The Floquet Space Representation

The form of the RF interaction Hamiltonian in Fourier space in Eq. 23a suggests that we can transform it to a space where it becomes time independent. Transforming the Fourier density operator to a new interaction frame defined by 

This new representation is the Floquet space representation, which is the N-interaction representation of and is still defined by the Fourier states 

The definition of the matrix elements of the BMFT Hamiltonian is straightforward, as well as the definition of the initial density operator  

The choice of this form for the initial density matrix is in line with the above definitions of the Fourier and Floquet space, and maintains the form of all operators in Floquet space as in Eq. 28. 

The back transformation of operators from Floquet space to Hilbert space results in the expression originally derived by Chu et al. [92,93]. Using the expressions for and in Eq. 29  

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