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Open Physics

Tavis–Cummings model in the presence of a deformed field and time-dependent coupling

Mariam Algarni, S. Abdel‐Khalek, K. Berrada

Published Jan 1, 2025• 0 citations
Publisher

Abstract

Abstract In this work, we introduce a model for a two-atom (T–A) system interacting with a field mode initially prepared in a coherent state of a Para Bose–field (P–F). The T–As are initially represented by a Bell state, and we present the quantum framework for the whole system by solving the dynamical equations. We investigate the time-dependent behavior of essential quantum resources relevant to various tasks in quantum optics and information science, including atomic population inversion, T–As entanglement, T–As-P–F entanglement, and the statistical properties of the P–F as they relate to the model parameters. Our analysis reveals how these quantum resources are affected by different parameters in the T–As-P–F model. Finally, we illustrate the evolving interdependencies among these quantum resources within the system.

DOI
10.1515/phys-2024-0118

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Abstract In this work, we introduce a model for a two-atom (T–A) system interacting with a field mode initially prepared in a coherent state of a Para Bose–field (P–F). The T–As are initially represented by a Bell state, and we present the quantum framework for the whole system by solving the dynamical equations. We investigate the time-dependent behavior of essential quantum resources relevant to various tasks in quantum optics and information science, including atomic population inversion, T–As entanglement, T–As-P–F entanglement, and the statistical properties of the P–F as they relate to the model parameters. Our analysis reveals how these quantum resources are affected by different parameters in the T–As-P–F model. Finally, we illustrate the evolving interdependencies among these quantum resources within the system.
We introduce a framework presenting the interaction between a four-level atom (F-LA) and a field mode that begins in a coherent state within the para-Bose field (P-BF). The F-LA is considered in a cascade configuration and initially prepared in the upper level. We display the system dynamics by solving the motion equation. We discuss various dynamical behaviors of fundamental quantum resources used in quantum optics and information tasks, including atomic population inversion, quantum entanglement (QE), and the statistical properties of the P-BF based on the parameters of the quantum model. In this context, we demonstrate the impact of various system parameters on these quantum resources. Finally, we illustrate the dynamic relationships among the quantum resources within the model.
Abstract This study explores the dynamics of a two two-level atomic system interacting with a parity-deformed field, modeled as a coherent state. By varying the parity deformation parameter and incorporating the effects of intensity-dependent coupling, we examine the time evolution of key quantum phenomena. These include atomic population inversion, von Neumann entropy, concurrence, quantum Fisher information, and the Mandel parameter, where each serves as a critical indicator. Our analysis reveals how the interplay between the deformation parameter and coupling effects governs the quantum dynamics, influencing entanglement, parameter estimation, and statistical properties of the field. These insights contribute to a more comprehensive understanding of how to control and optimize quantum phenomena, highlighting the model’s relevance for quantum information processing technologies.
In this paper, we introduce the parity extension of the harmonic oscillator systems to develop the generalized Tavis-Cummings model (T-CM) based on a specific deformation of the Heisenberg algebra. We present a quantum scheme of a two-qubit system (TQS) interacting with a quantized field that is initially prepared in parity deformed coherent states (PDCSs). The dynamical features of the considered system are explored in the presence of parity deformed parameter (PDP) and time-dependent coupling (t-dc). In particular, we examine the amount of the entanglement formed in the qubit–field and qubit–qubit states. We find that the maximal amount of the entanglement may be occurred periodically during the time evolution. Finally, we investigate the influence of PDP on the Fisher information and the photon statistics of the deformed field with respect to the main parameters of the system.
Abstract In this paper, we demonstrate the exact solution of the nonstationary Schrodinger equation for the Tavis–Cummings model, in which three identical two-level atoms (qubits) are prepared in an arbitrary superposition of 8 Hilbert space vectors and which resonantly interact with a coherent resonator field mode of any intensity. The exact solution was used to calculate the parameters of atom–atom and atom-field entanglement: linear entropy, pairwise and three-particle negativity, and population inversion of three atoms. The results of computer modeling have shown that the degree of correlation between the atoms and the resonator field can significantly depend on the initial state of the atoms. Separable, biseparable, and genuine entangled W -type states demonstrate a high rate of energy exchange between atoms and the resonator field mode and the effect of sudden death of pairwise entanglement of atoms. On the contrary, all GHZ-states exhibit stable pairwise and three-particle entanglement between atoms and a slow rate of energy exchange between atoms and the resonator field mode. We also demonstrate the effect of the sudden death of three-particle entanglement for various states of atoms, the collapse and revival of the Rabi oscillations of the population inversion of three atoms, and the effect of the transition of entanglement from a subsystem of atoms to the total system. These results can be used for optimal operation of quantum networks.
We present a two-mode squeezed Jaynes–Cummings model, built upon the formalism of pair coherent states (PCSs), to investigate the dynamics of a two-level atom interacting with a two-mode quantized field. By solving the time-dependent Schrödinger equation under the rotating-wave approximation, we elucidate the system’s quantum evolution, with particular emphasis on how the squeezing degree and photon number difference modulate atomic population inversion and entanglement. We further quantify the nonclassical traits of the two-mode squeezed PCSs via Mandel’s parameter and the violation of the Cauchy–Schwarz inequality, highlighting their sensitivity to model parameters. These findings illuminate the subtle interplay of squeezing, photon statistics, and entanglement in advanced quantum optical systems.
The coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.