${\mathrm{H}}_2^{\hspace{0.5em}+}$ photodissociation by an intense pulsed photonic Fock state

We study the photodissociation of the ${\mathrm{H}}_2^{\hspace{0.5em}+}$ molecule by ultrashort Fock-state electromagnetic pulses (EMPs). We use the Born-Oppenheimer treatment combined with an explicit photon number representation via diabatic electrophoton potential surfaces for simplification of the basic equations. We discuss the issue of the number of photon states required and show that six photon states enable good accuracy for photoproduct kinetic energies of up to $3$ eV. We calculate photodissociation probabilities and nuclear kinetic-energy (KE) distributions of the photodissociation products for $800$-nm, $50$-TW$/$cm${}^2$ pulses. We show that KE distributions depend on three pulse durations of $10$, $20$, and $45$ fs and on various initial vibrational states of the molecule. We compare the Fock-state results to those obtained by “conventional,” i.e., coherent-state, laser pulses of equivalent electric fields and durations. The effects of the quantum state of EMPs on the photodissociation dynamics are especially strong for high initial vibrational states of ${\mathrm{H}}_2^{\hspace{0.5em}+}$. While coherent-state pulses suppress photodissociation for the high initial vibrational states of ${\mathrm{H}}_2^{\hspace{0.5em}+}$, the Fock-state pulses enhance it.

Figure 1

The full lines correspond to the ground $u_0(R)$ and the excited $u_1(R)$ adiabatic potentials. The dashed lines are first potentials on the diagonal of the potentials matrix $W(R)$ of Eq. (14) formed from photon-displaced adiabatic potentials $u_0$ and $u_1$.

Figure 2

The total asymptotic KE distribution in ${\mathrm{H}}_2^{\hspace{0.5em}+}$ photodissociation (internal vibrational state $v=6$) photodissociation by a 45 fs Fock-state electromagnetic pulse calculated using $M=2,4,6$ and 8 electro-photonic potentials.

Figure 3

The adiabatic-dressed electrophotonic states at maximal electric field coupling $E_0$ (see Table ), with $M=2$, 4, 6, and 8 states. Avoided crossing gaps: hexagon $\approx$2.5 eV, circle $\approx$0.1 eV, square $\approx$0.01 eV, and triangle $\approx$0.001 eV.

Figure 4

The total asymptotic KE distribution in ${\mathrm{H}}_2^{\hspace{0.5em}+}$ photodissociation for 45 fs pulses when the initial molecular state is a sharp vibrational state ($v=3$–8) and the electromagnetic field is in a coherent or a Fock state. Red (blue) arrow is the kinetic energy corresponding to absorption of a one (two) photon(s). Pulse parameters are given in Table .

Figure 5

The total asymptotic KE distribution in ${\mathrm{H}}_2^{\hspace{0.5em}+}$ photodissociation for 45 fs pulses when the initial molecular state is a sharp vibrational state ($v=9$–14), and the electromagnetic field is in a coherent or a Fock state. Red (blue) arrow is the kinetic energy corresponding to absorption of a one (two) photon(s). Pulse parameters are given in Table .

Figure 6

The dissociation probability as a function of the initial vibrational state of ${\mathrm{H}}_2^{\hspace{0.5em}+}$ for three pulse durations. Pulse parameters are given in Table .

Figure 7

The total asymptotic KE distributions in ${\mathrm{H}}_2$ pump-probe photodissociation using probe pulses of pulse duration ${\tau }_P$$=$10, 20, and 45 fs with pump-probe delay time of ${\tau }_D$$=$0, 10, and 20 fs. The legend indicates the total photodissociation probability $P$. It is assumed that the initial molecular state is the ground $v=0$ ${\mathrm{H}}_2$ vibrational wave packet (Franck-Condon approximation).