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

Journal of the Optical Society of America B

Entanglement generation and entropy growth due to intrinsic decoherence in the Jaynes-Cummings model

A.‐S. F. Obada, H. A. Hessian

Published Aug 1, 2004• 43 citations
Publisher

Abstract

We study how intrinsic decoherence leads to growing entropy and a strong degradation of the maximal generated entanglement in the multiquanta Jaynes–Cummings model. We find an exact solution of the Milburn equation in multiquanta precesses and calculate the partial entropy of the particle (atom or trapped ion) and field subsystem as well as total entropy. As the total entropy is not conserved, and it is shown to increase as time develops, one cannot use the partial field or atomic entropy as a direct measure of particle–field entanglement. For a good entropy measure, we also calculate the negativity of the eigenvalues of the partially transposed density matrix. We find that, at least qualitatively, the difference of the total entropy to the sum of field and atom partial entropies can be also used as an entanglement measure. Our results show that the degree of entanglement is very sensitive to any change in the intrinsic decoherence parameter.

DOI
10.1364/josab.21.001535

Related papers

Entropy Growth and Formation of Stationary Entanglement due to Intrinsic Noise in the Two-Mode JC Model

H. A. Hessian

Abstract: We investigate the dynamics of the two-mode Jaynes–Cummings model with generalized nonlinear coupling including intrinsic noise as described by the Milburn equation. Based on a general analytic solution of the corresponding master equation, we calculate the growth of entropy in the system at the special case of two Raman–coupled long lived atomic states as well as the partial entropies of the atom and field subsystem. We see that the system is very sensitive to phase noise, if both fields are initially in a coherent state. The dynamics then rapidly leads to suppression of quantum revivals and a steady entanglement between the fields and the atom. This hints for serious limitations for the use of Raman induced transitions in quantum information processing setups. For an alternative entanglement measure we calculate the negativity of the eigenvalues of the partially transposed density matrix and compare it to the difference of the total entropy to the sum of field and atom partial entropies.

Quantum Physics Letters•Apr 1, 2013•1 citation

Entropy and Entanglement in Master Equation of Effective Hamiltonian for Jaynes–Cummings Model

H. A. Hessian, F.A Mohammed, A.‐B. A. Mohamed

In this paper, we analytically solve the master equation for Jaynes–Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model. The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.

Communications in Theoretical Physics•Apr 1, 2009•0 citations

ENTROPY GROWTH AND DEGRADATION OF ENTANGLEMENT DUE TO DAMPING OF THE ATOMIC DECAY IN THE JC MODEL

H. A. Hessian

In this presentation, we considered the atomic decay (but not for the cavity) for a two-level atom interacting with a single mode of electromagnetic field. The exact solution of the master equation in the case of a high-Q cavity with atomic decay is found. The effects of the atomic damping for a thermal reservoir on the temporal evolution of partial entropies of the atom or the field, and the total entropy as a quantitative entanglement, was measured. The degree of entanglement, through the sum of the negative eigenvalues of the partially transposed density matrix and the negative mutual information, has been studied and compared with other measures.

International Journal of Modern Physics B•Sep 20, 2008•1 citation

Entropy exchange and entanglement in the Jaynes-Cummings model

Erez Boukobza, David J. Tannor

The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.

arXiv:quant-ph/0505119•Physical Review A•Jun 29, 2005•73 citations

Intrinsic decoherence of entanglement of a single quantized field interacting with a two-level atom

Bin Shao

How the mean photon number,the probability of excited state and intrinsic decoherence coefficient influence the time evolution of entanglement is unknown,when a single-mode quantized optic field and a two-level atom coupling system is governed by Milburn equation.The Jaynes-Cummings model is considered.A lower bound of concurrence is proposed to calculate the entanglement.Simulation results indicate that the entanglement of system increases following the increasing of intrinsic decoherence coefficient or the decreasing of the mean photon number.Besides that,the entanglement of the system decreases,while the probability of the exited state increases from 0 to 0.1,and increases,while the probability of the exited state increases from 0.1 to 1.

