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arXiv:2602.04543

Effect of initial intrasystem entanglement on entropy growth in generalized Jaynes-Cummings models

Daria Gaidukevich

quant-phSubmitted Feb 4, 2026• Announced Feb 5, 2026• 0 citations• Revised Feb 25, 2026 (v4)
v1 · Feb 4, 2026v2 · Feb 6, 2026v3 · Feb 10, 2026v4 · Feb 25, 2026
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Abstract

We investigate how initial intrasystem entanglement influences the entropy generated in atomic systems interacting with a photonic environment in several generalizations of the Jaynes-Cummings model with two or more subsystems. Since the initial entanglement does not uniquely determine the final entropy, we focus on ensemble-averaged behavior. We consider ensembles of initial system states, including pure and mixed Haar-random states, ensembles with fixed average energy or fixed mixedness, and varying initial photon numbers in the environment. In all cases, we observe a positive correlation between the initial entanglement and the entropy growth, although the fractional contribution of the initial entanglement varies. Our results emphasize the role of intrasystem correlations as a factor contributing to entropy growth in quantum informational processes.

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9 pages, 5 figures

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We investigate how initial intrasystem entanglement influences the entropy generated in atomic systems interacting with a photonic environment in several generalizations of the Jaynes-Cummings model with two or more subsystems. Since the initial entanglement does not uniquely determine the final entropy, we focus on ensemble-averaged behavior. We consider ensembles of initial system states, including pure and mixed Haar-random states, ensembles with fixed average energy or fixed mixedness, and varying initial photon numbers in the environment. In all cases, we observe a positive correlation between the initial entanglement and the entropy growth, although the fractional contribution of the initial entanglement varies. Our results emphasize the role of intrasystem correlations as a factor contributing to entropy growth in quantum informational processes.
The effects of a chaotic field on the entanglement dynamics in a system of interaction of a two-level atom with a single-mode cavity field prepared in a Glauber–Lachs state were investigated in the framework of the Jaynes–Cummings model. We found that the entanglement is a non-monotonic function of the ratio of the mean numbers of thermal photons and coherent photons or, equivalently, the degree of initial mixedness of the system. There is an optimal value of this ratio up to which thermal photons contribute increasingly to the entanglement and after which they weaken the strength of the entanglement.
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.
The information entropy squeezing properties of the atom interacting with the Glauber-Lachs state in multi-photon Jaynes-Cummings model are studied by means of the full quantum theory.The influences of the mean number of the coherent photons,the average number of the thermal photons,the number of the transition photons and the atomic initial state on the information entropy squeezing of the atom are discussed.The results indicate that there is no entropy squeezing in the Xcomponent of information entropy of the atom at any instant of the time evolution of the system.But there exists an entropy squeezing in the Ycomponent of information entropy of the atom during the time evolution when the mean number of coherent photons takes an appropriate value.The mean number of thermal photons and the number of the transition photons have a destructive effect on the Ycomponent of information entropy of the atom.The atomic initial state has no effect on the entropy squeezing in the Ycomponent of information entropy of the atom.If the number of the transition photons equals to two,the time evolution of the entropy squeezing factor appears periodic change.
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.
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.