Controlling laser-dressed resonance line shape using attosecond extreme-ultraviolet pulse with a spectral minimum

Abstract

High-harmonic generation from a gas target exhibits sharp spectral features and rapid phase variation near the Cooper minimum. By applying spectral filtering, shaped isolated attosecond pulses can be generated where the pulse is split into two in the time domain. Using such shaped extreme-ultraviolet (XUV) pulses, we theoretically study attosecond transient absorption (ATA) spectra of helium [Formula: see text] autoionizing state which is resonantly coupled to the [Formula: see text] dark state by a time-delayed infrared laser. Our simulations show that the asymmetric [Formula: see text] Fano line shape can be readily tuned into symmetric Lorentzian within the time delay of a few tens of attoseconds. Such efficient control is due to the destructive interference in the generation of the [Formula: see text] state when it is excited by a strongly shaped XUV pulse. This is to be compared to prior experiments where tuning the line shape of a Fano resonance would take tens of femtoseconds. We also show that the predicted ATA spectral line shape can be observed experimentally after propagation in a gas medium. Our results suggest that strongly shaped attosecond XUV pulses offer the opportunity for controlling and probing fine features of narrow resonances on the few-ten attoseconds timescale.

Keywords: Cooper minimum; Fano resonance; attosecond transient absorption; doubly excited state.

Fig. 1.

(A) Schematic of a three-level model of a helium atom, including the ground state $1s^2$, autoionizing states $2s2p$ and $2s^2$, and continuum states $1sEp$ and $1sEs$, where $E$ is the energy of the continuum electron. In this model, the XUV pulse pumps the system from $1s^2$ to $2s2p$ and $1sEp$ states, and the IR laser couples $2s2p$ and $1sEs$ states and also $2s2p$ and $2s^2$ states. Through configuration interaction, the system decays from $2s2p$ to $1sEp$ state and from $2s^2$ to $1sEs$ state. (B) Electric envelopes of a Gaussian (blue) and a shaped (red) XUV pulses. (C) Spectral distributions of amplitude (solid line) and phase (dashed line) of a shaped XUV pulse taken from ref. . Single-atom ATA spectra from a Gaussian (D) and a shaped XUV (E) pulse. Parameters of the XUV pulse: duration is $\sim$ 200 as, peak intensity is 10${}^{10}$ W/cm${}^2$, and central frequency is 60.15 eV. Parameters of the dressed IR laser: pulse duration is 9 fs, carrier frequency is 2.3 eV (period is 1.8 fs), peak intensity is 2 $\times$ 10${}^{12}$ W/cm${}^2$, and carrier-envelope phase is 0. A positive time delay means the XUV pulse is ahead of the IR laser. (F) Analytic (dashed line) and fitted (dot) $q$ parameters for the ATA spectra using the shaped XUV pulse. (G–I) The absorption spectral lines (normalized) at selected time delays; see text.

Fig. 2.

(A and B) Populations of $2s2p$ (red solid lines) and $2s^2$ (blue solid lines) states at a time delay of 0 fs between the XUV pulse and the IR laser. In addition, the populations of $2s2p$ state without the IR laser (dashed green lines) and without the autoionizing configuration interaction (CI) (dashed black lines) are shown. Electric field envelopes of Gaussian and shaped XUV pulses are given (purple solid lines). Note that the population of $2s2p$ by shaped XUV pulse undergoes a sharp drop in the second half of the pumping process. (C and D) Populations of $2s2p$ and $2s^2$ states at the end of the XUV pulse as a function of time delay. (E) The ratio of $2s^2$ and $2s2p$ populations from (D). (F) Normalized populations of $2s2p$ and $2s^2$ states (plotted in linear scale) after complete shutdown of external fields as a function of time delay. Results for Gaussian pulse are moved up by one in arbitrary units. Comparison of absorption spectral lines using the shaped XUV pulse at time delays of 0 fs (G) and 0.45 fs (H) obtained by numerical solutions of TDSE and analytic solutions in Eq. 1. The dashed line in (G) is the fitted Lorentz curve.

Fig. 3.

(A) Sketch of a two-level model with the ground state $\left|g\right.〉$ and an excited state $\left|a\right.〉$ (Left), and the temporal profile of a shaped XUV pulse with two peak amplitudes, $A_1$ and $A_2$ (Right). (B) Population (normalized) of the excited state vs time when $A_2$ = $A_1$. (C) Same as (B) but for $A_2$ = 0.6$A_1$. Results obtained by numerical solutions of coupled equations (red lines) are compared to analytic solutions of Eq. 3 (black lines).

Fig. 4.

(A) Optical density (OD) after propagation in a 0.5-mm long gas with a pressure of 25 Torr by a shaped XUV pulse. (B) Macroscopic OD in a gas with a length of 0.1 mm and pressure of 5 Torr. (C) Macroscopic OD as a function of propagation distance at 25 Torr when the time delay is fixed at 0 fs. (D) OD lines in (B) for selected time delays.

Fig. 5.

ATA spectra when the minimum position of shaped XUV pulse is shifted by (A and B) 0.3 eV; (C and D) 0.9 eV; (E and F) 1.6 eV. Note that the oscillation with half optical period of IR laser can be clearly seen in (A), but not as obvious in (C) and (E).