Attosecond light-pulse-induced photoassociation

We explore stimulated photoassociation in the context of attosecond pump-probe schemes of atomic matter. An attosecond pulse—the probe—is used to induce photoassociation of an electronic wave packet which had been created before, typically with an attosecond pump pulse at an atomic center different from the one of photoassociation. We will show that the electron absorption is maximal for a certain delay between the pulses. Two ways of enhancing and controlling stimulated photoassociation are proposed, namely, using an additional infrared pulse to steer the electronic wave packet and using a train of attosecond pulses instead of a single pair. A direct application of ultrafast stimulated photoassociation is the measurement of atomic distances.

Figure 1

(Color online) Electron density as a function of time, under the action of a single attosecond pulse of 40, 60, and 80 nm central wavelength and $N=6\text{cycles}$ (the central time of the pulse is approximately 16.5, 25, and 33 a.u., respectively). The wells with potentials $W_{\pm }$ are located at $\pm 20\text{a.u.}$, marked by horizontal dashed lines. The electronic ionization path predicted according to Eq. (6) (solid) and Eq. (7) (dashed) is indicated.

Figure 2

(Color online) Probability of the induced photoassociation at $W_{-}$ as a function of the delay between the pulses, for three photon wavelengths: $\lambda =40$, 60, and 80 nm (one-dimensional calculations). The predicted optimal delay according to Eqs. (6, 7) is indicated with dashed and dotted lines, respectively. The arrows highlight the difference between the real and calculated values if the potential energy is ignored.

Figure 3

Full line, asymmetry parameter as a function of the time delay [Eq. (16)], for $\lambda =80\text{nm}$ and the same laser parameters as in Fig. 2. Dashed line, IPA probability (population at $W_{-}$), shown for comparison.

Figure 4

(Color online) The same as Fig. 2 but in two dimensions.

Figure 5

Probability of the induced photoassociation at $W_{-}$ as a function of the carrier-envelope phase of the infrared pulse. The insets show the total field for $\varphi =0$ and $\pi$.

Figure 6

(Color online) Bending of the electron trajectory caused by the infrared field ($\lambda =800\text{nm}$, $I={10}^{13}\text{W}/{\text{cm}}^2$). Left, with carrier-envelope phase $\varphi =0$ in the infrared pulse (see the insets in Fig. 5). Right, the same situation when $\varphi =\pi$. Dashed black line, position of the nucleus $W_{-}$. Dashed white line, position of the center of the second attosecond pulse. Full line, expected trajectory following Eq. (6).

Figure 7

(Color online) Electron trajectories calculated with Eq. (6) in the presence of the wells (dashed lines), the infrared field (dotted lines), or both of them (full lines), for carrier-envelope phases of $\varphi =0$ or $\varphi =\pi$. The position of the wells is indicated by the dashed lines. The origin in time is the center of the first attosecond pulse.

Figure 8

(Color online) Probability of induced photoassociation at $W_{-}$ as a function of the carrier-envelope phase of the infrared pulse, for 2, 4, and 8 attosecond pulses in the train. Intensities, $I_{\text{IR}}={10}^{13}\text{W}/{\text{cm}}^2$, and $I_{\text{UV}}={10}^{15}\text{W}/{\text{cm}}^2$.