Attosecond counter-rotating-wave effect in xenon driven by strong fields

We investigate the subfemtosecond dynamics of a highly excited xenon atom coherently driven by a strong control field at which the Rabi frequency of the system is comparable to the frequency of a driving laser. The widely used rotating-wave approximation breaks down at such fields, resulting in features such as the counter-rotating-wave (CRW) effect. We present a time-resolved observation of the CRW effect in the highly excited $4d^{-1}np$ xenon using attosecond transient absorption spectroscopy. Time-dependent many-body theory confirms the observation and explains the various features of the absorption spectrum seen in experiment.

Figure 1

Experimental setup for attosecond transient absorption spectroscopy Attosecond XUV pulses are generated from neon gas, using few-cycle femtosecond NIR pulses (4 fs, 800 nm, 0.3 mJ). A concentric two-segment curved mirror along with a special metal filter (see Appendix), separates the attosecond XUV and the NIR pulses and provides a precision delay between them. The two beams are then focused collinearly onto a quasistatic gas cell containing xenon as a target gas. The absorption spectrum is obtained by measuring the transmitted spectrum $\left(I_{\mathrm{gas}}\right)$ from the gas target and also a spectrum in the absence of the gas target $\left(I_0\right)$ as a function of delay between NIR and XUV pulses.

Figure 2

Attosecond transient absorption spectrum of Xe. (a) Experimental absorption spectra at different delays between XUV and NIR pulse at NIR intensity of about $2\times {10}^{13}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. (b) TDCIS calculations under similar conditions. (c) Inner-shell excited states of xenon with a hole in the $4d_{5/2}$ and $4d_{3/2}$ shell. The ionization thresholds of the various shells are shown in the third column. (d) Subcycle oscillation seen at the 65-eV line ($4d_{5/2}^{-1}6p$, blue curve) in the experimental spectrum, averaged over 200 meV bandwidth shown using two black lines in (a). The $cos\left(2\omega \tau \right)$ fit to the experimental data is shown in red. Negative delays correspond to the arrival of an XUV pulse before an NIR pulse.

Figure 3

Change of absorption line of the $4d_{5/2}^{-1}6p$ state for different conditions of the control field. (a) Calculations are done for different intensities (1, 2, $4\times {10}^{13}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$). As the ratio of Rabi frequency to the control field frequency increases, the oscillating features become more prominent. (b) Calculations are done at a fixed intensity of $2\times {10}^{13}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$ with scaling the separation of all the $4d_{5/2}^{-1}nd, 4d_{5/2}^{-1}ns$ states with respect to the $4d_{5/2}^{-1}6p$ state by a factor of 0.5, 1, and 1.5. As the scaling increases, the oscillating effect diminishes considerably.

Figure 4

CRW oscillation in the $4d_{5/2}^{-1}6p$ absorption line for different IR pulse durations. Calculations are done for (a) 5.3 fs (1.7 cycles) and (b) 21.3 fs (6.9 cycles) pulses. For both cases, the field strength is kept the same; namely, $\mathrm{\Omega }/\omega$ is the same. (c) The cut along an Autler-Townes branch [indicated by the black lines in (a), (b)] is shown. The amplitudes are rescaled so that they are in the same range. The $2\omega$ oscillation (period is $\sim 1.6\mathrm{fs}$) is clearly seen for both pulses in the overlapping region, which is highlighted in gray for the 5.3-fs pulse in (c).

Figure 5

(a) Raw transient absorption spectrum obtained for xenon and various delays between IR and XUV pulse. (b) The spectrum obtained after smoothening and filtering the original spectrum shown in (a).