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

Chinese Physics Letters

Bistable Behaviour of N Two-Level Atoms Interacting with the Field inside a High- Q Cavity Containing a Nonlinear Kerr-Like Medium

Luo Jin-Ming, Jiahua Li, Xiao-Tao Xie

Published Jun 28, 2006• 0 citations
Publisher

Abstract

Taking the intensity-dependent coupling between atoms and cavity mode into account, we investigate a system consisting of N homogeneously broadened two-level atoms interacting with the field inside a single-mode Fabry–Perot cavity containing a nonlinear Kerr-like medium. We derive the steady-state bistable behaviour of the system, and further analyse in details the influence of several critical parameters on the bistable behaviour.

DOI
10.1088/0256-307x/23/7/032

Related papers

Bistable Behaviour of N Two-Level Atoms Interacting with the Field inside a High-Q Cavity Containing a Nonlinear Kerr-Like Medium

罗进明, 李家华, 谢小涛

拿在原子和洞模式之间联合进帐号的紧张依赖者,我们调查同类地由 N 组成的一个系统拓宽的二水平的原子在包含非线性的象 Kerr 一样媒介的一个单个模式的 Fabry-Perot 洞内与这域交往。Wederive 系统的不变的双稳态的行为,和在细节的进一步的分析双稳态的行为上的几个批评参数的影响。

Chinese Physics Letters•Jan 1, 2006•0 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

A moving four-levelN-type atom interacting with cavity fields

N. H. Abdel-Wahab

We study the non-resonant interaction of a moving four-level N -type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.

Journal of Physics B Atomic Molecular and Optical Physics•May 6, 2008•31 citations

Optical bistability through nonlinear dispersion and absorption

Govind Prasad Agrawal, H. J. Carmichael

A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.

Physical Review A•May 1, 1979•168 citations

Dynamics of a deformed atom cavity field system in presence of a Kerr-like medium

Arpita Chatterjee

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.

Journal of Modern Optics•Mar 1, 2019•8 citations

Nondegenerate two-photon optical bistability in a Fabry-Perot cavity filled with large-permanent-dipole molecules

T. Kobayashi, Nitin C. Kothari, Hisao Uchiki

A semiclassical theoretical model is described under the plane-wave and mean-field approximations on the transmission characteristics of a system of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity and driven by two coherent two-photon resonant fields. In the steady-state situation, the coupled field equations are solved by eliminating one of the field variables to obtain the state equation. This state equation is numerically analyzed in detail, thus providing the regions on two-dimensional maps corresponding to one, three, and five stationary states of the system. The linear stability analysis is also carried out for the case when the length of the cavity is such that the medium-relaxation times are much shorter than the cavity-photon life times for both the waves. The simple stability criterion that the negative-slope regions of the transmission curves are unstable holds, but only the lowest positive-slope branches show stability in all of the cases we tested numerically.

Physical Review A•May 1, 1984•26 citations
Taking the intensity-dependent coupling between atoms and cavity mode into account, we investigate a system consisting of N homogeneously broadened two-level atoms interacting with the field inside a single-mode Fabry–Perot cavity containing a nonlinear Kerr-like medium. We derive the steady-state bistable behaviour of the system, and further analyse in details the influence of several critical parameters on the bistable behaviour.
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 non-resonant interaction of a moving four-level N -type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.
A general theory of optical bistability for a homogeneously broadened two-level system in a Fabry-Perot interferometer is presented. Both absorptive and dispersive mechanisms are included, and in the mean-field approximation a cubic state equation is derived relating transmitted intensity to all physical parameters. From the perspective of catastrophe theory, this equation describes an elementary cusp catastrophe. We show that bistable switching may follow not only from sweeping the incident laser intensity, but also with continuous variation of atomic or cavity detuning, or atomic density, with the laser intensity fixed. For the case having incident intensity as the variable control, the domain of bistability is studied in some detail as a function of the remaining fixed parameters. Stability criteria are considered for the general case including both absorption and dispersion.
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.
A semiclassical theoretical model is described under the plane-wave and mean-field approximations on the transmission characteristics of a system of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity and driven by two coherent two-photon resonant fields. In the steady-state situation, the coupled field equations are solved by eliminating one of the field variables to obtain the state equation. This state equation is numerically analyzed in detail, thus providing the regions on two-dimensional maps corresponding to one, three, and five stationary states of the system. The linear stability analysis is also carried out for the case when the length of the cavity is such that the medium-relaxation times are much shorter than the cavity-photon life times for both the waves. The simple stability criterion that the negative-slope regions of the transmission curves are unstable holds, but only the lowest positive-slope branches show stability in all of the cases we tested numerically.