Unitary description of the Jaynes-Cummings model under fractional-time dynamics

• URL: http://arxiv.org/abs/2409.05841v2
• Date: Tue, 04 Feb 2025 14:24:43 GMT
• Title: Unitary description of the Jaynes-Cummings model under fractional-time dynamics
• Authors: Danilo Cius,
• Abstract summary: We show that a unitary evolution can be achieved for a traceless two-level Hamiltonian. We take into account the fractional-order parameter $alpha$ and its effect in unitary quantum dynamics.
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• Abstract: The time-evolution operator corresponding to the fractional-time Schr\"odinger equation is nonunitary because it fails to preserve the norm of the vector state in the course of its evolution. However, in the context of the time-dependent non-Hermitian quantum formalism applied to the time-fractional dynamics, it has been demonstrated that a unitary evolution can be achieved for a traceless two-level Hamiltonian. This is accomplished by considering a dynamical Hilbert space embedding a time-dependent metric operator concerning which the system unitarily evolves in time. This allows for a suitable description of a quantum system consistent with the standard quantum mechanical principles. In this work, we investigate the Jaynes-Cummings model in the fractional-time scenario taking into account the fractional-order parameter $\alpha$ and its effect in unitary quantum dynamics. We analyze the well-known dynamical properties, such as the atomic population inversion and the atom-field entanglement, when the atom starts in its excited state and the field in a coherent state.

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