Fock expansion state generation

We can treat FD quantum-optical states as those of a real single-mode electromagnetic field, which fulfill the condition of truncated Fock expansion. These states can directly be generated by the truncation schemes (the quantum scissors) proposed by Pegg et al. [44] and then generalized by other authors [45-47]. Alternatively, one can analyze states obtained by a direct truncation of operators rather then of their Fock expansion. Such an operator truncation scheme, proposed by Leonski et al. [48-50], will be discussed in detail in the next chapter [51]. 

The CC (Coupled-Cluster) method is an attempt to find such an expansion of the wave function in terms of the Slater determinants, which would preserve size consistency. In this method the wave function for the electronic ground state is obtained as a result of the operation of the wave operator exp(f) on the Hartree-Fock function (this ensures size consistency). The wave operator exp(f) contains the cluster operator T, which is defined as the sum of the operators for the /-tuple excitations, 7) up to a certain maximum I = /max- Each fi operator is the sum of the operators each responsible for a particular l-tuple excitation multiplied by its amplitude t. The aim of the CC method is to find the t values, since they determine the wave function and energy. The method generates non-linear... 

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