# Optical Nutation

Time dependent quantum mechanics describes the evolution of a molecular state as it becomes entangled with another state (in our case, the means of entanglement is the applied electromagnetic field). Before the field is applied, only one state is populated so ca=1 and cb=0. Turning on an electromagnetic field then changes the amplitudes so cadecreases while cb increases until ca=0 and cb=1. Assuming state ωba > 0 (i.e. state b is more energetic than a), the molecule is absorbing energy from the field. After this point the evolution reverses so that caincreases while cb decreases until ca=1 and cb=0.  The molecule is now emitting energy to the field, a process called stimulated emission. The intensity of the exciting field alternately dims during the absorption phase of the cycle and brightens during the stimulated emission phase. This cycling is known as optical nutation (see an example video of a system undergoing optical nutation). The entire cycle from the initial state and back is called a Rabi oscillation and its period depends on the light intensity. It is analogous to pushing a child on a swing- the harder you push, the more rapidly the oscillation builds up. There are two time periods, the natural period of the child and swing and the time required to build-up the oscillation. Quantum mechanically, there are also two frequencies- the Rabi frequency that is intensity dependent and the faster Bohr difference frequency, $\omega_{ba}=\omega_a-\omega_b$. The Rabi frequency is

$$\Omega \equiv \frac{\vec{\mu} \cdot \vec{E}}{2\hbar}$$

where μ is the transition dipole corresponding to the transition induced by the electromagnetic field, E.  Light intensity, color and duration all affect how far one processes into the Rabi cycle; it is by these parameters that one can control the superposition state of the system of interest.  Optical nutation and its mechanics are discussed more extensively here.