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Dynamics of quantum coherence in the Jaynes–Cummings model with quenched disorder

J.H. Warnes, F. M. de Paula, Natanael C. Costa, O. P. de Sá Neto

Published Mar 2, 2023• 5 citations
Publisher

Abstract

We have applied the quantum coherence theory to the Jaynes–Cummings model for three types of quenched disorder distribution: uniform, Gaussian, and Cauchy-Lorentz. Under certain conditions, we have observed a beat-damping behavior on the dynamics of the l1-norm of coherence. This phenomenon is more evident for the uniform disorder distribution.

DOI
10.1016/j.physo.2023.100146

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We have applied the quantum coherence theory to the Jaynes–Cummings model for three types of quenched disorder distribution: uniform, Gaussian, and Cauchy-Lorentz. Under certain conditions, we have observed a beat-damping behavior on the dynamics of the l1-norm of coherence. This phenomenon is more evident for the uniform disorder distribution.
In this paper, we present a simple approach for understanding some general aspects of the irreversible dynamics of the generalized Jaynes-Cummings model. By working in the dressed-state representation, it is possible to split the dynamics of populations and coherences. Then it can be shown that the coherence dynamics may present localization and dispersivelike decay behavior, whereas the population dynamics are characterized in terms of a classical diffusive process. These phenomena are studied by developing a perturbation theory that provides simple analytical results that could be applicable to any general source of irreversibility in the Jaynes-Cummings model. As an application, we extend and analytically characterize our previous reported results on heating and decoherence in trapped ions [Phys. Rev. A 65, 041402 (2002)].
The distribution of entanglement of typical multiparty quantum states is not uniform over the range of the measure utilized for quantifying the entanglement. We intend to find the response of quenched disorder in the state parameters on this non-uniformity for typical states. We find that the typical entanglement, quenched averaged over the disorder, is taken farther away from uniformity, as quantified by decreased standard deviation, in comparison to the clean case. The feature is seemingly generic, as we see it for Gaussian and non-Gaussian disorder distributions, for varying strengths of the disorder, and for disorder insertions in one and several state parameters. The non-Gaussian distributions considered are uniform and Cauchy-Lorentz. Two- and three-qubit pure state Haar-uniform generations are considered for the typical state productions. We also consider noisy versions of the initial states produced in the Haar-uniform generations. A genuine multiparty entanglement monotone is considered for the three-qubit case, while concurrence is used to measure two-qubit entanglement.
We study the quantum dynamics of a two-mode two-photon Jaynes–Cummings model of a two-level atom interacting with the correlated two-mode SU(1, 1) coherent states. The collapse and revival patterns in this case are noted to be quite different from those in the case of uncorrelated coherent states and correlated pair-coherent states. As an example of the time evolution of the field statistics we show that violation of the Cauchy–Schwartz inequality by the initial field states may be nullified. We also discuss the evolution of the variance of the two-mode field quadrature operator.
Abstract We consider the average quantum coherences of typical redits and qudits—vectors of real and complex Hilbert spaces—with the analytical forms stemming from the symmetry of Haar-uniformly distributed random pure states. We subsequently study the response to disorder in spread of the typical quantum coherence in response to glassy disorder. The disorder is inserted in the state parameters. Even in the absence of disorder, the quantum coherence distributions of redits and qudits are not uniform over the range of quantum coherence, and the spreads are relatively lower for higher dimensions. On insertion of disorder, the spreads decrease. This decrease in the spread of quantum coherence distribution in response to disorder is seen to be a generic feature of typical pure states: we observe the feature for different strengths of disorder and for various types of disorder distributions, viz. Gaussian, uniform, and Cauchy–Lorentz. We also find that the quantum coherence distributions become less asymmetric with increase in dimension and with infusion of glassy disorder.
The time evolution of the Wehrl entropy and Wehrl phase distribution for the multiphoton Jaynes Cummings model, where the dynamics is described by the phase-damped terms, is studied. Analytical and numerical results under certain parametric conditions are obtained by means of which we analyze the influence of dissipation on the dynamics of Husimi Q-function, Wehrl entropy and Wehrl phase distribution for different values of the Stark shift parameter. Our results show that information about the dynamical properties of the system can be obtained through the Wehrl entropy and Wehrl phase distribution from the point of view of phase-space information. An interesting relation between the correlation, Stark shift and decoherence effect is observed.