Floquet Hamiltonian coherent states

In the presence of the field, the molecular states are coherent superpositions of the states AM ) A ). In principle, the basis set must include an infinite number of states A ). However, the Floquet Hamiltonian matrix is block-diagonal and the diagonal matrix elements of the Floquet matrix separate in values SiS k-k increases. This suggests that it may be possible to include in the basis set a finite number of states from - max to max seek convergence with respect to In other words, the eigenstates of the Floquet Hamiltonian... 

The energy levels of a molecule placed in an off-resonant microwave field can be calculafed by diagonalizing fhe mafrix of fhe Floquef Hamiltonian in the basis of direct products y) ), where y) represents in the eigenstates of the molecule in the absence of the field and ) - fhe Fourier componenfs in Eq. (8.21). The states k) are equivalent to photon number states in the alternative formalism using the quantum representation of the field [11, 15, 26], The eigensfales of the Floquet Hamiltonian are the coherent superpositions... 

The Schrodinger equation of the Floquet Hamiltonian in JT, where 9 is a dynamical variable, is equivalent, in an interaction representation, to the semiclassical Schrodinger equation in where 0 is considered as a parameter corresponding to the fixed initial phase. The dynamics of the two models are identical if the initial photon state in the Floquet model is a coherent state. 

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