Isotope Effect in Tunneling Ionization of Neutral Hydrogen Molecules

It has been recently predicted theoretically that due to nuclear motion light and heavy hydrogen molecules exposed to strong electric field should exhibit substantially different tunneling ionization rates [O. I. Tolstikhin, H. J. Worner, and T. Morishita, Phys. Rev. A 87, 041401(R) (2013)]. We studied that isotope effect experimentally by measuring relative ionization yields for each species in a mixed ${\mathrm{H}}_2/{\mathrm{D}}_2$ gas jet interacting with intense femtosecond laser pulses. In a reaction microscope apparatus, we detected ionic fragments from all contributing channels (single ionization, dissociation, and sequential double ionization) and determined the ratio of total single ionization yields for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. The measured ratio agrees quantitatively with the prediction of the generalized weak-field asymptotic theory in an apparent failure of the frozen-nuclei approximation.

Figure 1

Momentum spectra for ${\mathrm{D}}^{+}$ (a) and ${\mathrm{H}}^{+}$ (b), as well as for ${\mathrm{D}}_2^{+}$ and ${\mathrm{H}}_2^{+}$ (respective insets). (c) The sketch of the experimental apparatus (REMI: reaction microscopes, AP: aperture, QWP: quarter-wave-plate).

Figure 2

Potential energy curves of ${\mathrm{H}}_2$ (green), two lowest electronic states $X^2{\mathrm{\Sigma }}_g^{+}$ (red), and $A^2{\mathrm{\Sigma }}_u^{+}$ (blue) of ${\mathrm{H}}_2^{+}$, and ${\mathrm{H}}_2^{++}$ Coulombic $1/R$ curve ($R$ is internuclear distance). Cation ${\mathrm{H}}_2^{+}$ formed by single ionization can remain bound (Ch 1), dissociate (Ch 2), or undergo second ionization by the same pulse followed by Coulomb explosion (Ch 3).

Figure 3

(a) The measured time-of-flight spectrum of mixed ${\mathrm{H}}_2/{\mathrm{D}}_2$ gas ionized by circularly polarized pulses with central wavelength of 800 nm, pulse duration FWHM of 28 fs, and peak intensity of $(4.5\pm 0.4)\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$. (b) The corresponding kinetic energy spectra for ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$. The bond-softening (BS) and enhanced-ionization (EI) peaks are distinct in kinetic energy spectrum for both ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$. Green dashed line represents the boundary between BS and EI bands used to determine the total overall single ionization yield.

Figure 4

(a) The ratio of the total overall single ionization yield for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ versus the laser peak field. The red squares are the experimental data. For comparison, the ratio of the ionization rate for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ predicted by the TWM theory [4] is plotted at the same time (blue solid line). (b) The calculated ionization probability vs laser peak intensity for ${\mathrm{H}}_2$.