Journal of Atomic and Molecular Physics•Jan 1, 2006•0 citations

Entropies and entanglement for decoherence without energy relaxation in a two-level atom

A.‐S. F. Obada, H. A. Hessian, A-B A Mohamed

In this paper, we investigate the temporal evolution of various measures of degree of entanglement and total correlation of a single-mode light field interacting with a two-level atom. The phase-damped cavity is taken into account. The effects of phase damping on a temporal of partial entropies for the atom and the field, total entropy, the entropy difference and the sum of negative eigenvalues of the partially transposed density matrix as a quantitative entanglement measure for the master equation in the dressed-state approximation are taken into account.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 5, 2007•33 citations
We study how intrinsic decoherence leads to growing entropy and a strong degradation of the maximal generated entanglement in the multiquanta Jaynes–Cummings model. We find an exact solution of the Milburn equation in multiquanta precesses and calculate the partial entropy of the particle (atom or trapped ion) and field subsystem as well as total entropy. As the total entropy is not conserved, and it is shown to increase as time develops, one cannot use the partial field or atomic entropy as a direct measure of particle–field entanglement. For a good entropy measure, we also calculate the negativity of the eigenvalues of the partially transposed density matrix. We find that, at least qualitatively, the difference of the total entropy to the sum of field and atom partial entropies can be also used as an entanglement measure. Our results show that the degree of entanglement is very sensitive to any change in the intrinsic decoherence parameter.
Abstract: We investigate the dynamics of the two-mode Jaynes–Cummings model with generalized nonlinear coupling including intrinsic noise as described by the Milburn equation. Based on a general analytic solution of the corresponding master equation, we calculate the growth of entropy in the system at the special case of two Raman–coupled long lived atomic states as well as the partial entropies of the atom and field subsystem. We see that the system is very sensitive to phase noise, if both fields are initially in a coherent state. The dynamics then rapidly leads to suppression of quantum revivals and a steady entanglement between the fields and the atom. This hints for serious limitations for the use of Raman induced transitions in quantum information processing setups. For an alternative entanglement measure we calculate the negativity of the eigenvalues of the partially transposed density matrix and compare it to the difference of the total entropy to the sum of field and atom partial entropies.
In this paper, we analytically solve the master equation for Jaynes–Cummings model in the dispersive regime including phase damping and the field is assumed to be initially in a superposition of coherent states. Using an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix we find a very strong sensitivity of the maximally generated entanglement to the amount of phase damping. Qualitatively this behavior is also reflected in alternative entanglement measures, but the quantitative agreement between different measures depends on the chosen noise model. The phase decoherence for this model results in monotonic increase in the total entropy while the atomic sub-entropy keeps its periodic behaviour without any effect.
In this presentation, we considered the atomic decay (but not for the cavity) for a two-level atom interacting with a single mode of electromagnetic field. The exact solution of the master equation in the case of a high-Q cavity with atomic decay is found. The effects of the atomic damping for a thermal reservoir on the temporal evolution of partial entropies of the atom or the field, and the total entropy as a quantitative entanglement, was measured. The degree of entanglement, through the sum of the negative eigenvalues of the partially transposed density matrix and the negative mutual information, has been studied and compared with other measures.
The Jaynes-Cummings model (JCM) is the simplest fully quantum model that describes the interaction between light and matter. We extend a previous analysis by Phoenix and Knight [Ann. Phys. 186, 381 (1988)] of the JCM by considering mixed states of both the light and matter. We present examples of qualitatively different entropic correlations. In particular, we explore the regime of entropy exchange between light and matter, i.e., where the rate of change of the two are anticorrelated. This behavior contrasts with the case of pure light-matter states in which the rate of change of the two entropies are positively correlated and in fact identical. We give an analytical derivation of the anticorrelation phenomenon and discuss the regime of its validity. Finally, we show a strong correlation between the region of the Bloch sphere characterized by entropy exchange and that characterized by minimal entanglement as measured by the negative eigenvalues of the partially transposed density matrix.
How the mean photon number,the probability of excited state and intrinsic decoherence coefficient influence the time evolution of entanglement is unknown,when a single-mode quantized optic field and a two-level atom coupling system is governed by Milburn equation.The Jaynes-Cummings model is considered.A lower bound of concurrence is proposed to calculate the entanglement.Simulation results indicate that the entanglement of system increases following the increasing of intrinsic decoherence coefficient or the decreasing of the mean photon number.Besides that,the entanglement of the system decreases,while the probability of the exited state increases from 0 to 0.1,and increases,while the probability of the exited state increases from 0.1 to 1.
In this paper, we investigate the temporal evolution of various measures of degree of entanglement and total correlation of a single-mode light field interacting with a two-level atom. The phase-damped cavity is taken into account. The effects of phase damping on a temporal of partial entropies for the atom and the field, total entropy, the entropy difference and the sum of negative eigenvalues of the partially transposed density matrix as a quantitative entanglement measure for the master equation in the dressed-state approximation are taken into account.