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Quantum Physics Letters

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

H. A. Hessian

Published Apr 1, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.12785/qpl/020101

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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.
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.
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.
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.
An exact solution of the problem of two-atom one- and two-mode Jaynes-Cummings model with intensity-dependent coupling is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for both models is shown. Conditions and times of disentanglement are derived.
An exact density matrix of a phase-damped Jaynes-Cummings model (JCM) with entangled Bell-like initial states formed from a model two-state atom and sets of adjacent photon number states of a single-mode radiation field is presented. The entanglement of the initial states and the subsequent time evolution is assured by finding a positive lower bound on the concurrence of local $2\ifmmode\times\else\texttimes\fi{}2$ projections of the full $2\ifmmode\times\else\texttimes\fi{}\ensuremath{\infty}$ JCM density matrix. It is found that the time evolution of the lower bound of the concurrence systematically captures the corresponding collapse and revival features in atomic inversion, relative entropies of atomic and radiation, mutual entropy, and quantum deficit. The atom and radiation subsystems exhibit alternating sets of collapses and revivals in a complementary fashion due to the initially mixed states of the atom and radiation employed here. This is in contrast with the result obtained when the initial state of the dissipationless system is a factored pure state of the atom and radiation, where the atomic and radiation entropies are necessarily the same. The magnitudes of the entanglement lower bound and the atomic and radiation revivals become larger as both the magnitude and phase of the Bell-like initial state contribution increase. The time evolution of the entropy difference of the total system and that of the radiation subsystem exhibit negative regions called ``supercorrelated'' states which do not appear in the atomic subsystem. Entangled initial states are found to enhance this supercorrelated feature. Finally, the effect of phase damping is to randomize both the subsystems for asymptotically long times. It may be feasible to experimentally investigate the results presented here using the Rabi oscillation methods of microwave and optical cavity quantum electrodynamics since pure photon number states have recently been produced and observed.