A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators is analyzed. The metric which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed, which correspond to the pseudo-Hermitian supersymmetric system of the boson-phermion oscillator. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.

http://arxiv.org/abs/1009.5293
Quantum Physics (quant-ph)