Rabi oscillations in extreme ultraviolet ionization of atomic argon

We demonstrate Rabi oscillations in nonlinear ionization of argon by an intense femtosecond extreme ultraviolet (XUV) laser field produced by high-harmonic generation. We monitor the formation of $\mathrm{A}{\mathrm{r}}^{2+}$ as a function of the time delay between the XUV pulse and an additional near-infrared (NIR) femtosecond laser pulse, and show that the population of an $\mathrm{A}{\mathrm{r}}^{+*}$ intermediate resonance exhibits strong modulations both due to an NIR laser-induced Stark shift and XUV-induced Rabi cycling between the ground state of $\mathrm{A}{\mathrm{r}}^{+}$ and the $\mathrm{A}{\mathrm{r}}^{+*}$ excited state. Our experiment represents a direct experimental observation of a Rabi-cycling process in the XUV regime.

Figure 1

$\mathrm{A}{\mathrm{r}}^{2+}$ ion yield as a function of the XUV pump-NIR probe time delay for different NIR intensities. The experimental yields (symbols) were extracted by integrating $\mathrm{A}{\mathrm{r}}^{2+}$ signals over 256 laser shots. The error bars correspond to the standard deviation of two independent measurements. Different symbols correspond to different intensities indicated on the left side as a fraction of $I_{\mathrm{NIR}}^{\mathrm{MAX}}$. Numerical modeling yields $I_{\mathrm{NIR}}^{\mathrm{MAX}}=2.0\times {10}^{12}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$. The experimental data is fitted (continuous lines) using the expression given in Eq. (4) for $t\to \infty$. Vertical black lines at 0 and 50 fs time delay indicate modulations in the $\mathrm{A}{\mathrm{r}}^{2+}$ ion yield explained in the text.

Figure 2

(a) Experimental $\mathrm{A}{\mathrm{r}}^{2+}$ (blue dots) and $\mathrm{A}{\mathrm{r}}^{+}$ yield (red triangles), and their sum (black diamonds) as a function of the XUV-NIR time delay for $I_{\mathrm{NIR}}^{\mathrm{MAX}}$. Continuous lines are a linear fit of the summed yield (black) and sigmoidal fits of the $\mathrm{A}{\mathrm{r}}^{2+}$ and $\mathrm{A}{\mathrm{r}}^{+}$ yields (blue and red), respectively. The ionic yields were extracted by integrating over 256 laser shots. The error bars correspond to the standard deviation of nine independent measurements. (b) Log-log plot of the $\mathrm{A}{\mathrm{r}}^{2+}$ yield as a function of the $\mathrm{A}{\mathrm{r}}^{+}$ yield, obtained by recording 1000 single-shot time-of-flight spectra at a 300 fs XUV-NIR time delay, for $I_{\mathrm{NIR}}^{\mathrm{MAX}}$. The dots are the mean of binned experimental data and the error bars correspond to the standard deviation. The linear fit (continuous blue line) gives a slope of $1.99\pm 0.11$, and illustrates that the $\mathrm{A}{\mathrm{r}}^{2+}$ yield depends quadratically on the XUV intensity.

Figure 3

(a) Angle-integrated low kinetic energy photoelectron spectrum for ionization of Ar atoms with an XUV pump and an NIR probe delayed by 300 fs, derived from the normalized differential two-color 2D photoelectron momentum distribution shown in the inset. (b) Energy diagram (not scaled), depicting double ionization of Ar by two XUV photons, where the second XUV photon is H17, and one NIR photon. Excited ions, $\mathrm{A}{\mathrm{r}}^{+*}$, prepared by absorption of the H17 photon, are ionized by the NIR photon.

Figure 4

Populations, $|C_0\left(t\right){|}^2$ (continuous green line) and $|C_1\left(t\right){|}^2$ (continuous orange line), of the $\mathrm{A}{\mathrm{r}}^{+}$ ground and excited states, respectively, along with the relative field envelopes, $f_{\mathrm{NIR}}\left(t\right)$ (dashed red line) and $f_{\mathrm{XUV}}\left(t\right)$ (dashed blue line) and the time-integrated ionization probability $S_{\mathrm{A}{\mathrm{r}}^{2+}}\left(t\right)$ (dotted black line), for $I_{\mathrm{NIR}}^{\mathrm{MAX}}$, at two XUV-NIR pulses delay times: (a) 0 fs, (b) 50 fs, and (c) 130 fs.