Quantum-classical correspondence and the extended Jaynes- Cummings model

Hiromi Ezaki, Seiji Miyashita, Eiichi Hanamura

Масуд Чайчиан, Demosthenes Ellinas, P. P. Kulish

The q-deformations of the quantum harmonic oscillator are used for to describe the generalized Jaynes-Cummings model (JCM) by using the q-analog of the Holstein-Primakoff realization of the su(1,1). The corresponding dynamical symmetry is described by a quantum algebra. The q-analogs of the Barut-Girardello and the Perelomov coherent states are introduced and the expectation value of ${\mathrm{\ensuremath{\sigma}}}_{3}$ is calculated. The periodic revivals of the generalized JCM are destroyed for increasing deformation parameter q. The deformed original JCM in the rotating-wave approximation can be described by the u(1\ensuremath{\Vert}1${)}_{\mathit{q}}$, while its relaxation extends the dynamical algebra to the osp(2\ensuremath{\Vert}2${)}_{\mathit{q}}$ quantum superalgebra.

A. O. Bolivar

Ivan A. Bocanegra-Garay, Miguel Castillo-Celeita, J. Negro +2 more

The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled entirely. A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques, providing an overview of its dynamics and extending the calculation to full photon counting statistics. The approach is general and can be applied to determine the high-order cumulants given an initial state. The analysis reveals that engineering the collapse-revival behavior and the quantum properties of the interacting field is possible by controlling the initial state of the atomic subsystem and the corresponding atomic frequency in the AJC model. The substantial potential for applications of supersymmetric techniques in the context of photonic quantum technologies is thus demonstrated. Published by the American Physical Society 2024

Zou Yan

The quantum properties of Jaynes-Cummings model are expounded in this paper.Several extended Jaynes-Cummings models and their Hamiltonians are also introduced.On this basis,the quantum properties in the systems when they interact with one or two mode fields are discussed.