AtomicDensityMatrix`
AtomicDensityMatrix`

# RotatingWaveTransformMatrix

RotatingWaveTransformMatrix[sys,{ω,tr}]

finds the transformation matrix suitable for applying the rotatingwave 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.

# Examples

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## Basic Examples(2)

Define a two-level system:

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.

Define a three level system:

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:

## Options(2)

### Method(1)

With , RotatingWaveTransformMatrix shifts the energy of the upper state to eliminate the optical frequency:

Method->"ShiftLowerState" can be used to instead shift the energy of the lower state:

### TimeVariable(1)

Find an RWA transformation matrix using a different time variable: