Preparation and probing of coherent vibrational wave packets in the ground electronic state of HD${}^{+}$

We have investigated the formation of coherent vibrational wave packets in the ground electronic state of HD${}^{+}$ on exposure to intense ultrashort laser pulses of wavelength 1060 nm. The effects of the duration and field strength of the pulse on the final composition of the residual bound nuclear wave packet generated by such impulsive excitations have been studied. The resulting wave packet is allowed to evolve freely on the potential surface for some time, after which a weak pulse of sufficiently large duration is used for probing its composition. This pulse can cause only single-photon dissociation. The simulations have been performed with different probe wavelengths for accessing information about different portions of the wave packet in the vibrational quantum number space. Our aim was to investigate the extent to which information obtained from the kinetic-energy spectra of the photofragments induced by the probe pulse can be correlated to the structure of the wave packet. Simple time-dependent perturbation calculations have also been performed for obtaining the relative strengths of photofragment signals arising from different vibrational levels due to wave-packet dissociation. A comparison with our numerical results indicates that though the general features of the photofragment kinetic-energy spectra from a wave packet are consistent with the perturbation theory results in the intensity regime studied, dynamical evolution during a long pulse can modify the relative heights of the kinetic-energy peaks through nonperturbative interactions in some cases.

Figure 1

Vibrational distribution in the residual wave packets obtained at the end of a 15 fs, 1060 nm wavelength laser pulse of three different intensities for initial states: (a) $v$ $=$ 0, (b) $v$ $=$ 2, and (c) $v$ $=$ 4, respectively.

Figure 2

Vibrational distribution in the residual wave packets created by three different pulse times with the peak intensity, $I^0$ $=$ 5 $\times$ 10${}^{14}$ W/cm${}^2$ of a 1060 nm wavelength laser pulse for initial states: (a) $v$ $=$ 0, (b) $v$ $=$ 2, and (c) $v$ $=$ 4, respectively.

Figure 3

Relative population in the residual wave packet is plotted as a function of the vibrational quantum number using two different temporal pulse shapes, sin${}^2$ and Gaussian, having the same peak intensity and FWHM starting from initial state $v$ $=$ 4 for (a) FWHM $=$ 5 fs, $I^0$ $=$ 5 $\times$ 10${}^{14}$ W/cm${}^2$, (b) FWHM $=$ 7.5 fs, $I^0$ $=$ 3.5 $\times$ 10${}^{14}$ W/cm${}^2$, and (c) FWHM $=$ 7.5 fs, $I^0$ $=$ 5 $\times$ 10${}^{14}$ W/cm${}^2$.

Figure 4

Wave-packet evolution initiated by a 1060 nm wavelength laser pulse of duration 15 fs and intensity 5 $\times$ 10${}^{14}$ W/cm${}^2$ for initial vibrational level (a) $v$ $=$ 0 and (b) $v$ $=$ 2. The shaded portion denotes the wave-packet shape near the end of the pulse.

Figure 5

Single-photon dressed potential energy curves and the corresponding adiabatic potentials at $I^0$ $=$ 5 $\times$ 10${}^{11}$ W/cm${}^2$ for three different probe wavelengths 157, 354, and 780 nm, respectively. The solid lines represent the dressed potentials and the dashed lines represent the corresponding adiabatic potentials.

Figure 6

Kinetic-energy spectra of the photofragments obtained from the wave packet created by a 1060 nm, 15 fs pulse of peak intensity 5 $\times$ 10${}^{14}$ W/cm${}^2$ from an initial state $v$ $=$ 2, for the probe pulse of $I^0$ $=$ 5 $\times$ 10${}^{11}$ W/cm${}^2$ and duration 96 fs in the case of (a), (b), and (c) and 240 fs in the case of (d), (e), and (f) for the respective probe wavelengths.

Figure 7

Normalized results of photofragmentation probability of the different vibrational eigenstates in the wave packet, created by a 1060 nm, 15 fs pulse of peak intensity 5 $\times$ 10${}^{14}$ W/cm${}^2$ from an initial state $v$ $=$ 2, calculated from perturbation theory. The magnitudes of the peak heights in the kinetic-energy spectra are also plotted as functions of vibrational quantum number for 2$\sigma$ $=$ 96 fs and 240 fs and $I^0$ $=$ 5 $\times$ 10${}^{11}$ W/cm${}^2$ for wavelengths (a) 157, (b) 354, and (c) 780 nm, respectively. The solid lines represent the fragmentation probability and the dashed and dotted lines represent the kinetic-energy peak heights.

Figure 8

Normalized results of photofragmentation probability of the different vibrational eigenstates in the wave packet, created by a 1060 nm, 15 fs pulse of peak intensity 5 $\times$ 10${}^{14}$ W/cm${}^2$ from an initial state $v$ $=$ 2, from perturbation theory. The magnitudes of the peak heights in the kinetic-energy spectra are also plotted as functions of vibrational quantum number for 2$\sigma$ $=$ 96 fs and $I^0$ $=$ 1 $\times$ 10${}^{11}$ W/cm${}^2$, 5 $\times$ 10${}^{11}$ W/cm${}^2$, and 1 $\times$ 10${}^{12}$ W/cm${}^2$ for wavelengths (a) 157, (b) 354, and (c) 780 nm, respectively. The solid lines represent the fragmentation probability and the dashed, dotted, and dash-dotted lines represent the kinetic-energy peak heights.