Calculation of the evolution of the population in a 3-level A system using the STIRAP scheme (bare state representation).Consider the 3-level system shown in the figure below, Note the sequential form of the coupling, i.e. level |1> is coupled to
level |2>, and |2> to |3> but |1> not- directly to |3> In a rotating frame, and making the RWA the Schrödingcr equation can be written:
with A sufficient condition
for the population in level |2> to remain approximately 0 is that
In physical terms, the time rate of change of
involves two contributions, that from level |1>
and that from level |3>.
If these two contributions are equal and opposite, the population in level |2>
will remain constant. At early times, when
is large and is small,
must be small and
must be large in order for the contributions to cancel; at late times the situation is reversed. This is a simple but unconventional interpretation of the counterintuitive ordering of the pulses in the STIRAP scheme.
with 
A sufficient condition
for the population in level |2> to remain approximately 0 is that
In physical terms, the time rate of change of 
involves two contributions, that from level |1>
and that from level |3>.
If these two contributions are equal and opposite, the population in level |2>
will remain constant. At early times, when 
is large and 
is small, 
must be small and 
must be large in order for the contributions to cancel; at late times the situation is reversed. This is a simple but unconventional interpretation of the counterintuitive ordering of the pulses in the STIRAP scheme.