  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 to engineer the quantum state of light to steer chemical
processes. The quantum field description of the photon mode allows to
manipulate the light-matter interaction directly in phase-space. In this paper
we will 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 new 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.
