Quantum interference in laser-induced nonsequential double ionization

Quantum interference plays an important role in various intense-laser-driven atomic phenomena, e.g., above-threshold ionization and high-order-harmonic generation, and provides a useful tool in ultrafast imaging of atomic and molecular structure and dynamics. However, it has eluded observation in nonsequential double ionization (NSDI), which serves as an ideal prototype to study electron-electron correlation. Thus far, NSDI usually could be well understood from a semiclassical perspective, where all quantum aspects have been ignored after the first electron has tunneled. Here we perform coincidence measurements for NSDI of xenon subject to laser pulses at 2400 nm. It is found that the intensity dependence of the asymmetry parameter between the yields in the second and fourth quadrants and those in the first and third quadrants of the electron-momentum-correlation distributions exhibits a peculiar fast oscillatory structure, which is beyond the scope of the semiclassical picture. Our theoretical analysis indicates that this oscillation can be attributed to interference between the contributions of different excited states in the recollision-excitation-with-subsequent-ionization channel. Our work demonstrates the significant role of quantum interference in NSDI and may create an additional pathway towards manipulation and imaging of the ultrafast atomic and molecular dynamics in intense laser fields.

Figure 1

Picture of the ionization pathways of RESI. The thick blue horizontal arrow indicates the time axis. The blue curve denotes the laser electric field. As time evolves, one of the valence electrons is liberated through tunneling at $t_b$. This electron is accelerated into a recollision with the core at the time $t_c$ when there are two pathways: (i) it will knock out the other electron to induce double ionization (RII) (not shown here) or (ii) it will pump the core into one of several excited states and the excited core will be further ionized by the laser electric field (RESI) at $t_i$. One typical rescattering orbit is indicated by the black curve. The electron wave packets from different excited-core channels will interfere, which leads to an oscillation of the intensity dependence of the asymmetry parameter of the EMCD (see text for details). The three pictures in the lower part depict three key steps of the physical process in question.

Figure 2

Measured longitudinal momentum distributions of (a)–(c) the ${\mathrm{Xe}}^{2+}$ ion and (d)–(f) the EMCDs from NSDI of Xe by a linearly polarized laser field at 2400 nm. The laser intensities are as follows: (a), (d) $I=1.7\times {10}^{13}$ W/${\mathrm{cm}}^2$; (b), (e) $I=3.2\times {10}^{13}$ W/${\mathrm{cm}}^2$; and (c), (f) $I=4.8\times {10}^{13}$ W/${\mathrm{cm}}^2$. (g) Measured asymmetry parameter $\alpha$ as a function of the laser intensity for NSDI of Xe at 2400 nm.

Figure 3

Semiclassical simulation results corresponding to the experimental results of Fig. 2. The calculated asymmetry parameter $\alpha$ includes (a) all DI events, (b) only RII events, and (c) only RESI events. The EMCDs are calculated for RESI at (d) $2.0\times {10}^{13}$ W/${\mathrm{cm}}^2$, (e) $4.0\times {10}^{13}$ W/${\mathrm{cm}}^2$, and (f) $6.0\times {10}^{13}$ W/${\mathrm{cm}}^2$. These intensities are indicated by the red arrows in (c).

Figure 4

The asymmetry parameters $\alpha$ calculated with the SFA (a) for the RII process and (b) for the RESI process. For the red arrows in (b), see the caption of Fig. 5.

Figure 5

EMCDs of the two electrons for RESI pathway based on the SFA calculation at three typical intensities, which are indicated by the red arrows in Fig. 4: (a), (d), (g) $1.7\times {10}^{13}$ W/${\mathrm{cm}}^2$; (b), (e), (h) $2.6\times {10}^{13}$ W/${\mathrm{cm}}^2$; and (c), (f), (i) $5.3\times {10}^{13}$ W/${\mathrm{cm}}^2$. (a)–(c) $5p^{4}5d$ channel, (d)–(f) $5p^{4}6s$ channel, and (g)–(i) coherent sum of the two channels.

Figure 6

Real part (the first row) and imaginary part (the second row) of the transition amplitude vs momentum of the second electron at different intensities. See the text for more details. (a), (b) $1.7\times {10}^{13}$ W/${\mathrm{cm}}^2$, (c), (d) $2.6\times {10}^{13}$ W/${\mathrm{cm}}^2$, and (e), (f) $5.3\times {10}^{13}$ W/${\mathrm{cm}}^2$.