Femtosecond photoionization of atoms under noise

We investigate the effect of incoherent perturbations on atomic photoionization due to a femtosecond midinfrared laser pulse by solving the time-dependent stochastic Schrödinger equation. For a weak laser pulse which causes almost no ionization, an addition of a Gaussian white noise to the pulse leads to a significantly enhanced ionization probability. Tuning the noise level, a stochastic resonancelike curve is observed showing the existence of an optimum noise for a given laser pulse. Besides studying the sensitivity of the obtained enhancement curve on the pulse parameters, such as the pulse duration and peak amplitude, we suggest that experimentally realizable broadband chaotic light can also be used instead of the white noise to observe similar features. The underlying enhancement mechanism is analyzed in the frequency domain by computing a frequency-resolved atomic gain profile, as well as in the time domain by controlling the relative delay between the action of the laser pulse and noise.

Figure 1

(Color online) The ionization probability $P_l$ as a function of the laser peak amplitude $F_0$. The insets show the ionization flux versus time for two different pulses (top parts of the curves) of amplitudes, $F_0=0.05$ and $F_0=0.02$, marked by arrows on the IP curve. Here $\omega =0.057$, $\delta =0.0$, $T_p=20\pi ∕\omega$, and $\tau =2\pi ∕\omega$.

Figure 2

(Color online) Ionization flux for a weak laser pulse $F_0=0.02$, with three values of noise amplitude: (a) $\sqrt{D}=0.00024$, (b) 0.0015, and (c) 0.018. Background featureless curves (red) show the corresponding purely noise-driven $\left(F_0=0\right)$ flux. The flux is averaged over 50 realizations.

Figure 3

(Color online) The ionization probability versus the noise amplitude $\sqrt{D}$ for the noise alone $P_n$ (diamonds) and for the laser pulse $\left(F_0=0.02\right)$ with noise $P_{l+n}$ (squares). The points A–C correspond to the three cases considered in Fig. 2. The dashed line shows the limit of vanishing noise, i.e., the probability due to the laser pulse alone $P_l$. Inset: An example of laser pulse and noise.

Figure 4

The enhancement in photoionization due to quantum SR. The points marked A–C correspond to the noise amplitudes of Figs. 2a, 2b, 2c, respectively. At point B the ratio $\sqrt{D_{opt}}∕F_0=0.075$. The error bars indicate the standard deviation of $\eta$ calculated using more than 1000 different noise realizations.

Figure 5

(Color online) The enhancement factor versus the noise amplitude for four different values of pulse durations $T_p$: 5, 10, 20, and 30 optical period $T_0$. Here $F_0=0.02$, and other parameters are the same as in previous figures.

Figure 6

The dependence of enhancement on $F_0$ for a fixed noise amplitude $\sqrt{D}=0.0015$. (a) Ionization probabilities versus $F_0$ for laser only $P_l$, and for laser with noise $P_{l+n}$. The dashed line shows the limiting value of $P_n$. (b) The enhancement versus the $F_0$ curve obtained from the probability curves shown in (a).

Figure 7

(Color online) Enhancement induced by a broadband chaotic light. The peak amplitude and frequency of the 20 cycle laser pulse are $F_0=0.02$ and $\omega =0.057$, respectively. The bandwidth of chaotic light is $\Delta \omega =0.75$ with central frequency ${\omega }_0=0.375$. Inset: power spectral density (PSD) of the chaotic light compared to the one for the white noise.

Figure 8

(Color online) Frequency-resolved gain $G\left({\omega }_p\right)$ of the atom, which is driven by a ten cycle laser pulse of $F_0=0.02$ at $\omega =0.057$. The atomic gain is probed by a simultaneous application of a weak probe beam $F_p=0.0002$ of tunable frequency ${\omega }_p$. Both the depletion of the ground state population (thick red line) and the net absorption of energy (black) due to the probe are plotted. The gain of the driven atom is also compared with the bare atomic gain (thin gray line).

Figure 9

(Color online) Enhancement curves due to chaotic light spectrum perforated by holes at the first three resonance frequencies. Difference curves correspond to the increasing hole widths of $w=0.0$, 0.013, 0.03, 0.1, and 0.15.

Figure 10

(Color online) Enhancement factor $\eta$ versus the noise amplitude $\sqrt{D}$ for various cases, application of noise first and then the laser pulse (empty squares), application of laser pulse first and then noise (filled squares), simultaneous application of laser and noise (circles). The insets depict the schematically temporal signal applied to the atom for corresponding cases.