The Franck-Condon overlap and squeezed states

Several years ago Wheeler [25] advanced a conjecture about the parallelism between the FC and squeezed states. Here, we will outline how the operator algebra formalism can be used to develop a unifying scheme from which both phenomena are obtained as particular cases. The close connection between squeezed and the FC states can be seen by considering the case of amplitude-squared squeezed states [26] or, better yet, by considering the recurrence relations and closed formulas which are common to both phenomena [27]. 

In general this operator will distort a general ket m) 

In fact O is a superoperator which maps ladder operators from one space of operators to another  

Using equation (12) we can show that both sets of ladder operators are connected by 

From these operator equations there follow recurrence relations. Indeed, there is a correspondence between the algebraic expressions of the two sets of operators and the associated recurrence relations. The latter in FC factors follows immediately by making z = - nj8 and a = In this context, the 

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