Vibrational chirp in the dynamic Stokes-shift process due to ultrafast geometrical relaxation in a polydiacetylene

Relaxation kinetics of photoexcitation in a blue-phase polydiacetylene has been investigated by difference absorption spectroscopy with extremely high time- and energy-resolution using broadband sub-$5\text{−}\mathrm{fs}$ optical pulses. One-fs-step tracking of an induced emission peak has enabled us to separate the vibrational dynamics during geometrical relaxation and internal conversion into modulations of transition-peak energy and transition probability. The peak energy shows redshift of about $60\mathrm{meV}$ and the instantaneous frequency of the “$\mathrm{C}\mathrm{C}$” stretching mode is positively “chirped” starting from $1600\pm 100{\mathrm{cm}}^{-1}$ $(21\pm 2\mathrm{fs})$ and ending in $2100\pm 100{\mathrm{cm}}^{-1}$ $(16\pm 1\mathrm{fs})$. This positive chirp indicates a huge dynamic structural change from ${(\mathrm{C}R\mathit{C}\mathit{C}\mathrm{C}{R}^{\prime })}_n$–like to ${(\mathrm{C}R\mathrm{C}\mathrm{C}\mathrm{C}{R}^{\prime })}_n$–like structured bonds in the polymer backbone during the internal conversion process within $100\mathrm{fs}$. This corresponds to the reduction of the bond length from $1.32\pm 0.04\mathrm{\AA }$ to $1.19\pm 0.04\mathrm{\AA }$ by about $0.13\mathrm{\AA }$, which was estimated from the bond lengths in literatures determined by the x-ray analysis for several polydiacetylenes.

Figure 1

Difference absorption spectra of blue-phase PDA-3BCMU at a delay time of $20–50\mathrm{fs}$ with a $1\text{−}\mathrm{fs}$ step probed at $1.68–2.28\mathrm{eV}$. Each curve is shifted up by $\Delta A=0.0125$ from the next later delay step by $1\mathrm{fs}$. The mark 0 on the ordinate corresponds to null $\Delta A$ for the bottom curve.

Figure 2

(a) The essential states to the nonlinearity and the excited-state transitions (Refs. 51, 52) relevant to this pump-probe experiment. (b) Decomposed difference absorption spectra: $\Delta A_1$ due to the population distribution $P_1\left(t\right)$ in $1{}^{1}B_u$ state and $\Delta A_2$ due to the population distribution $P_2\left(t\right)$ in $2{}^{1}A_g$ state. (c) Laser spectrum of the sub-$5\text{−}\mathrm{fs}$ pump and absorption spectrum of the blue-phase PDA-3BCMU sample.

Figure 3

Time traces of (a) the energy and (b) the intensity of an induced emission peak near $1.89\mathrm{eV}$. Smooth monotonically decaying curves are single-exponential fits convoluted with the pulse duration. Oscillating curves represent the best fits to Eq. (7). (c) A schematic cross-section diagram of the potential hypersurfaces of $1{}^{1}A_g$, $1{}^{1}B_u$-STE, and $2{}^{1}A_g$ states along the $\mathrm{C}\mathrm{C}$ stretching coordinate in configuration space. (d) Short-decay time determined by the biexponential decay fitting for the time trace of $\Delta A$ at each probe energy.