Rabi cycling of a vibrational wavepacket between two harmonic potentials.
Consider a system with Hamiltonian
having only two eigenstates,
and
with energies
Define
The most general wavefunction for this system may be written as
The coefficients
a(t) and
b(t) are subject to the constraint that
If we couple this system to a light field, represented as
then we may write the Time Dependent Schrödinger Equation in matrix form as:
Invoking the Rotating Wave Approximation (neglecting the effort of
and choosing intial conditions
the populations as functions of time are given by:
where
and the Rabi frequency,
is defined as
The movie shows the evolution of a wavepacket between two harmonic surfaces under strong field excitation. For
the system reduces to a 2-level system and the Rabi solution is recovered (with the addition of the counterrotating terms).
