Time-dependent susceptibility of a helium atom in intense laser pulses

We analyze the time-dependent nonlinear response of helium atom to a strong laser pulse in form of the induced nonlinear electric susceptibility. Our theoretical predictions are based on ab initio solutions of the time-dependent Schrödinger equation obtained using a numerical basis state method and the short-time Fourier transform. The results qualitatively reproduce features seen in recent experimental data. In particular, we observe deviations from the adiabatic (field-following) response in the electric susceptibility at high intensities. According to our analysis a shift of the peak towards the front of the pulse and changes in the concavity of the slope in the trailing edge of the pulse can be related to the population of continuum states and bound excited states with high angular quantum number during the interaction of the atom with the laser pulse.

Figure 1

Time-dependent susceptibility of helium interacting with intense laser pulses at a wavelength of 800 nm and a pulse length of 10 cycles (FWHM of the Gaussian envelope). Peak intensities are $150{\mathrm{TW}/\mathrm{cm}}^2$ (dashed-dotted line), $200{\mathrm{TW}/\mathrm{cm}}^2$ (dotted line), $250{\mathrm{TW}/\mathrm{cm}}^2$ (dashed line), and $300{\mathrm{TW}/\mathrm{cm}}^2$ (solid line). Time is given in terms of the electric field cycle, where $t=0$ cycles denote the center of the pulse.

Figure 2

(a) Field-free bound-bound contribution to the time-dependent susceptibility and (b) population in the field-free bound excited states of the spectrum, taken at the zeros of the driving field. Laser parameters and line styles are the same as in Fig. 1.

Figure 3

The same as Fig. 2, but for the continuum part of the field-free spectrum.

Figure 4

Same as Fig. 2 but for the cross-term contributions.

Figure 5

Population in (a) field-free bound states and (b) field-free continuum states with $l\le 1$. The lines represent the results of calculations for pulses with peak intensity $150{\mathrm{TW}/\mathrm{cm}}^2$ (dashed-dotted line), $200{\mathrm{TW}/\mathrm{cm}}^2$ (dotted line), $250{\mathrm{TW}/\mathrm{cm}}^2$ (dashed line), and $300{\mathrm{TW}/\mathrm{cm}}^2$ (solid line).

Figure 6

Same as Fig. 5, but for $l>1$.

Figure 7

Contributions to the total susceptibility from (a) low ($l\le 1$) and (b) high ($l>1$) angular momentum states. Laser parameters and line styles as in Fig. 5.