Multiphoton dissociation of HeH${}^{+}$ below the He${}^{+}$(1$s$)+H(1$s$) threshold

We discuss the strong-field dynamics of HeH${}^{+}$, the simplest stable heteronuclear molecule, focusing on identifying a laser regime for which there is a sufficient dissociation signal for experimental measurement. We numerically solve the time-dependent Schrödinger equation to obtain total dissociation probabilities, kinetic-energy release spectra, and momentum distributions for wavelengths from 800 to 2400 nm. The suitability of this simple system as a prototype for understanding the strong-field nuclear dynamics of heteronuclear dissociation is discussed.

Figure 1

Coordinates used in the Hamiltonian.

Figure 2

(a) The adiabatic potential-energy curves [30] for the ground state of HeH${}^{+}$, $X^1{\Sigma }^{+}$, and the first excited singlet state, $A^1{\Sigma }^{+}$. (b) The $X^1{\Sigma }^{+}$ potential used in our calculations [29] plotted along with the vibrational levels for zero orbital angular momentum. The arrows indicate the energy after dissociation from the absorption of 800-, 1200-, 1600-, 2000-, and 2400-nm (from left to right) photons from the vibrational ground state.

Figure 3

The body frame $z$-axis projection of the $X^1{\Sigma }^{+}$ permanent dipole $\langle {\Phi }_1\left|\mathbf{d}\right|{\Phi }_1\rangle$ and $X^1{\Sigma }^{+}$–$A^1{\Sigma }^{+}$ transition dipole $\langle {\Phi }_1\left|\mathbf{d}\right|{\Phi }_2\rangle$ from Ref. [30] along with our approximate permanent dipole $\langle \Phi \left|\mathbf{d}\right|\Phi \rangle$ from Eq. (7).

Figure 4

Total dissociation probability $P$ as a function of intensity for different wavelengths, pulse lengths, and initial vibrational states. The top figures are for five-cycle pulses, while the bottom figures are for ten-cycle pulses. From left to right, the columns correspond to the initial vibrational states $v=0$, 3, 6, and 9.

Figure 5

Bound-free dipole matrix elements, Eq. (13), as a function of KER $E$ for $v=6$ and $v=9$. The horizontal arrows represent the range of energies expected for one-photon absorption for wavelengths between 2400 and 800 nm.

Figure 6

The KER spectrum for an initial vibrational state of $v=3$ in a five-cycle pulse The vertical dashed line at $E/\omega =0.26$ corresponds to the expected location of the first peak, and the dashed diagonal line shows the $dP/dE\propto I^n$ behavior expected from lowest-order perturbation theory.

Figure 7

“Momentum” distribution from Eq. (15) plotted as a function of KER $E$ and angle ${\theta }_k$ for an initial rovibrational state with $v=3$ and $J=0$ in a five-cycle pulse with an intensity of $8.9\times {10}^{13}$ W/cm${}^2$ and a wavelength of 2400 nm. The upper-axis label $n$ indicates the net number of photons absorbed.