q-Deformed Barut–Girardello su(1, 1) coherent states and Schrödinger cat states

Abstract

We define Schrödinger cat states as superpositions of q-deformed Barut–Girardello su(1, 1) coherent states with an adjustable angle φ in a q-deformed Fock space. We study the statistical properties of the q-deformed Barut–Girardello su(1, 1) coherent states and Schrödinger cat states. The statistical properties of photons are always sub-Poissonian for q-deformed Barut–Girardello su(1, 1) coherent states. For Schrödinger cat states in the cases φ = 0, π/2, π, the statistical properties of photons are always sub-Poissonian if φ = π/2, and the other cases are hard to determine because they depend on the parameters q and k. Moreover, we find some interesting properties of Schrödinger cat states in the limit |z| → 0, where z is the parameter of those states. We also derive that the statistical properties of photons are sub-Poissonian in the undeformed case where π/2 ≤ φ ≤ 3π/2.