Coherent and Supercoherent States with Some Recent Applications

Monique Combescure, Didier Robert

Sumiyoshi Abe

Jean-Pierre Antoine, Bagarello, Fabio, Jean‐Pierre Gazeau

Carlos Aragone, Fredy R. Zypman

The authors present the supercoherent states. They are introduced as the eigenstates of the supersymmetric annihilation operator of the quantum mechanical supersymmetric harmonic oscillator. They have a compact expression in terms of the standard (bosonic) coherent states. For each value of the complex parameter z there are two linearly independent orthogonal supercoherent states. One of them has pure fermionic character and is the more classical, while the other is fully supersymmetric (i.e. the mean value of the Klein operator when the system is set in this state vanishes). There are no purely bosonic supercoherent states. The supercoherent fermionic states saturate both the Heisenberg uncertainty relation and the new entropic uncertainty recently introduced by Deutsch (1983), while the supersymmetric ones almost (but not exactly) make it. They give a classical (or almost classical) mean value for the energy of the system and do not spread along their time evolution.

A. M. Perelomov

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Two photon supercoherent states are the eigenstates of square of the supersymmetric annihilation operator In this paper we investigate the entanglement of two classes of these states To this end orthogonal and normalized bosonic bases are introduced and supercoherent states would be transformed to the twoqubit ones with the use of them It is observed that twophoton supercoherent states are entangled and their entanglement depends on the coherency parameter unlike the onephoton supercoherent states The entanglement behavior of these two classes of states are different for large values of the coherency parameter However the maximum of fluctuation of entanglement occurs for both of these two classes in small values of coherency parameter