Engineering quantum wave-packet dispersion with a strong nonresonant femtosecond laser pulse

A nondispersing wave packet has been attracting much interest from various scientific and technological viewpoints. However, most quantum systems are accompanied by anharmonicity, so that retardation of quantum wave-packet dispersion is limited to very few examples only under specific conditions and targets. Here we demonstrate a conceptually universal method to retard or advance the dispersion of a quantum wave packet through “programmable time shift” induced by a strong nonresonant femtosecond laser pulse. A numerical simulation has verified that a train of such retardation pulses stops wave-packet dispersion.

Figure 1

Schematic of the spreading-control experiment. (a) Scenario of the spreading control based on the quantum interference induced by the strong nonresonant NIR pulse. In this sketch, the spreading is retarded by the irradiation of the NIR pulse. (b) Potential energy curves of ${\mathrm{I}}_2$. The $B$-state wave packet is created by the pump pulse, and is modulated by the strong NIR pulse at $t={\tau }_{\mathrm{NIR}}$. The modulated wave packet is excited to the $E$ state by the probe pulse at $t={\tau }_{\mathrm{probe}}$, and its fluorescence signal is detected. (c) Pulse sequence for the observation of the temporal evolution of the wave packet after the irradiation of the NIR pulse. (d) Pulse sequence for the eigenstate interferogram.

Figure 2

Experimental results of the spreading control. (a) Free temporal evolution of the wave packet. (b, c) Actively controlled wave-packet spreading advanced and retarded by the NIR pulse shined at ${\tau }_{\mathrm{NIR}}\sim$ 5.07 ps and 5.36 ps, respectively. To remove the effect of the NIR pulse on the wave packet generated in the $E$ state by the probe pulse, the NIR pulse is blocked when the probe pulse is shined before the NIR pulse. (d) (Dotted line) Eigenstate interferograms of $v_{\mathrm{B}}=30({\tau }_{\mathrm{rel}}<0)$ and $v_{\mathrm{B}}=29({\tau }_{\mathrm{rel}}>0)$ without the NIR pulse. (Red line) Fitted sine curve for $v_{\mathrm{B}}=30$. (Blue line) Fitted sine curve for $v_{\mathrm{B}}=29$. (e) Similar to (d) with the NIR pulse shined at ${\tau }_{\mathrm{NIR}}\sim 5.07\mathrm{ps}$. (f) Relative phases of $v_{\mathrm{B}}=29$ and 31 to $v_{\mathrm{B}}=30$ obtained from the eigenstate interferograms exemplified in (d) and (e). The green shows the results without the NIR pulse. The blue and red show the results with the NIR pulse shined at ${\tau }_{\mathrm{NIR}}\sim$ 5.07 ps and ${\tau }_{\mathrm{NIR}}\sim$ 5.36 ps, respectively, as seen in (b) and (c).

Figure 3

(a) Numerical simulation of the quantum beats when the NIR pulse is shined at ${\tau }_{\mathrm{NIR}}=5.02\mathrm{ps}$ to 5.46 ps at every 0.04 ps. The quantum beat at the top (green) is a reference curve simulated without the NIR pulse. The blue trace corresponds to ${\tau }_{\mathrm{NIR}}=5.10\mathrm{ps}$, in which the NIR pulse is shined at the local minimum after the eleventh beat structure. The red trace corresponds to ${\tau }_{\mathrm{NIR}}=5.34\mathrm{ps}$, in which the NIR pulse is shined around a half vibrational period after the blue trace. These two timings are compared to the experimental traces of Figs. 2 and 2, where NIR pulses are shined at the similar timings of the traces with the same colors. (b) Simulated shift of the relative phase ${\theta }_{v_{\mathrm{B}}}\left({\tau }_{\mathrm{NIR}}\right)$ of each eigenstate obtained by changing ${\tau }_{\mathrm{control}}$ from 6.50 ps to 6.50 ps $+$ 5 fs. The solid lines with square and circle markers correspond to $v_{\mathrm{B}}=29$ and $v_{\mathrm{B}}=31$, respectively. The two vertical dotted lines indicate the timings of the NIR pulse ${\tau }_{\mathrm{NIR}}=5.10\mathrm{ps}$ and 5.34 ps.

Figure 4

Simulated wave-packet spreading suppressed by a train of strong NIR pulses. The wave packet here is an isolated three-level system composed of the eigenstates $v_{\mathrm{B}}=29$, 30, and 31 of the iodine molecule with their population ratio 1:1:1 at the time origin $t=0$. (a, b) The wave-packet density at the interatomic distance of 3.92 Å is plotted as a function of time $t$. (c, d) The wave-packet density at $t$ = 8.315 ps is plotted as a function of the interatomic distance. (a, c) Free wave packet without NIR pulses. (b, d) Wave packet controlled with a train of six NIR pulses shined at $t$ =$(3n-1.5)T$ with $n=1$, 2,..., 6 where $T=475$ fs is a classical oscillation period of the wave packet. These timings are indicated by the arrows in Fig. 4. Each NIR pulse has a Gaussian envelope with a temporal width of 0.05 $T$ (FWHM). The spreading of the wave packet is stopped almost completely by the NIR pulses. Plots (a) and (c) are vertically offset for better visibility. The movies of these wave packets are given in Video S1 in the Supplemental Material [39].