Efficient and Long-Lived Field-Free Orientation of Molecules by a Single Hybrid Short Pulse

We show that a combination of a half-cycle pulse and a short nonresonant laser pulse produces a strongly enhanced postpulse orientation. Robust transients that display both efficient and long-lived orientation are obtained. The mechanism is analyzed in terms of optimal oriented target states in finite Hilbert subspaces and shows that hybrid pulses can prove useful for other control issues.

Figure 1

Numerical contour plot of $\underset{s}{max}|⟨\cos \theta ⟩|$ as a function of the total (dimensionless) areas $A_{\mathrm{L}}$ and $A_{\mathrm{HCP}}$. The straight line $A_{\mathrm{HCP}}=2.5A_{\mathrm{L}}$ approximately indicates the maximum for given $A_{\mathrm{HCP}}$.

Figure 2

As a function of $A_{\mathrm{HCP}}$, for $A_{\mathrm{L}}=A_{\mathrm{HCP}}/2.5$, upper panel: (i) $\underset{s}{max}|⟨\cos \theta ⟩|$ (solid line, right axis); (ii) for comparison, same quantity with $A_{\mathrm{L}}=0$ (dotted line); (iii) duration $\Delta$ for which $|⟨\cos \theta ⟩|>0.5$ (dashed line, left axis). Lower panel: square modulus $P_N=|⟨{\chi }_{-}^{(N)}|\varphi (s_{\max })⟩{|}^2$ of the projection of the state at the time giving the maximum of $|⟨\cos \theta ⟩|$ on the optimal state $|{\chi }_{-}^{(N)}⟩$ (solid line, right axis); dimension $N$ of the corresponding subspace (step function, left axis).

Figure 3

Orientation as a function of dimensionless time for (i) $A_{\mathrm{HCP}}=3$ and $A_{\mathrm{L}}=3/2.5$ (solid line) and (ii) the optimal state ${\chi }_{-}^{(5)}$ with a time translation (dashed line).

Figure 4

Same as Fig. 1 for the dimensionless temperature $\tilde{T}=5$.