Vector Cooper pairs and coherent-population-trapping-like states in ensemble of interacting fermions

Using the standard Hamiltonian of the BCS theory, we show that in an ensemble of interacting fermions with the spin 1/2 there exist coherent states |NC〉, which nullify the Hamiltonian of the interparticle interaction (scattering). These states have an analogy with the well-known in quantum optics the coherent population trapping (CPT) effect. The structure of these CPT-like states corresponds to Cooper pairs with the total spin S = 1. The found states have a huge degree of degeneracy and carry a macroscopic magnetic moment, that allows us to construct a new model of the magnetism connected with the delocalized electrons in metals (conductors). A principal possibility to apply the obtained results to the superfluid ³He is also demonstrated.