d}}_p$ the Fourier transform of the function $d_p$ in Eq. (27), for ${\omega }_0=21.3$ eV, $E_0{d}_0=0.5$ eV, ${\gamma }_P=0.41$ eV and for $\gamma =0.21$ eV (left) and $\gamma =1.37$ eV (right).

Figure 6

Three-dimensional plot of $-\omega \mathrm{Im}\left[{\tilde{d}}_p\left(\omega \right)\right]/d_0$ (normalized to the maximum height), with ${\tilde{d}}_p$ the Fourier transform of the function $d_p$ in Eq. (27), as a function of the dipole lifetime $1/\gamma$ at delay $\tau =0$ for ${\omega }_0=21.3$ eV, $E_0{d}_0=0.2$ eV, ${\gamma }_P=0.125$ eV. Arrows indicate the extra peaks discussed in the text.

Figure 7

Transient ionization yield per spin (solid line) in the HF and 2B (indistinguishable) and amplitude of the pump pulse (dashed line) in arbitrary units.

Figure 8

TPA spectrum (normalized to the maximum height) of a krypton gas in the HF (top) and 2B (bottom) approximations. Dashed (white) lines in the bottom panel are guides for the eye, to better visualize the retardation effect. Pump and probe pulses are given in the text.