Physics – Quantum Physics
Scientific paper
1996-08-14
Phys.Rev. A54 (1996) 5253
Physics
Quantum Physics
to appear in Phys. Rev. A, REVTeX, 18 pages, 3 figures (compressed PostScript, available at http://www.technion.ac.il/~brif/
Scientific paper
10.1103/PhysRevA.54.5253
We introduce a set of coherent states which are associated with quantum systems governed by a trilinear boson Hamiltonian. These states are produced by the action of a nonunitary displacement operator on a reference state and can be equivalently defined by some eigenvalue equations. The system prepared initially in the reference state will evolve into the coherent state during the first instants of the interaction process. Some properties of the coherent states are discussed. In particular, the resolution of the identity is derived and the related analytic representation in the complex plane is developed. It is shown that this analytic representation coincides with a double representation based on the Glauber coherent states of the pump mode and on the SU(1,1) Perelomov coherent states of the signal-idler system. Entanglement between the field modes and photon statistics of the coherent states are studied. Connections between the coherent states and the long-time evolution induced by the trilinear Hamiltonian are considered.
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