New Families of Coherent States for the Supersymmetric Oscillator

David J. Fernández C., Véronique Hussin, Vicente Said Morales-Salgado

Kengatharam Thirulogasanthar, Adam Krzyżak, Qutaibeh Deeb Katatbeh

Isiaka Aremua, Mahouton Norbert Hounkonnou, Komi Sodoga +1 more

Matthias Ihl

Mordechai Kornbluth, Fredy R. Zypman

This study generalizes the supersymmetric coherent states introduced by Aragone and Zypman in 1986. The Hamiltonian of the supersymmetric quantum harmonic oscillator leads to the definition of the generalized supersymmetric annihilation operators as a 3-parameter family. Their eigenstates are the generalized supercoherent states, which can be calculated explicitly for three relevant regions of parameter space. The uncertainty in position and momentum is discussed, with specific concentration on where the uncertainty is saturated, where it is bounded, and where it is unbounded.

Fredy R. Zypman

We introduce, generate and study a family of supersymmetric displaced number states (SDNS) that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.