Zero-energy proton dissociation of ${\mathrm{H}}_2^{+}$ through stimulated Raman scattering

We experimentally investigate dissociation of ${\mathrm{H}}_2^{+}$ in the (near-)zero proton energy region. Based on our experimental results we conclude that the underlying mechanism for the production of protons with such low energy in strong two-color and broadband laser fields is a stimulated Raman-scattering-based zero-photon-dissociation process, ${\mathrm{ZPD}}_{\text{stR}}$, taking place on the electronic ground state. It is furthermore shown that in the (near-)zero energy region the asymmetry in proton ejection induced by asymmetric laser fields is due to the interplay of several processes, rather than only pathway interferences, with vibrational trapping (or bond hardening) taking a key role.

Figure 1

Schematic of dissociation processes of ${\mathrm{H}}_2$ relevant for the production of protons with near-zero energy in a two-color laser field (pink waveform in the lower left). Vertical blue and half-as-long vertical red arrows indicate photons with 400- and 800-nm wavelength, respectively. ZPD and BSD denote zero photon dissociation and bond-softening dissociation, respectively. ${\mathrm{ZPD}}_{\mathrm{stR}}$ indicates ZPD via a stimulated Raman scattering process proceeding only on the $1s{\sigma }_g$ potential energy curve of ${\mathrm{H}}_2^{+}$, and ${\mathrm{ZPD}}_{2p{\sigma }_u}$ denotes ZPD by transient population of the $2p{\sigma }_u$ curve via absorption of a 400-nm photon and later emission of an 800-nm photon.

Figure 2

Momentum distributions of protons along the laser polarization direction $z$. (a) Distributions measured with narrow-band pulses [FWHM bandwidth (BW) 50 nm around 800 nm, duration 25 fs] (blue line), in comparison with broadband laser pulses [FWHM BW roughly 300 nm around 740 nm, duration 5 fs] (red line), indicated by arrows, normalized to maximum. Intensities of both pulses are $2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. CE, Coulomb explosion. (b) Distributions measured with narrow-band 400-nm pulses generated by frequency doubling (normalized) for two pulse peak intensities (in ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, encoded by colors and indicated by arrows). Inset: Same distributions on a logarithmic scale. (c) Distributions measured with two-color pulses (800 nm + 400 nm) for two cases: overlap of the two pulses, and separated in time (see text for details), as indicated by colors and arrows. Peak intensity is $1\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$ for each color. (d) Ratio of yields taken from (c) between the cases with and without temporal overlap of the two pulses, normalized to the yield of ${\mathrm{H}}_2^{+}$.

Figure 3

(a) Asymmetry of proton emission (as defined in the text) as a function of $|p_z|$ over the relative phase $\mathrm{\Delta }\phi$ between 800- and 400-nm pulses. (b) Proton momentum distributions in the low-momentum region over $\mathrm{\Delta }\phi$. (c) Mean momentum values over $\mathrm{\Delta }\phi$ calculated for the distributions in (b) (red circles) and for ${\mathrm{H}}_2^{+}$ (green squares). (d) Yields of protons from (b) (red circles) and for ${\mathrm{H}}_2^{+}$ (green squares) over $\mathrm{\Delta }\phi$, both normalized at their respective maxima.