RotatingWaveTransformMatrix

RotatingWaveTransformMatrix[sys, {, tr}]
finds the transformation matrix suitable for applying the rotating-wave approximation on atomic system sys, assuming an optical field with angular frequency acting on transitions specified by tr.
RotatingWaveTransformMatrix[sys, {{1, tr1}, {2, tr2}, ...}]
finds the transformation matrix assuming optical fields with angular frequencies i acting on transitions specified by tri.
RotatingWaveTransformMatrix[sys, ]
finds a heuristically generated transformation matrix appropriate for a single optical field.
  • The atomic system sys is specified as a list of AtomicState objects.
  • The following options can be given:
MethodAutomaticthe method to use for performing the RWA
TimeVariableAutomaticsymbol used to represent the time variable
In[1]:=
Click for copyable input
Define a two-level system:
In[2]:=
Click for copyable input
Out[2]=
Find a transformation matrix suitable for applying the rotating-wave approximation, assuming that a field of frequency couples the lower state 1 to the upper state 2:
In[3]:=
Click for copyable input
Out[3]//MatrixForm=
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:
In[4]:=
Click for copyable input
Out[4]//MatrixForm=
 
Here is an example with three levels and two fields.
Define a three level system:
In[1]:=
Click for copyable input
Out[1]=
Find a transformation matrix for the RWA assuming that Energy[a]<Energy[b]<Energy[c]:
In[2]:=
Click for copyable input
Out[2]//MatrixForm=
If, instead, we assume that Energy[a]<Energy[c]<Energy[b], we obtain a different transformation matrix:
In[3]:=
Click for copyable input
Out[3]//MatrixForm=
[an error occurred while processing this directive]