Femtosecond photodissociation of molecules facilitated by noise

We investigate the dynamics of diatomic molecules subjected to both a femtosecond midinfrared laser pulse and Gaussian white noise. The stochastic Schrödinger equation with a Morse potential is used to describe the molecular vibrations under noise and the laser pulse. For weak laser intensity, well below the dissociation threshold, it is shown that one can find an optimum amount of noise that leads to a dramatic enhancement of the dissociation probability. The enhancement landscape, which is shown as a function of both the noise and the laser strength, exhibits a global maximum. A frequency-resolved gain profile is recorded with a pump-probe setup which is experimentally realizable. With this profile we identify the linear and nonlinear multiphoton processes created by the interplay between laser and noise and assess their relative contribution to the dissociation enhancement.

Figure 1

Dissociation probability $P_L$ as function of the laser peak amplitude $F_0$ over long time $t$ $\left(t\gg T_p\right)$ with $\omega =0.007\text{a.u.}$, $\delta =0.0$, and $T_p=30\pi /\omega$. The arrow indicates the value of $F_0=0.04\text{a.u.}$ for which $P_L\sim 0$ is far less than the dissociation threshold. The inset shows the corresponding 15 optical cycle laser pulse $F\left(t\right)$ (light solid line) and the schematic pictures of a diatomic molecule HF (two nuclei separated by $R$, with $R_0$ being the equilibrium internuclear distance) and the Morse potential $V\left(x\right)$ (thick solid line), with $x=R-R_0$.

Figure 2

(Color online) Average dissociation probability of the molecule for noise only $P_N$ (square) and for the simultaneous application of the laser pulse and the noise $P_{L+N}$ (circle). The total number of realization $N_r=100$ and the laser peak amplitude is kept fixed at $F_0=0.04\text{a.u.}$

Figure 3

Factor of enhancement $\eta$ vs the noise amplitude $\sqrt{D}$ for the 15 cycle long MIR pulse with $F_0=0.04\text{a.u.}$ and $\omega =0.007\text{a.u.}$

Figure 4

(Color online) Enhancement landscape $\eta \left(\sqrt{D},F_0\right)$ vs the peak pulse amplitude $F_0$ and the noise amplitude $\sqrt{D}$. Other parameters are kept fixed as in Fig. 3. Contour lines of equal enhancement are also shown on the $\left(\sqrt{D},F_0\right)$ plane.

Figure 5

(Color online) (a) Frequency-resolved gain $G\left(\omega \right)$ for the driven HF molecule measured using a simultaneous pump-probe setting without noise. $G\left(\omega \right)$ for the bare molecule is also shown (black curve) for comparison. (b) Various single-photon and mutiphoton transitions corresponding to the peaks in $G\left(\omega \right)$ are classified as $A$ series, $B$ series, and $C$ series that involve first two, three, and four vibrational levels of HF, respectively. Thick red arrow denotes the pump photon $\left(\omega =0.007\text{a.u.}\right)$ and thin black arrow is for tunable weak probe pulse. Pulse bandwidth here is negligible compared to the photon energies. (c) Enhancement curve for the chaotic light with a perforated spectrum of hole widths 0.004 a.u. is compared with the broadband light of $\text{BW}=1.0\text{a.u.}\text{.}$