Attosecond interference in strong-field nonsequential double ionization

Kinetic-energy spectra of a single electron from strong-field nonsequential double ionization are investigated in a high-intensity regime with a quantum mechanical model. We find interference fringes with large energy spacings, which increases with the electron kinetic energy. These interference fringes originate from the electronic wave packets born in the recollision by the returning electronic wave packets from the “short” and the “long” quantum paths. Since the recollision happens in a fraction of a near-infrared (NIR) optical cycle, i.e., in an attosecond time interval, the resulting interference fringes exhibit energy spacings much larger than the NIR photon energy. The comparison of the quantum mechanical results with a classical collision model suggests a near-equal energy sharing between two electrons during the recollision process at very high intensities, in contrast to the extremely unequal energy sharing at low intensities.

Figure 1

The quantum mechanically calculated kinetic-energy spectra of one electron from nonsequential double ionization of He atoms by 800 nm, linearly polarized laser pulses as a function of the laser intensity. (a) Side-by-side emission and (b) back-to-back emission.

Figure 2

Kinetic-energy spectra of one electron from nonsequential double ionization of He atoms by 800 nm, linearly polarized laser pulses at intensities (a) $4.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and (b) $12\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The vertical dashed lines indicate the classical kinetic-energy limit of a direct ejected electron born with zero momentum: $2U_p$.

Figure 3

Simulations of correlated two-electron momentum distributions with a classical collision model at intensities (a)–(e) $4.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and (f)–(j) $12\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. In this model, we assume that the remaining energy-sharing ratio between the recolliding and the second electrons upon recollision is (a),(f) 1:0, (b),(g) 0.75:0.25, (c),(h) 0.5:0.5, (d),(i) 0.25:0.75, and (e),(j) 0:1, respectively. The red open circles represent the final momenta of electrons $e_1$ and $e_2$ in binary collision and the blue solid circles represent the same in recoil collision. The dash squares indicate the corresponding classical kinetic-energy limit of a direct ejected electron born with zero momentum: $2U_p$.

Figure 4

Calculated correlated momentum distributions of electrons $e_1$ and $e_2$ from the double ionization of He atoms with a quantum mechanical model by 800 nm, linearly polarized laser pulses at intensities (a) $4.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and (b) $12\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. The corresponding classical simulations from Fig. 3 for an energy-sharing ratio of 1:0 at $4.5\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ and 0.5:0.5 at $12\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ are superimposed. The red open circles represent the final momenta of electrons $e_1$ and $e_2$ in binary collision and the white solid circles represent the same in recoil collision.