Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1702.03740

Dynamic correlation funtions of the generalized Tavis-Cummings model

N. M. Bogoliubov, Igor Ermakov, Rybin, Andrey

Published Feb 13, 2017• 2 citations
arXivHTMLPDF

Abstract

The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution obtained by application of the quantum inverse method (QIM). The dynamic correlation functions are calculated and transition elements of photons are represented in the determinant form. The obtained answers depend on the solutions of Bethe equations. We provide the numerical solutions of these equations for the different parameters of the model and study the behaviour of certain dynamical correlation functions.

DOI
10.48550/arxiv.1702.03740

Related papers

Time evolution of the atomic inversion for the generalized Tavis–Cummings model—QIM approach

N. M. Bogoliubov, Igor Ermakov, Andrei V. Rybin

Abstract A model describing the interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution obtained by application of the quantum inverse method (QIM). Time evolution of the atomic inversion is calculated and transition elements of photons are represented in the determinant form. The obtained answers depend on the solutions of the Bethe equations. We provide the numerical solutions of these equations for the different parameters of the model and study the behaviour of certain dynamical correlation functions.

Journal of Physics A Mathematical and Theoretical•Oct 23, 2017•8 citations

Exact solution of generalized Tavis - Cummings models in quantum optics

N. M. Bogoliubov, R. Bullough, JUSSI TIMONEN

Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogeneous ordinary differential equation of second order. Generalization of the method to the case of several cavity modes is indicated.

Journal of Physics A Mathematical and General•Oct 7, 1996•108 citations

Dynamics of entanglement in a two-mode nonlinear Jaynes-Cummings mode

A. B. M. Ahmed, S. Sivakumar

Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.

arXiv:0907.2992•Jul 17, 2009•2 citations

Dynamics of atom-field interaction inside a nonlinear Kerr-like medium filled optical cavity

Naveen Kumar, Arpita Chatterjee

In this paper, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of the time-dependent Schrödinger equation that provides a comprehensive framework for analyzing the system's quantum properties. To characterize the nonclassical features of the radiation field, we examine photon number distribution, second-order correlation function 𝑔2⁡(0), squeezing properties, and Mandel's 𝑄𝑀 parameter. These properties reveal significant insights into the quantum statistical behaviour of the field and its deviation from classicality under different interaction regimes. In addition, we quantify the atom-atom entanglement using linear entropy which captures the mixedness of the atomic subsystem and elucidates the interplay between atom-atom interactions. The results highlight the crucial role of nonlinear interactions and the Stark shift in shaping the quantum correlations and nonclassical phenomena of the system.

arXiv:2503.16866•Journal of Modern Optics•Mar 18, 2025•1 citation

Effect of an external radiation field on the properties of the atoms and cavity field in the two-atom Tavis–Cummings model

Wang Zhong-Chun, Wang Qi, Zhang Yong-Sheng +1 more

We study the properties of atoms and cavity field in the two-atom Tavis–Cummings model where the two atoms interact with each other and are also driven by an external classical field. We consider the special case that the cavity is initially in a coherent state. The atomic inversion, the average photons number and the Mandel parameter in the driven Tavis–Cummings model are given and analysed numerically. We pay special attention to the dynamical behaviour of the atoms and the cavity field modified by the external field.

Chinese Physics•Dec 23, 2004•2 citations

Dynamics of a nonlinear time-dependent two two-level atoms in a two-mode cavity

Sameh T. Korashy, Tarek M. El-Shahat, Nabil Habiballah +2 more

In this paper, we present some properties through two two-level atoms interacting with a two-mode quantized cavity field. We study this system in the presence of detuning parameter, Kerr nonlinearity, Stark shift, relative phase and intensity-dependent atoms-field coupling. Also, the coupling parameter is modulated to be time dependent. The exact solution of this model is given by using the Schrődinger equation when the atoms and the field are initially prepared in superposition states and coherent states, respectively. We employed the results to calculate some aspects such as linear entropy, total atomic inversion and cross-correlation function.

International Journal of Quantum Information•Apr 1, 2020•7 citations
The model describing interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution obtained by application of the quantum inverse method (QIM). The dynamic correlation functions are calculated and transition elements of photons are represented in the determinant form. The obtained answers depend on the solutions of Bethe equations. We provide the numerical solutions of these equations for the different parameters of the model and study the behaviour of certain dynamical correlation functions.
Abstract A model describing the interaction between two-level atoms and a single mode field in an optical cavity enclosed by a medium with Kerr nonlinearity is considered in our paper. We study the model within the framework of the analytical solution obtained by application of the quantum inverse method (QIM). Time evolution of the atomic inversion is calculated and transition elements of photons are represented in the determinant form. The obtained answers depend on the solutions of the Bethe equations. We provide the numerical solutions of these equations for the different parameters of the model and study the behaviour of certain dynamical correlation functions.
Quantum inverse methods are developed for the exact solution of models which describe N two-level atoms interacting with one mode of the quantized electromagnetic field containing an arbitrary number of excitations M. Either a Kerr-type nonlinearity or a Stark-shift term can be included in the model, and it is shown that these two cases can be mapped from one to the other. The method of solution provides a general framework within which many related problems can similarly be solved. Explicit formulae are given for the Rabi splitting of the models for some N and M, on- and off-resonance. It is also shown that the solution of the pure Tavis - Cummings model can be reduced to solving a homogeneous ordinary differential equation of second order. Generalization of the method to the case of several cavity modes is indicated.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.
In this paper, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of the time-dependent Schrödinger equation that provides a comprehensive framework for analyzing the system's quantum properties. To characterize the nonclassical features of the radiation field, we examine photon number distribution, second-order correlation function 𝑔2⁡(0), squeezing properties, and Mandel's 𝑄𝑀 parameter. These properties reveal significant insights into the quantum statistical behaviour of the field and its deviation from classicality under different interaction regimes. In addition, we quantify the atom-atom entanglement using linear entropy which captures the mixedness of the atomic subsystem and elucidates the interplay between atom-atom interactions. The results highlight the crucial role of nonlinear interactions and the Stark shift in shaping the quantum correlations and nonclassical phenomena of the system.
We study the properties of atoms and cavity field in the two-atom Tavis–Cummings model where the two atoms interact with each other and are also driven by an external classical field. We consider the special case that the cavity is initially in a coherent state. The atomic inversion, the average photons number and the Mandel parameter in the driven Tavis–Cummings model are given and analysed numerically. We pay special attention to the dynamical behaviour of the atoms and the cavity field modified by the external field.
In this paper, we present some properties through two two-level atoms interacting with a two-mode quantized cavity field. We study this system in the presence of detuning parameter, Kerr nonlinearity, Stark shift, relative phase and intensity-dependent atoms-field coupling. Also, the coupling parameter is modulated to be time dependent. The exact solution of this model is given by using the Schrődinger equation when the atoms and the field are initially prepared in superposition states and coherent states, respectively. We employed the results to calculate some aspects such as linear entropy, total atomic inversion and cross-correlation function.