Phase reconstruction of a strong-laser-field-excited complex molecular system

We study the dynamic evolution of the excited dye molecule IR144 in the liquid phase by performing transient-absorption measurement. The time-delay-dependent absorption spectra show different behaviors when the pump pulse either precedes or follows the probe pulse. Assuming the excited molecule as a multilevel system, we reproduce the experimental results based on the density matrix theory. As a system's quantum dynamics is closely related to its absorption spectral shape, the quantum evolution of the excited dye molecule IR144 is analyzed and the system's phase information is extracted from the intensity-dependent absorption spectra. The present work finds us a route for the full understanding and control of the quantum dynamics in a complex system excited by an external pulsed laser field.

Figure 1

(a) The transient-absorption measurement schematic based on the pump-probe configuration. The absorption spectrum of the probe pulse are measured with a time delay $\tau$ respecting the pump pulse after interacting with the target. The positive time ($\tau >0$) means the pump pulse precedes the probe pulse. (b) The structure of the dye molecule IR144. (c) The absorption spectrum of the dye molecule IR144 (the black solid line) and the laser spectrum measured before the sample (the red dotted line). (d) The multilevel scheme used to model the dye molecule IR144 interacting with the laser pulses.

Figure 2

The dependence of the residual sum of squares ${\chi }^2$ on the relative phase changes on (a) the probe-pump and (b) pump-probe sides, respectively. Different lines in each panel correspond to different pump-pulse intensities. The coordinates of $x$ axis is just a relative location respecting these phase changes $\left\{{\varphi }_{\mathrm{N},i}^{\mathrm{B}}\right\}$ or $\left\{{\varphi }_{\mathrm{P},i}^{\mathrm{B}}\right\}$.

Figure 3

The sketch of the experimental setup for the transient-absorption measurement. Here B1 and B2 are the fused silica beam splitters with the same thickness, F1 and F2 are the continuously variable neutral density (ND) filters with the same product model, I1–I4 are the irises, and M1–M11 are the high reflectively mirrors.

Figure 4

The time-delay-dependent absorption spectra with a fixed probe-pulse intensity of $I_{\mathrm{pr}}=5.6\times {10}^9\mathrm{W}/{\mathrm{cm}}^2$. (a) and (b) The experimental results with $I_{\mathrm{pu}}=1.2\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$ and $I_{\mathrm{pu}}=6.6\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$, respectively, while (c) and (d) display the corresponding simulation results. The absorption spectra at $\tau =-20$ fs and $\tau =20$ fs are lined out in all these panels by the blue solid and black dotted lines, respectively. With $I_{\mathrm{pu}}=1.2\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$, the extracted phase changes $\left\{{\varphi }_{\mathrm{N},i}^{\mathrm{B}}\right\}$ are $\{0.096\pi$, $0.096\pi$, $0.093\pi$, $0.089\pi$, $0.092\pi$, $0.091\pi$, $0.084\pi$, $0.095\pi$, $0.094\pi$, $0.089\pi \}$ for these ten electronic transition dipoles ranging from 1.527 to 1.644 eV, and $\left\{{\varphi }_{\mathrm{P},i}^{\mathrm{B}}\right\}$ are $\{-0.095\pi$, $-0.093\pi$, $-0.095\pi$, $-0.094\pi$, $-0.094\pi$, $-0.096\pi$, $-0.092\pi$, $-0.093\pi$, $-0.005\pi$, $-0.006\pi \}$. $\left\{{\varphi }_{\mathrm{N},i}^{\mathrm{B}}\right\}$ are $\{0.48\pi$, $1.25\pi$, $0.29\pi$, $0.84\pi$, $1.32\pi$, $0.35\pi$, $0.24\pi$, $0.34\pi$, $0.36\pi$, $0.31\pi \}$, and $\left\{{\varphi }_{\mathrm{P},i}^{\mathrm{B}}\right\}$ are $\{-0.30\pi$, $-0.32\pi$, $-0.81\pi$, $-0.62\pi$, $-0.55\pi$, $-0.38\pi$, $-0.29\pi$, $-0.34\pi$, $-0.43\pi$, $-1.34\pi \}$, when the pump-pulse intensity is increased to $I_{\mathrm{pu}}=6.6\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$. The phase changes $\left\{{\varphi }_{\mathrm{P},i}^{\mathrm{B}}\right\}$ are shown with a subtraction of $2\pi$ to compare with the results on the probe-pump side.

Figure 5

The pump-pulse intensity-dependent absorption spectra. (a) and (b) The experimental results with time delays of $\tau =-20$ fs and $\tau =20$ fs, respectively, while (c) and (d) display the corresponding simulation results. The probe-pulse intensity is fixed to $I_{\mathrm{pr}}=5.6\times {10}^9\mathrm{W}/{\mathrm{cm}}^2$, while the pump-pulse intensity $I_{\mathrm{pu}}$ is tuned from $1.2\times {10}^{10}$ to $9.0\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 6

The pump-pulse intensity-dependent phase evolution of the molecular system obtained by the artificial-phase method, when the probe pulse (a) precedes and (b) follows the pump pulse, respectively.