Quantum oscillations between close-lying states mediated by the electronic continuum in intense high-frequency pulses

The dynamics of neighboring states exposed to short intense laser pulses of carrier frequencies well above the ionization threshold of the system is investigated theoretically in the dipole approximation. It is shown that the ionizing pulse induces a time-dependent non-Hermitian coupling between these states determined by the Raman coupling and the direct ionization probability. This coupling induces quantum oscillations between the neighboring states while the strong pulse is on. The phenomenon opens the possibility to achieve a coherent control over the populations of neighboring states by short intense ionizing pulses. The present numerical results suggest exciting applications for free-electron lasers and attosecond experiments.

Figure 1

Results for the model of two neighboring electronic states of which one is initially unpopulated. The system is exposed to a high-frequency ionizing laser pulse (see text for details). Upper panel shows residual populations of the states after the ionizing pulse has expired as a function of the peak intensity of the pulse. Population transfer between the states and quantum oscillations are clearly seen. Lower panel shows photoelectron spectra for the peak intensity ${10}^{15}{\mathrm{W}/\mathrm{cm}}^2$. Due to the population transfer dictated by the non-Hermitian coupling between the states in Eq. (6), each spectrum exhibits two peaks instead of only one expected in a weak field at either 29.9 or 30.1 eV as indicated by vertical lines.

Figure 2

Results for the model of two neighboring electronic states where both are initially coherently populated, for example, by a pump pulse (conditions at $t=0$: $a_1^0=a_2^0=1/\sqrt{2}$). After a time delay of $\Delta t$ the system is exposed to a weak high-frequency ionizing probe pulse (see text for details). Upper panel shows the total ionization yield (solid curve) and residual populations of the states after the probe pulse has expired (broken curves) as a function of the time-delay between the pump and probe pulses. Lower panel shows the photoelectron spectra computed for those time delays $\Delta t$ which are indicated in the upper panel by vertical arrows.

Figure 3

As in Fig. 2 except that the probe pulse is now more intense (peak intensity ${10}^{15}$ instead of ${10}^{13}{\mathrm{W}/\mathrm{cm}}^2$). In addition to Fig. 2, the spectra computed by neglecting the pulse-induced coupling between the states are also shown for comparison in the lower panel (dashed curves).