Modifying H${}^{-}$ resonance asymmetries with short light pulses

We present a method based on time-dependent perturbation theory and complex rotation to treat the interaction of a short light pulse with a correlated atomic system. The pulse is built from two short and weak pulses with Gaussian envelopes that are centered at two different frequencies. The method is applied to the negative hydrogen ion in the vicinity of a doubly excited resonance and it is shown that the two light pulses can be used to alter the Fano profile of a resonance.

Figure 1

Overview of resonances that can be reached with two photons from the H${}^{-}$ ground state in the region just below the H($n=2$) threshold. The ${}^1{S}^{\text{e}}$ channel is shown in blue (solid line) and the ${}^1{D}^{\text{e}}$ channel in red (dashed-dotted line). The vertical line at $-0.125$ a.u. shows the position of the H($n=2$) threshold.

Figure 2

Example of a vector potential used in the present calculations. The upper panel shows the two pulses as a function of time. The lower panel shows the Fourier transform of the $A$ field. The pulses are chosen such that absorption and/or emission of photons corresponding to the energy of the central frequencies of both pulses match the excitation energy of the ${}^1{S}^{\text{e}}$ resonance. In this example absorption of the central frequency of the higher-energy pulse (blue dashed-dotted line), corresponding to $\sim$13 eV is sufficient to reach the $H(n=3)$ threshold, at $\sim$12.8 eV. Through subsequent emission of a photon with an energy corresponding to the central frequency of the lower-energy pulse (solid red line) the ${}^{1}S$ resonance, at $\sim$10.3 eV, can be populated.

Figure 3

Energy-level diagram of H${}^{-}$ showing ground state and resonances of ${}^{1}S$ and ${}^{1}P$ symmetry up to the H$(n=3)$ threshold. States of even ${}^{1}S$ symmetry are shown with blue short dashed lines and those of odd ${}^{1}P$ symmetry with red long dashed lines. The arrows show the central frequencies of the three different investigated light pulses.

Figure 4

Upper panel shows the energy distribution in the vicinity of the ${}^1{S}^{\text{e}}$ resonance after exposure to a light field consisting of two equal pulses, each with a central frequency matching half the needed excitation energy ($0.19\text{a.u.}\approx 5.2$ eV). Lower panel shows the vector potential.

Figure 5

Upper panel shows the energy distribution in the vicinity of the ${}^1{S}^{\text{e}}$ resonance after exposure to a light field consisting of one pulse with a central frequency corresponding to $0.10\text{a.u.}\approx 2.7$ eV, and one with a central frequency corresponding to $0.28\text{a.u.}\approx 7.$6 eV. Lower panel shows the vector potential.

Figure 6

Upper panel shows the energy distribution in the vicinity of the ${}^1{S}^{\text{e}}$ resonance after exposure to a light field consisting of one pulse with a central frequency corresponding to $0.48\text{a.u.}\approx 13.1$ eV, and one with a central frequency corresponding to $0.10\text{a.u.}\approx 2.7$ eV. Lower panel shows the vector potential.

Figure 7

Comparison between energy distributions in vicinity of the ${}^1{S}_e$ resonance at $\sim -0.15$ a.u. for different light pulses. The three profiles are normalized to the same maximum height to facilitate comparison.

Figure 8

Fano profile fits [cf. Eq. (32)] of the resonance profile when excited with different light pulses. The blue dots show the calculated points and the red lines are the fits. The left panel shows the profile after excitation with one pulse where the central frequency matches half of the excitation energy (cf. Fig. 4). The middle panel shows the profile after excitation with two pulses centered at different frequencies, both tuned below the excitation energy (cf. Fig. 5), and the right panel shows the profile when the frequency of one of the pulses is tuned above the excitation energy (cf. Fig. 6). The dimensionless parameter $\eta$, as well as the asymmetry parameter $q$, are defined in Eq. (32). The three profiles are normalized to the same height.