Buildup time of Autler-Townes splitting in attosecond transient absorption spectroscopy

Although the time-dependent buildup processes of Autler-Townes splitting in attosecond transient absorption spectra have been observed in plenty of experiments, there still exists an open question of when the splitting is maximized, which tells us how fast the system responds to the pump field and how well the adiabatic following is in a slowly varying few-cycle laser pulse. In this Letter we work out a compact formula to quantify the buildup time of the Autler-Townes splitting, which is related to multiple timescales of the laser-atom system, e.g., the Rabi period, the laser cycle, and the pulse duration, according to a universal power law. This scaling law applies not only to singly excited states, but also to doubly excited states in which complex electron-electron interaction gets involved. Our findings have potential applications in calibrating the zero delay in a transient absorption spectroscopy.

Figure 1

(a) Scheme of the attosecond transient absorption spectroscopy. (b) Absorption line profiles at several typical time delays, where a clear signature of the Autler-Townes splitting can be seen, but the splitting does not maximize at the zero delay; instead, it maximizes at around $\tau =T$ in this example.

Figure 2

(a) Simulated ATAS under the RWA condition. The black solid lines are the quasistatic Floquet states calculated following the envelope of the IR pulse. The laser parameters are $I=5\mathrm{TW}/{\mathrm{cm}}^2, {\omega }_{\text{IR}}=0.82\mathrm{eV}$, and $n=10$. (b) Line profile at the frequencies ${\omega }_{\text{AT}}={\mathrm{\Delta }}_{ga}\pm \frac{{\mathrm{\Omega }}_0}{2}$ (white dashed line) as a function of the time delay. The red dashed curve shows a universal line profile predicted by Eq. (2). The results are normalized at the peak for clear comparison. Also shown is (c) the effect of avoided crossing in the superstrong-coupling regime ($I=20\mathrm{TW}/{\mathrm{cm}}^2$) and (d) the CEP effect in the few-cycle limit ($n=3$). See the text and [48] for details.

Figure 3

Buildup time of the Autler-Townes splitting for different laser parameters: (a) the pulse duration, (b) the laser wavelength, and (c) the laser intensity. In each plot, when the variable indicated by the horizontal axis is changed, the other parameters are kept the same as that given in Fig. 2. The solid lines are the analytical predictions by Eq. (3). The scatters are numerical results calculated in the frameworks of the RWA (red $•$) and the non-RWA (gray $▴$ and $▾$ for the upper and lower branches, respectively, due to the symmetry break). The shaded area represents the SSC regime.

Figure 4

Ab initio calculation of the ATAS of He at $5\mathrm{TW}/{\mathrm{cm}}^2$ and ${\varphi }_{\text{CEP}}=0$. The white solid lines show the quasistatic Floquet states corrected by the AC Stark effect and then displaced by an amount of time as predicted by Eq. (4), which fully explains the main structures of the ATAS.