RotatingWaveTransformMatrix
RotatingWaveTransformMatrix[sys,{ω,tr}]
finds the transformation matrix suitable for applying the rotating‐wave approximation on atomic system sys, assuming an optical field with angular frequency ω acting on transitions specified by tr.
RotatingWaveTransformMatrix[sys,{{ω1,tr1},{ω2,tr2},…}]
finds the transformation matrix assuming optical fields with angular frequencies ωi acting on transitions specified by tri.
RotatingWaveTransformMatrix[sys,ω]
finds a heuristically generated transformation matrix appropriate for a single optical field.
Details and Options
- The atomic system sys is specified as a list of AtomicState objects.
- Transitions are specified as described in the notes for RotatingWaveApproximation.
- The transformation matrix is constructed according to the method described in the notes for RotatingWaveApproximation.
- The unitary transformation obtained from RotatingWaveTransformMatrix can be supplied as the value of the TransformMatrix option for RotatingWaveApproximation. This is done automatically when TransformMatrix->Automatic is used. It can also be supplied as an argument to EffectiveHamiltonian.
- The following options can be given:
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Method 
Automatic the method to use for performing the RWA TimeVariable 
Automatic symbol used to represent the time variable
Examples
open allclose allBasic Examples (2)
Find a transformation matrix suitable for applying the rotating-wave approximation, assuming that a field of frequency ω couples the lower state 1 to the upper state 2:
For this system, RotatingWaveTransformMatrix can guess that state 1 is the lower state and state 2 is the upper state, so it is not necessary to specify the transition:
Here is an example with three levels and two fields.
Find a transformation matrix for the RWA assuming that Energy[a]<Energy[b]<Energy[c]:
If, instead, we assume that Energy[a]<Energy[c]<Energy[b], we obtain a different transformation matrix: