Fractional-Time Jaynes-Cummings Model: Unitary Description of its Quantum Dynamics, Inverse Problem and Photon Statistics

TL;DR

This paper explores the fractional-time Jaynes-Cummings model's quantum dynamics, revealing how fractional derivatives influence non-classical features, with a transition at alpha=0.50 leading to stable, periodic evolution and enhanced quantum properties.

Contribution

It introduces a unitary framework for fractional-time quantum dynamics and analyzes the effects of fractional derivatives on photon statistics and non-classical states.

Findings

Fractional evolution causes transient dynamics and increased sensitivity to coupling.

A transition at alpha=0.50 shifts from collapse-revival to stable periodic evolution.

Enhanced non-classical properties like sub-Poissonian statistics and Schrödinger cat states.

Abstract

We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schr\"odinger equation. We examine how the fractional derivative order $\alpha$ influences non-classical features under different initial conditions. For an initial Fock state, fractional evolution introduces transient dynamics and heightened sensitivity to coupling strength. Through an inverse problem approach, we interpret these effects as arising from an effective time-dependent coupling with a strong initial pulse. For an initial coherent state, the fractional order tunes the system between dynamical regimes, with a transition at $\alpha = 0.50 $ where standard collapse-and-revival is replaced by stable, periodic evolution. This regime enhances non-classical field properties, including stronger sub-Poissonian statistics, periodic quadrature squeezing, and the formation of Schr\"odinger cat states.