Quantum control with quantum light of molecular nonadiabaticity

Coherent control experiments in molecules are often done with shaped laser fields. The electric field is described classically and control over the time evolution of the system is achieved by shaping the laser pulses in the time or frequency domain. Moving on from a classical to a quantum description of the light field allows one to engineer the quantum state of light to steer chemical processes. The quantum field description of the photon mode allows one to manipulate the light-matter interaction directly in phase space. In this paper we demonstrate the basic principle of coherent control with quantum light on the avoided crossing in lithium fluoride. Using a quantum description of light together with the nonadiabatic couplings and vibronic degrees of freedoms opens up alternative perspective on quantum control. We show the deviations from control with purely classical light field and how back-action of the light field becomes important in a few-photon regime.

Figure 1

(a) Potential energy curves of the ${\mathrm{\Sigma }}_1$ (red solid line) and ${\mathrm{\Sigma }}_2$ (green dashed line) electronic states of the LiF molecule applied in the present work. (b) The corresponding transition dipole moment and nonadiabatic coupling ($f_{{\mathrm{\Sigma }}_1{\mathrm{\Sigma }}_2}$) curves are shown by blue dashed and black solid lines, respectively.

Figure 2

Illustration of the interaction of a molecule with a coherent state (a) and a squeezed vacuum state (b) in a wave-packet picture. The nuclear wave packet follows the gradient on the potential energy curve from the Franck-Condon point ($\approx 1.6\AA$) towards the avoided crossing (black circle at $\approx 8\AA$).

Figure 3

Final ${\mathrm{\Sigma }}_1$ state populations for (a) coherent and (b) squeezed vacuum initial states as a function of the initial phase and the initial squeezing phase, respectively. In the case of the coherent states (a), several initial average photon numbers are considered. For comparison, the classical field description results are presented by the black line where the electric field amplitude is determined from $E_c=\chi {\omega }_c{x}_{\max }$. In the case of the coherent states the coupling strength parameter is scaled according to $\chi /\sqrt{\langle n\rangle }$. For the squeezed vacuum initial states (b), four different squeezing parameters are considered. In both panels ${\omega }_c=0.037$ eV and $\chi =0.01$ are applied. The horizontal dashed lines show the field-free final populations in both panels.

Figure 4

Final ${\mathrm{\Sigma }}_1$ state populations calculated as a function of the $\phi$ initial phase and the $\theta$ initial squeezing phase, using squeezed-coherent initial states. The applied parameters are $\left|\alpha \right|=1$, $r=1$ (a) and $\left|\alpha \right|=1$, $r=2$ (b). In both panels the coupling strength and the transition frequency are $\chi =0.01$ and ${\omega }_c=0.037$ eV, respectively.