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arXiv:2507.05407 · Physica Scripta

Curvature-induced nonclassicality in a generalized Jaynes–Cummings model

Somayeh Kourkinejat, Ali Mahdifar, Ehsan Amooghorban

Published Jun 25, 2026• 1 citation
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Abstract

Abstract In this paper, we investigate the influence of spatial curvature on the Jaynes–Cummings model (JCM). We employ an analog model of general relativity, where the cavity field is represented by oscillators on a circle instead of a straight line, so that increasing curvature corresponds to decreasing the circle’s radius. We investigate the nonclassical features of this quantum system arising from the interaction between a two-level atom and a deformed harmonic oscillator on a circle, which serves as curved-space counterpart to the flat oscillator. We also propose an experimental scheme to realize this curvature-dependent JCM, based on the intensity-dependent Jaynes–Cummings interaction that appears in a laser-driven trapped ion inside a Kerr medium. By analyzing the time evolution of the atom-field system, we examine how spatial curvature influences the Mandel parameter, entropy, and the behavior of the Wigner distribution function. Our results demonstrate that the spatial curvature plays a crucial role in controlling these nonclassical properties.

DOI
10.1088/1402-4896/ae82ca

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Abstract In this paper, we investigate the influence of spatial curvature on the Jaynes–Cummings model (JCM). We employ an analog model of general relativity, where the cavity field is represented by oscillators on a circle instead of a straight line, so that increasing curvature corresponds to decreasing the circle’s radius. We investigate the nonclassical features of this quantum system arising from the interaction between a two-level atom and a deformed harmonic oscillator on a circle, which serves as curved-space counterpart to the flat oscillator. We also propose an experimental scheme to realize this curvature-dependent JCM, based on the intensity-dependent Jaynes–Cummings interaction that appears in a laser-driven trapped ion inside a Kerr medium. By analyzing the time evolution of the atom-field system, we examine how spatial curvature influences the Mandel parameter, entropy, and the behavior of the Wigner distribution function. Our results demonstrate that the spatial curvature plays a crucial role in controlling these nonclassical properties.
Abstract In this article, we introduce generalized Gilmore-Perelomov-type coherent states of a quantum harmonic oscillator on a circle and demonstrate that their underlying algebra is a deformed su(1,1). The effects of the circle’s spatial curvature are inherently encoded in these states, making them suitable for investigating curvature-induced phenomena in quantum optical processes at laboratory scales. Furthermore, we propose an experimental scheme to realize these states based on the intensity-dependent version of the Jaynes–Cummings model appearing in a laser-driven trapped ion. Employing the nonlinear coherent states of the atomic center of mass motion of a trapped ion, it is possible to control the laser-ion interaction in such a way that Gilmore-Perelomov-type circle coherent states are obtained as motional dark states of the system. Finally, by examining quadrature squeezing, we demonstrate that unlike standard coherent states which exhibit no squeezing, these curvature-dependent states display curvature-tunable squeezing effects. This property makes them particularly valuable for applications in high-precision metrology.
In this paper, we investigate the interaction between a vee-type three-level atom and a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium and an intensity-dependent coupling. We have elucidated the system by a nonlinear Hamiltonian constructed from the standard Jaynes–Cummings model by deforming the field operators and adding some nonlinear terms. Using the initial conditions that the atom is prepared in an excited state and the field is in a coherent state, the state vector of the entire system is determined analytically. The time evolution of nonclassical properties such as Mandel Q, quantum entanglement and position-momentum uncertainty relation (squeezing) of the field are investigated. The quasiprobability distributions are also computed for the resultant state. The effects of the detuning parameters, generalized Kerr medium and intensity-dependent coupling on the previous nonclassicality signs are analysed, in detail.
In this article, we explore the interaction between a V-type atom inside a single mode deformed cavity field in the presence of an external microwave field. The Hamiltonian describing the system is derived from the standard Jaynes-Cummings model by deforming the field operators based on the Kerr-induced interaction. The total and reduced density matrices are obtained and the temporal evolution of nonclassical properties such as the Mandel Q parameter, quantum entanglement, and the position-momentum uncertainty relation (squeezing) of the field are examined. The impacts of coupling constant, generalized Kerr medium, and the intensity-dependent coupling function on the nonclassical indicators are thoroughly analyzed.
A theoretical study of the dynamical behaviors of the interaction between a two-level atom with a Morse potential in the framework of the Jaynes–Cummings model (JCM) is discussed. We show that this system is equivalent to an intensity-dependent coupling between the two-level atom and the non-deformed single-mode radiation field in the presence of an additional nonlinear interaction. We study the dynamical properties of the system such as, atomic population inversion, the probability distribution of cavity-field, the Mandel parameter and atomic dipole squeezing. It is shown how the depth of the Morse potential can be affected by non-classical properties of the system. Moreover, the temporal evolution of the Husimi-distribution function is explored.
The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement.
The nonclassical properties of light and atomic dynamics are studied. The system considered are two level atom interact with a quantized field in a high quality cavity, which is recognized as the Jaynes-Cumming Model. The time- and intensity-dependent atom-field coupling are applied to the system, with different initial field states and initial atomic states. We also extend the system for three level atom in a cavity, and include the dissipative mechanism in the system. We consider the laser driven three level atom in a cavity coupled to a reservoir. Interesting effects of the transient coupling are analyzed through the collapse-revival pattern in population inversion, while the nonclassicality of cavity field is studied through the features in the evolution ofWigner function. The inversion of initial superposed atomic state seems to be independent of initial classical fields but can be stimulated by the Schrodinger cat field. In two level system, the oscillatory coupling coefficient can prolong the occurrence of collapse, in analogy to the Zeno effect.The intensity atom-field coupling duration is an important parameter for controlling atomic inversion and producing frozen nonclassical light in the cavity after the atom-field coupling ceases. The theory developed will provide useful physical insights for future experimental work and enhance significant knowledge on the nonclassicality of light in matter-wave interaction. The research results will particularly benefit quantum information technology.