Decoherence of molecular vibrational wave packets: Oscillatory decay of purity

We study vibrational wave packet dynamics on realistic surfaces of diatomic molecules and focus on the loss of coherence induced by rovibrational coupling at finite temperature $T$. The expected revivals of the wave packet depend sensitively on the coherence between the vibrational states, and their suppression indicates decoherence. In order to investigate this loss of vibrational coherence more quantitatively, we focus on purity decay and observe, apart from an overall decay, a remarkable oscillatory behavior of purity on the vibrational time scale. We present fully quantum-mechanical calculations of purity decay and the signal measured in a typical femtosecond pump-probe experiment.

Figure 1

Excitation scheme for the ${\text{Na}}_2$ molecule at $\lambda =643\text{nm}$. The pump pulse creates a vibrational wave packet on the excited electronic $|e⟩$ state. For the given parameters the vibrational states contributing to the wave packet are centered around $n_e=7$.

Figure 2

Calculated pump-probe signal neglecting temperature averaging, i.e., taking only a single rotational state into account ($j_g=10,n_g=0$ are used). (a) Long-time pump-probe signal corresponding to 195 oscillation periods; (b) signal (enlarged detail) around half the revival time $t=T_{\text{rev}}/2$; (c) signal (enlarged detail) around the full revival time $t=T_{\text{rev}}$.

Figure 3

Calculated pump-probe signal $W_{\text{tot}}\left(\tau \right)$ for temperatures $T=100$ (top), 300 (middle), and 500 K (bottom). (a) Long-time pump-probe signal; (b) signal (enlarged detail) around half the revival time $t=T_{\text{rev}}/2$; (c) signal (enlarged detail) around the full revival time $t=T_{\text{rev}}$.

Figure 4

Time evolution of vibrational purity for different finite temperatures $T$. The inset shows the detailed oscillatory behavior immediately after the excitation for $T=100\text{K}$. The dotted lines mark the revival times $t=T_{\text{rev}}$ and $t=T_{\text{rev}}/2$ (see Fig. 3).

Figure 5

Squared modulus of the wave packet ${\left|{\psi }_{j_g}^{\left(e\right)}\left(R,t\right)\right|}^2$ on the excited Born-Oppenheimer surface $A{{}^1\Sigma }_u^{+}$. The initial state corresponds to $n_g=0$, $j_g=10$ (solid line) and $j_g^{\prime }=30$ (dashed line). (a) At time $t\approx 8.3\text{ps}$ (wave packet located at the inner turning point); (b) half a period later (wave packet located at the outer turning point) showing better overlap. Insets: dynamics of the overlap ${\mathbf{\left|}⟨{\psi }_{j_g}^{\left(e\right)}|{\psi }_{j_g^{\prime }}^{\left(e\right)}⟩\mathbf{\right|}}^2$ around $t=8\text{ps}$ for $j_g=10$ and $j_g^{\prime }=30$ (lowest curves), for $j_g=10$ and $j_g^{\prime }=20$ (middle curves), and for the constant case $j_g=j_g^{\prime }=10$ (top curves). The arrows mark the times corresponding to the wave functions drawn.