Dissociation dynamics of noble-gas dimers in intense two-color IR laser fields

We numerically model the dissociation dynamics of the noble-gas dimer ions He${}_2^{+}$, Ne${}_2^{+}$, Ar${}_2^{+}$, Kr${}_2^{+}$, and Xe${}_2^{+}$ in ultrashort pump and probe laser pulses of different wavelengths. Our calculations reveal a distinguished “gap” in the kinetic energy spectra, observed experimentally for the Ar${}_2$ dimer [J. Wu et al., Phys. Rev. Lett. 110, 033005 (2013)], for all noble-gas dimers for appropriate wavelength combinations. This striking phenomenon can be explained by the dissociation of dimer ions on dipole-coupled Born-Oppenheimer adiabatic potential curves. Comparing pump-probe-pulse-delay-dependent kinetic-energy-release spectra for different noble-gas dimer cations of increasing mass, we discuss increasingly prominent (i) fine-structure effects in and (ii) classical aspects of the nuclear vibrational motion.

Figure 1

Schematics of the nuclear wave-packet motion on generic $X_2$ and $X_2^{+}$ adiabatic molecular potential curves. Point $A$ indicates the center of the Franck-Condon region, points $B$–$E$ and $C$–$D$ correspond to one-photon transitions mediated by laser pulses of frequencies ${\omega }_1$ (1400 or 700 nm) and ${\omega }_2$ (800 or 500 nm). $V_{\mathrm{gr}}$ designates the ground-state adiabatic potential curve of $X_2$. $V_1$ and $V_2$ are the two lowest adiabatic potential curves of $X_2^{+}$.

Figure 2

Adiabatic potential energy curves for $X_2$ and $X_2^{+}$ dimers, calculated without including spin-orbit coupling. (a) Ground state of He${}_2$ (adapted from [17, 18]) and the two lowest states of He${}_2^{+}$ (from [19]). (b) Ground state of Ne${}_2$ (from [20]) and the two lowest states of Ne${}_2^{+}$ (from [21, 23]). (c) Ground state of Ar${}_2$ (from [22]) and the two lowest states of Ar${}_2^{+}$ (from [22, 23, 24]). (d) Ground state of Kr${}_2$ (from [25]) and the two lowest states of Kr${}_2^{+}$ (from [26]). (e) Ground state of Xe${}_2$ (from [25]) and the two lowest states of Xe${}_2^{+}$ (from [27]).

Figure 3

Adiabatic potential energy curves for $X_2$ and $X_2^{+}$ dimers, calculated including spin-orbit coupling. (a) Ground state of Ne${}_2$ (adapted from [20]) and the two lowest states of Ne${}_2^{+}$ (from [21]). (b) Ground state of Ar${}_2$ (from [22]) and the two lowest states of Ar${}_2^{+}$ (from [23]). (c) Ground state of Kr${}_2$ (from [25]) and the two lowest states of Kr${}_2^{+}$ (from [26]). (d) Ground state of Xe${}_2$ (from [25]) and the two lowest states of Xe${}_2^{+}$ (from [27]).

Figure 4

Probability density of the nuclear wave packet in the ${}^2$${\Sigma }_u^{+}$ state of Ar${}_2^{+}$ for a pump-probe delay of 150 fs and laser intensity of 10${}^{14}$ W/cm${}^2$, calculated 500 fs after the end (FWHM) of the probe pulse. The pump and probe pulses have wavelengths of 800 and 1400 nm, respectively. The dashed red line corresponds to the assumed limit $R_1$ $=$ 10 of the bound nuclear motion.

Figure 5

Probability density of $X_2^{+}$ nuclear wave packets as a function of the internuclear distance $R$ for field-free propagation in the $X_2^{+}$ [$I$(1/2)${}_u$] state (including spin-orbit coupling). (a) He${}_2^{+}$, (b) Ne${}_2^{+}$, (c) Ar${}_2^{+}$, (d) Kr${}_2^{+}$, and (e) Xe${}_2^{+}$ dimers. The propagation time is given in units of the respective revival times. The $X_2^{+}$ wave packets are launched by an 800 nm, 80 fs, 10${}^{14}$ W/cm${}^2$ laser pulse.

Figure 6

Position variance (Δ$R$)${}^2$, momentum variance (Δ$P$)${}^2$, and uncertainty product Δ$R$Δ$P$ as functions of time scaled with the respective revival times for Ne${}_2^{+}$, Ar${}_2^{+}$, Kr${}_2^{+}$, and Xe${}_2^{+}$ noble-gas dimer cations in the $I$(1/2)${}_u$ state. Due to the absence of a clear wave-function revival in our He${}_2^{+}$ propagation calculation (for the ${}^2{\Sigma }_u^{+}$ state), we scale the time in the first row by the approximate revival time 525 fs. The insets zoom into small time intervals where the variances and the uncertainty product are minimal.

Figure 7

KER spectra as functions of the pump-probe delay for the dissociation of (a) He${}_2^{+}$, (b) Ne${}_2^{+}$, (c) Ar${}_2^{+}$, (d) Kr${}_2^{+}$, and (e) Xe${}_2^{+}$. The calculations are based on dipole-coupled ${}^2{\Sigma }_u^{+}$ and ${}^2$${\Sigma }_g^{+}$ states of the dimer cations that do not include spin-orbit coupling for 80 fs, 10${}^{14}$ W/cm${}^2$ pump and probe pulses with wavelengths of 800 and 1400 nm.

Figure 8

(a) Same as Fig. 7a. (b)–(e) Same as Figs. 7b, 7c, 7d, 7e but for dipole-coupled $I$(1/2)${}_u$ and $II$(1/2)${}_g$ states that include spin-orbit coupling.

Figure 9

KER spectra as a function of the pump-probe delay for dipole-coupled $I$(1/2)${}_u$ and $II$(1/2)${}_g$ states of Kr${}_2^{+}$ and Xe${}_2^{+}$ including spin-orbit coupling. Parameters as in Figs. 8d and 8e, but for 500 and 700 nm pump and probe pulses.