Jaynes-Cummings model in a unitary fractional-time description

• URL: http://arxiv.org/abs/2409.05841v1
• Date: Mon, 9 Sep 2024 17:44:31 GMT
• Title: Jaynes-Cummings model in a unitary fractional-time description
• Authors: Danilo Cius,
• Abstract summary: We show that a unitary evolution can be achieved for a traceless two-level Hamiltonian. We apply the unitary description to the Jaynes-Cummings model in the fractional-time scenario.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The time-evolution operator derived from the fractional-time Schr\"odinger equation is considered non-unitary because it fails to preserve the norm of the vector state as time evolves. However, considering the time-dependent non-Hermitian quantum formalism 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, with respect to which the system evolves in a unitary manner, allowing for the proper interpretation of standard quantum mechanical probabilities. In this work, we apply the unitary description to the Jaynes-Cummings model in the fractional-time scenario for investigating the modification in terms of the fractional-order parameter $\alpha$ of the well-known dynamical properties, such as the atomic population inversion of the two-level atom, and the atom-field entanglement when the atom starts in its excited state and field is initially in a coherent state.

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