Unitary Description of the Jaynes-Cummings Model with Fractional Time: Photon Statistics

Recently, a unitary model for the fractional-time Jaynes-Cummings model was proposed. In this work, we deepen the understanding of the model by analyzing its photon statistics, considering an initial coherent state. Depending on the value of the fractional order $\alpha$, various interesting phenomena are affected, such as sub-Poissonian statistics, squeezing and cat states for the cavity mode. The case where $\alpha=0.50$ results in periodic squeezing and the formation of cat states. The latter aspect indicates similarities with the two-photon standard Jaynes-Cummings model.