Limit on Excitation and Stabilization of Atoms in Intense Optical Laser Fields

Atomic excitation in strong optical laser fields has been found to take place even at intensities exceeding saturation. The concomitant acceleration of the atom in the focused laser field has been considered a strong link to, if not proof of, the existence of the so-called Kramers-Henneberger (KH) atom, a bound atomic system in an intense laser field. Recent findings have moved the importance of the KH atom from being purely of theoretical interest toward real world applications; for instance, in the context of laser filamentation. Considering this increasing importance, we explore the limits of strong-field excitation in optical fields, which are basically imposed by ionization through the spatial field envelope and the field propagation.

Figure 1

Schematic sketch of the experimental setup and actual measurements of the atomic distribution on the detector. The laser intensities for (a)–(e) are the same as in Figs. 2, respectively.

Figure 2

Measured and calculated deflection of the c.m. of excited atoms after exposing ground state He atoms to laser pulses with the indicated peak intensities $I_0$ of (a) 1.3, (b) 4.4, (c) 8.8, (d) 13 and (e) 18 PW ${\text{cm}}^{-2}$. Experimental data, black curves; calculated distribution for bound trajectories, red (grey) curves; c.m. deflections for unbound trajectories, dashed blue curves. The vertical dashed green lines indicate the limits of deflection.

Figure 3

Population of excited states as a function of the radial distance $u$ for different peak intensities $I_0$ of (a) 4.4, (b) 8.8, (b) 13 and (d) 18 PW ${\mathrm{cm}}^{-2}$. The upper axis shows the intensity $I(u)$ normalized to the peak intensity $I_0$. The laser field is taken into account in the dipole approximation [the red (grey) curves], a plane-wave approximation (the black curves), and as a full field [the blue (noisy) curves]. The dashed curves give the population with double ionization included, the solid curves without. The dotted green curve gives the intensity gradient with the scale on the right side. Note that the population in the full field calculations [the blue (noisy) curves] oscillate erratically due to the combination of a reduced number of trajectories captured into bound states at high intensity gradients and a lower sampling volume.

Figure 4

The $n$ distributions (a) for a plane wave at different peak intensities, (b) for dipole approximation at a fixed effective intensity of $I=5.3\mathrm{PW}{\mathrm{cm}}^{-2}$ but including also the spatial field envelope at positions in the focus corresponding to different gradients, and (c) at a peak intensity $I_0=8.8\mathrm{PW}{\mathrm{cm}}^{-2}$ for the pure dipole approximation ($D$) and additionally including the field envelope at $w_0/2$ ($D+G$) and full field (full). (d) As in (c), except for $I_0=17.7\mathrm{PW}{\mathrm{cm}}^{-2}$. (e) TDSE calculations for a 40 fs laser pulse (${\cos }^2$ envelope), in the dipole approximation at a peak intensity $I_0=10\mathrm{PW}{\mathrm{cm}}^{-2}$ ($D_1$); at an effective intensity $I=6\mathrm{PW}{\mathrm{cm}}^{-2}$ (which corresponds to $u=w_0/2$) ($D_2$); and as ($D_2$), but with the field gradient ($D_2+G$).