Selective Enhancement of Spectroscopic Features by Quantum Optimal Control

Tailored light can be used to steer atomic motions into selected quantum pathways. In optimal control theory (OCT), the target is usually expressed in terms of the molecular wave function, a quantity that is not directly observable in experiment. We present simulations using OCT that optimize the spectroscopic signal itself. By shaping the optical pump, the x-ray stimulated Raman signal, which occurs solely during the passage through conical intersections, is temporally controlled and amplified by up to 2 orders of magnitude. This enhancement can be crucial in order to bring small coherence-based signatures above the detectable threshold. Our approach is applicable to any signal that depends on the expectation value of a positive definite operator.

Figure 1

Population dynamics and polarizability resulting from wave packet simulations in our effective uracil Hamiltonian [20, 25]. The time delay is measured between the optical pump and the x-ray probe and is noted as $T$ in Eq. (1). (a) A 34 fs optical pump [Fig. 3] creates a population in the bright $S_2$ state. After a period of free wave packet evolution, a conical intersection seam is reached, and the wave packet decays into $S_1$, where it eventually absorbed. (b) Magnitude of the expectation value of the transition polarizability operator. Being initially zero, it becomes nonvanishing once the conical intersection is reached, and a vibronic coherence is created. (c) Off-resonant transition polarizability in the two-dimensional nuclear space of uracil at 326 eV probe energy, calculated by Eq. (3). The conical intersection seam is located at $q_1=[1,2]$ and $q_2=0\AA$. (d) Level scheme of the experiment. A population is created in the bright $S_2$ state (blue) by the optical pulse ${ϵ}_p$. The x-ray fields ${ϵ}_0$ and ${ϵ}_1$ [compare Eq. (1)] probe the vibronic coherence between $S_2$ and $S_1$ via an off-resonant stimulated Raman process. C, N, and O are the carbon, nitrogen, and oxygen core states.

Figure 2

The transition polarizability expectation value, which is the optimization target in Eq. (2), and the time-dependent material quantity in the TRUECARS signal [Eq. (1)] after pulse optimization. The time delay is measured between the optical pump and the x-ray probe and is denoted $T$ in Eq. (1). Five different target times $T$ in the nuclear dynamics were chosen at 100, 120, 150, 175, and 200 fs. Compared to Fig. 1, the magnitude has been amplified significantly, with the maximum value located at the target time.

Figure 3

Optimized laser pulses, spectrograms, and TRUECARS signals (a) before and (b)–(f) after pulse optimization by iterative solution of Eq. (2). The top panels contain the TRUECARS signal according to Eq. (1), the middle panels depict the laser fields ${ϵ}_p$ that pump the system from $S_0$ to $S_2$, and the bottom panels show the pulse spectrograms calculated by Eq. (4). (a) Unoptimized, Gaussian-shaped pulse that has been used experimentally [27] and that serves as the guess field for OCT optimizations. (b)–(f) Optimized light fields for signal maximization at 100, 120, 150, 175, and 200 fs. Signal strengths are amplified by up to 200 orders of magnitude and precisely localized in time.