Transition from correlated to single-active-electron excitation in strontium nonlinear ionization

The nonlinear single and double ionization of Sr atoms as a result of their interaction with 800-nm Ti-sapphire laser pulses of 25-fs duration is experimentally investigated within the laser intensity range $I=3\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}–30\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$. The latter range includes the over-the-barrier intensities for both Sr and ${\mathrm{Sr}}^{+}$, while the corresponding Keldysh adiabaticity parameters are larger than unity. Nevertheless, for $I\ge 24\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$ the recorded photoelectron-energy spectra show evidence of the (partial) applicability of tunneling or over-the-barrier ionization concepts, whereas below this value they can be discussed in terms of multiphoton ionization processes. More importantly, the data additionally point towards a further division of the multiphoton regime into two subranges separated roughly at $I\sim 4\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$. Above this value above-threshold-ionization structures and the single-active-electron picture dominate. On the contrary, at the lowest laser intensities the photoelectron spectra and angular distributions reveal single ionization pathways where the remaining ion is left into excited states. These pathways also require photon absorption in the continuum, which in the case of strontium and other alkaline-earth-metal atoms is structured by the presence of doubly excited states which are embedded in it. Hence, in this case ionization proceeds via quasiresonant ionization ladders formed by these doubly excited states which are dominated by the interaction between the two valence electrons of Sr. We discuss in detail the above rich phenomenology and relevant ionization mechanisms and propose possible directions of further work towards the elucidation of the role of configuration interaction in ionization processes.

Figure 1

Partial, in-scale, energy-level diagram of Sr, depicting the most relevant atomic and ionic levels as well as the possible multiphoton single and double-ionization pathways. Dark gray shadings denote the ionization threshold and continua associated with each ionic level and the double-ionization limit. Light gray shading denotes the three- and four-photon effective laser bandwidth [49]. For the labeling of ionization processes see the text [and Eqs. (3, 4, 5, 6, 7, 8, 9)].

Figure 2

Schematic diagram of a ladder excitation scheme describing a possible (out of several) $5p_j\left(0\right)$ ionization pathway producing excited ions [Eq. (5)]. Gray shading denotes the ionization thresholds and continua associated with $5s$, 4d, and $5p_j$ ionic levels. At this particular scheme each ladder step involves single-electron transitions but, overall, both valence electrons are excited. Such ladders necessitate the existence of electron-electron correlation leading to strong configuration interaction and level structure embedded in the continuum, the latter characterizing Sr and the other alkaline-earth-metal atoms. Note that the experiment probes the population created in the excited ionic state but not the exact ladder scheme.

Figure 3

Log-log plots of the measured singly and doubly charged Sr yields as a function of laser intensity (lower $x$ axis) and as a function of the atomic and ionic Keldysh parameters ${\gamma }_{\mathrm{Sr}}$ and ${\gamma }_{{\mathrm{Sr}}^{+}}$, respectively (upper $x$ axes). Whenever the $y$ axis uncertainties are not indicated they are on the order of the symbol size. A dashed straight line corresponding to an $I^4$ intensity dependence is matched to the unsaturated part of the ${\mathrm{Sr}}^{+}$ curve. The latter is separated from the saturated one by the vertical dashed-dotted line. A quantifiable ${\mathrm{Sr}}^{2+}$ signal appears for intensities above the ${\mathrm{Sr}}^{+}$ saturation intensity. A fit of the doubly charged ion signal as a function of $I$ yields an $I^{3.0\pm 0.1}$ intensity dependence (not shown).

Figure 4

Electron-energy spectra acquired at the laser intensity values specified at each plot. The maximum signal of each PES is set equal to unity. In (a) the members of the atomic and ionic ATI series discussed in the text are indicated. The corresponding inverted (and symmetrized) image given in the inset shows the photoelectron momentum distributions (in atomic units, a.u.)/PADs. For better visibility of its weak features the image is drawn in logarithmic color scale covering three orders of magnitude (see the given color bar). The white double-headed arrow shows the direction of the linear laser polarization. Note that in (b) the number of ATI members increases further and a background starts to build up, while this background dominates in (c) and the ATI structure is greatly washed out.

Figure 5

Electron-energy spectra acquired at the lower intensity range $3.7–5\mathrm{TW}\mathrm{c}{\mathrm{m}}^{\text{–}2}$. The location of each spectrum along the $y$ direction is proportional to the intensity of the particular recording which is specified at each plot. For facilitating the discussion given in the text the graph also includes the predictions of Eq. (1) for the single-ionization pathways of Eqs. (3, 4, 5, 6, 7), ($k=0$ full vertical lines, $k>0$ dashed vertical lines) after including only the ponderomotive shift $U_p$. The $5s^2$ ground state AC Stark shift is ignored (i.e., $\mathrm{\Delta }{E}_{5s^2}=0$) because its inclusion using the existing theoretical value [57] considerably worsens the agreement with all experimental data. Furthermore, since within this intensity range double ionization is not apparent in Fig. 3, the relevant ionization processes are not included in the graph (for a more detailed discussion of this point see text).

Figure 6

(a) Inverted (and symmetrized) VMI images recorded at the indicated laser intensities. A logarithmic color scale covering three orders of magnitude is employed for better visibility of their weak features (see the given color bar). The scales of the vertical and horizontal axes are given for a single image but apply to all of them. They are expressed in atomic units of momentum. (b) Normalized polar plots of the PADs obtained from the images in (a) for the indicated electron energies. The evolution of their shapes with intensity and energy is discussed in the text. The angle θ with respect to which the PADs are described is shown in one distribution and it is measured with respect to the linear laser polarization. The direction of the latter is denoted by the black double-headed arrow drawn in (a).