Calculation of the evolution of the population in a 3-level A system using the STIRAP scheme (dressed state representation). Consider the 3-level system shown in the figure below:
In the rotating frame and making the RWA the Hamiltonian can be written:
with This matrix can be diagonalized yielding the eigenvalues,
and eigenvectors
Where The eigenvectors
are dressed states, i.e. eigenfunctions of the instantaneous Hamiltonian in the presence of the fields. Consider the adiabatic change in field intensities such that for
while for
This adiabatic transformation will leave the system in the dressed state
while changing its character from that of level |1> to that of level |3>. Since the dressed state
contains no component of level |2>, this adiabatic change leads to complete population transfer from level |1> to level |3>, without populating level |2>. This is the basis for the remarkable Stimulated Raman Adiabatic Passage
(STIRAP) scheme. Note the counterintuitive order of the pulses, i.e. precedes .
with 
This matrix can be diagonalized yielding the eigenvalues,
and eigenvectors
Where 
The eigenvectors 
are dressed states, i.e. eigenfunctions of the instantaneous Hamiltonian in the presence of the fields. Consider the adiabatic change in field intensities such that for
while for 
This adiabatic transformation will leave the system in the dressed state 
while changing its character from that of level |1> to that of level |3>. Since the dressed state 
precedes 
.