Resonance-induced ionization enhancement and suppression of circular states of the hydrogen atom in strong laser fields

We theoretically investigated the ionization dynamics of a hydrogen atom in circular excited states irradiated by the circularly polarized laser pulses by solving the time-dependent $\mathrm{Schr}\ddot{\mathrm{o}}\mathrm{dinger}$ equation. We calculated the ionization yields of the two excited states which are corotating and counter-rotating with respect to the laser fields as a function of the laser frequency. For the corotating excited state, our results show an obvious ionization suppression when the laser frequency is beyond the one-photon ionization threshold, and it is followed by a strong ionization enhancement when the laser frequency further increases. These ionization suppressions and enhancements are absent for the counter-rotating excited state. By tracing the ionization process, we found that resonance between the initial state and a lower-energy state occurs at the frequency of the ionization enhancement. Ionization from this lower-energy state is responsible for this ionization enhancement. At the frequency of ionization suppression, Rabi oscillation between the initial and the lower-energy state occurs, which prevents further ionization and thus suppresses the final ionization yield.

Figure 1

The ionization probabilities of two initial states of hydrogen atoms as a function of the laser frequency. The upper axis represents the Keldysh parameters, corresponding to the laser frequencies. In the legend “Co” indicates the initial state $(n,l,m)$ = (3,2,2) corotating with respect to the laser field, and “Counter” represents the initial state (3,2,-2) counter-rotating with respect to the laser field. The vertical dashed and dashed-dotted lines indicate the two- and one-photon ionization thresholds, respectively. The laser intensity is $8\times {10}^{12}$ W/${\mathrm{cm}}^2$. The pulse durations are (a) $\tau =8$ T and (b) $\tau =30$ T.

Figure 2

The ionization probabilities of two initial states of hydrogen atoms as a function of the laser frequency. In the legend “Co” indicates the initial state $(n,l,m)$ = (3,2,2) corotating with respect to the laser field, and “Counter” represents the initial state (3,2,-2) counter-rotating with respect to the laser field. The vertical dashed-dotted line indicates the one-photon ionization threshold. The laser intensities are $1\times {10}^{12}$ W/${\mathrm{cm}}^2$ for the cycles and triangles and $5\times {10}^{11}$ W/${\mathrm{cm}}^2$ for the squares and asterisks, respectively. The pulse duration is $\tau =30$ T.

Figure 3

The diagram of excitation pathways according to the dipole selection rules in lowest-order perturbation theory for (a) the corotating initial state $(n,l,m)=(3,2,2)$ and (b) the counter-rotating state (3,2,-2). The horizontal axis represents the angular quantum number $L$, and the vertical axis represents the magnetic quantum number $m$. The yellow (light gray) rectangle represents the initial state, and the green (dark gray) rectangle represents the excited states which are allowed by the dipole selection rules. The red (dark gray) arrow represents absorbing one photon and the blue hollow arrow represents emitting one photon.

Figure 4

The distribution of ($l,m$) states obtained by summing over $n$ by solving the 3D-TDSE for (a) corotating initial state $(n,l,m)=(3,2,2)$ and (b) counter-rotating initial state (3,2,-2) at the end of the laser pulse. The black asterisks mark the initial states. The horizontal axis represents the angular quantum number $L$ and the vertical axis represents the magnetic quantum number $m$. The laser frequency, laser intensity, and pulse duration are $\omega =0.027\text{a.u}.$, $I$ = $8\times {10}^{12}$ W/${\mathrm{cm}}^2$ and $\tau =8\text{T}$, respectively.

Figure 5

The $m$ distributions as a function of time by solving 3D-TDSE for (a) the corotating initial state $(n,l,m)$ = (3,2,2) and (b) the counter-rotating initial state (3,2,-2). The laser intensity is $8\times {10}^{12}$ W/${\mathrm{cm}}^2$, the pulse duration is $\tau =8\text{T}$, and the laser frequency is $\omega =0.081\text{a.u}.$ The red (dark gray) arrow represents absorbing one photon, and the blue hollow arrow represents emitting one photon.

Figure 6

The distribution of $m$ states as a function of time for the corotating initial state (3,2,2) and different laser frequencies for (a), (c) 0.066 a.u. and (b), (d) 0.081 a.u. Here the laser intensities are $8\times {10}^{12}$ W/${\mathrm{cm}}^2$ and the pulse durations are $\tau =8$ T. The red (dark gray) arrow represents absorbing one photon, and the blue hollow arrow represents emitting one photon.

Figure 7

The same as those in Fig. 6 but for pulse duration $\tau =30$ T.

Figure 8

The distribution of (a) $m=3$, (b) $m=2,$ and (c) $m=1$ states as a function of time and laser frequency for the corotating initial state H(3,2,2). The white dotted lines represent the single-photon ionization threshold $\omega =0.056$ a.u. The white ellipse represents the resonance region. The laser intensity is $8\times {10}^{12}$ W/${\mathrm{cm}}^2$, and the pulse duration is $\tau =8$ T.

Figure 9

The same as those in Fig. 8 but for $\tau =30$ T pulse duration.