Isotope effects on the ionization of hydrogen molecular ions in strong laser fields

Isotope effects on the ionization of hydrogen molecular ions in strong laser fields are studied by numerically simulating the time-dependent Schrödinger equation. Though the isotopes of hydrogen molecular ions have identical Born-Oppenheimer potential curves, the distinct ionization scenarios are observed for single-photon, multiphoton, and tunneling ionization. For multiphoton and tunneling ionization, the ionization rate of ${{\mathrm{H}}_2}^{+}$ is larger than that of ${{\mathrm{D}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$. The ratio of the intensity-dependent tunneling ionization probabilities of ${{\mathrm{H}}_2}^{+}$ (${{\mathrm{D}}_2}^{+}$) and ${{\mathrm{T}}_2}^{+}$ can be qualitatively explained by the adiabatic tunneling theories if a few-femtosecond ultrashort pulse is used. For tens of femtosecond laser pulses, the nuclear movement is unavoidable and the time-dependent Schrödinger equation simulation is necessary in order to calculate the ionization probability accurately. For single-photon ionization, the electron-nuclei joint energy spectra are distinct though the total ionization probabilities are similar. The elastic constant of potential curves can be retrieved by comparing the single-photon-induced electron-nuclei joint energy spectra of different isotopic molecular ions, which offers a potential technique to image molecules.

Figure 1

The JESs for (a) ${{\mathrm{H}}_2}^{+}$, (b) ${{\mathrm{D}}_2}^{+}$, and (c) ${{\mathrm{T}}_2}^{+}$ in the one-photon ionization process. (d) Difference of JESs for ${{\mathrm{H}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$. The laser intensity is $I=1.0\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$, the wavelength is 25 nm, and the energy resolutions are ${\epsilon }_e=0.006$ and ${\epsilon }_{\mu }=0.02$. The red dashed lines with the slope $-1$ indicate the energy sharing between the electron and nuclei.

Figure 2

(a) Initial nuclear wave-packet distributions of ${{\mathrm{H}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$. (b) Ionization probability as a function of the internuclear distance. The vertical dash-dotted lines mark the locations of the two crossings ($R_1$ and $R_2$) of the two curves for ${{\mathrm{H}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$. The locations of the crossings in (a) and (b) are same. The laser parameters are same as those in Fig. 1.

Figure 3

The JESs for the multiphoton ionization of (a) ${{\mathrm{H}}_2}^{+}$, (b) ${{\mathrm{D}}_2}^{+}$, and (c) ${{\mathrm{T}}_2}^{+}$. The laser pulse has an intensity $I=1.0\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$, a wavelength of 400 nm, and a pulse duration of 12 optical periods with a CEP $\varphi =0$. The energy resolutions are ${\epsilon }_e=0.004$ and ${\epsilon }_{\mu }=0.02$.

Figure 4

The JESs for the tunneling ionization of (a) ${{\mathrm{H}}_2}^{+}$, (b) ${{\mathrm{D}}_2}^{+}$, and (c) ${{\mathrm{T}}_2}^{+}$. The laser pulse has an intensity $I=4.0\times {10}^{14}$ $\mathrm{W}/{\mathrm{cm}}^2$, a wavelength of 800 nm, and a pulse duration of two optical periods with a CEP $\varphi =\pi /2$. The energy resolutions are ${\epsilon }_e=0.01$ and ${\epsilon }_{\mu }=0.02$.

Figure 5

Ratios of the ionization probabilities for ${{\mathrm{H}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$ as well as ${{\mathrm{D}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$ when the laser wavelength is (a) 400 nm, (b) 800 nm, and (c) 1200 nm. In each panel, the laser pulse duration has two optical cycles. For reference, the ratios calculated by the ADK theory and WFAT theory also are presented.

Figure 6

Ratios of the ionization probabilities for (a) ${{\mathrm{H}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$ and (b) ${{\mathrm{D}}_2}^{+}$ and ${{\mathrm{T}}_2}^{+}$ when the driving laser field has different optical cycles. The ratios predicted by the ADK theory and the WFAT are shown by the black solid and red dashed curves, respectively. The laser wavelength is 800 nm. For the lines using 7T and 10T, the lines are truncated when the ionization depletion is important.

Figure 7

Time-evolved probabilities of different vibrational states when the laser wavelength is (a) 800 nm and (c) 1200 nm. Also shown is the time-dependent internuclear distance of ${{\mathrm{H}}_2}^{+}$ when the laser wavelength is (b) 800 nm and (d) 1200 nm. The black dotted curves represent the two-cycle laser electric field.