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Journal of Optics B Quantum and Semiclassical Optics

A group property for the coherent state representation of fermionic squeezing operators

Hong-Yi Fan, Chao Li

Published May 29, 2004• 4 citations
Publisher

Abstract

For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.

DOI
10.1088/1464-4266/6/6/007

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For the two-mode fermionic squeezing operators we find that their coherent state projection operator representation make up a loyal representation, which is homomorphic to an SO(4) group, though the fermionic coherent states are not mutual orthogonal. Thus the result of successively operating with many fermionic squeezing operators on a state can be equivalent to a single operation. The fermionic squeezing operators are mappings of orthogonal transformations in Grassmann number pseudo-classical space in the fermionic coherent state representation.
We derive the general form of dynamical Hamiltonian generating the preassigned time-evolution of multimode fermionic squeezing. The fermionic squeezing is a quantum-mechanical image in fermionic Hilbert space corresponding to an orthogonal transformation in pseudo-classical Grassmann number space. The derivation is mainly based on the orthogonal properties of the transformation matrices. It is shown that some new fermionic operator realization of SO (2n) group and some new Hamiltonians can be obtained via this approach.