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arXiv:2306.03806

Effects of Markovian noise and cavity disorders on the entanglement dynamics of double Jaynes-Cummings models

Harsh Rathee, Kishore Thapliyal, Anirban Pathak

Published Jun 6, 2023• 0 citations
arXivHTMLPDF

Abstract

The ability to prepare and manipulate non-classical states, such as entangled qubits, is fundamental to the development of quantum information processing, communication, and computation. In this work, we investigate the dynamics of a double Jaynes-Cummings model, a well-established theoretical framework for studying light-matter interactions that captures essential features of a wide range of quantum systems, including circuit QED, optomechanics, and atomic cavity systems. We examine the model under the influence of Markovian noise and static (glassy) cavity disorder. The study aims to elucidate the impact of these imperfections on entanglement dynamics. The system is initialized with the cavity fields in vacuum and the two atoms in a specific entangled superposition state. Through numerical simulations, we observe that the presence of noise and nonlinear pumping gives rise to nontrivial features in the entanglement evolution, including the emergence of entanglement sudden death (ESD) and subsequent revivals in scenarios where such phenomena are absent in the idealized model. Markovian noise leads to a monotonic decay of entanglement, while disorder tends to wash out the entanglement features. Nonlinear interactions, on the other hand, accelerate the dynamical evolution. The combined and competing effects of noise, disorder, and nonlinearity are systematically analyzed, revealing rich and intricate behavior in the entanglement dynamics. These results contribute to a deeper understanding of the robustness and control of entanglement in open quantum systems with imperfections, which is essential for realistic implementations of quantum technologies.

DOI
10.48550/arxiv.2306.03806

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The ability to prepare and manipulate non-classical states, such as entangled qubits, is fundamental to the development of quantum information processing, communication, and computation. In this work, we investigate the dynamics of a double Jaynes-Cummings model, a well-established theoretical framework for studying light-matter interactions that captures essential features of a wide range of quantum systems, including circuit QED, optomechanics, and atomic cavity systems. We examine the model under the influence of Markovian noise and static (glassy) cavity disorder. The study aims to elucidate the impact of these imperfections on entanglement dynamics. The system is initialized with the cavity fields in vacuum and the two atoms in a specific entangled superposition state. Through numerical simulations, we observe that the presence of noise and nonlinear pumping gives rise to nontrivial features in the entanglement evolution, including the emergence of entanglement sudden death (ESD) and subsequent revivals in scenarios where such phenomena are absent in the idealized model. Markovian noise leads to a monotonic decay of entanglement, while disorder tends to wash out the entanglement features. Nonlinear interactions, on the other hand, accelerate the dynamical evolution. The combined and competing effects of noise, disorder, and nonlinearity are systematically analyzed, revealing rich and intricate behavior in the entanglement dynamics. These results contribute to a deeper understanding of the robustness and control of entanglement in open quantum systems with imperfections, which is essential for realistic implementations of quantum technologies.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.
Abstract We consider a generalized double Jaynes–Cummings model consisting of two isolated two-level atoms, each contained in a lossless cavity that interact with each other through a controlled photon-hopping mechanism. We analytically show that at low values of such a mediated cavity–cavity interaction, the temporal evolution of entanglement between the atoms, under the effects of cavity perturbation, exhibits the well-known phenomenon of entanglement sudden death (ESD). Interestingly, for moderately large interaction values, a complete preclusion of ESD is achieved, irrespective of its value in the initial atomic state. Our results provide a model to sustain entanglement between two atomic qubits, under the adverse effect of cavity induced perturbation, by introducing a non-intrusive inter-cavity photon exchange that can be physically realized through cavity-QED setups in contemporary experiments.
We analytically investigate the fidelity dynamics of a Jaynes--Cummings qubit coupled to a single-mode cavity in the presence of stochastic fluctuations of the qubit--cavity coupling. Such fluctuations naturally arise in cavity- and circuit-QED platforms due to fabrication imperfections, control-field noise, mechanical vibrations, and environmental disturbances. Since the qubit--cavity coupling governs the rate of coherent energy and information exchange, understanding the effects of its fluctuations is essential for assessing the performance of quantum communication, quantum sensing, and quantum information-processing protocols. We consider both Gaussian white noise and Ornstein--Uhlenbeck noise with finite correlation time as models for the coupling fluctuations. Exploiting the closed dynamics within each excitation manifold, we derive exact analytical expressions for the noise-averaged density matrix and the fidelity relative to the ideal noiseless evolution. We show that the fidelity is determined by a single decoherence factor governed by the integrated noise correlation function, establishing a direct connection between microscopic coupling fluctuations and macroscopic coherence loss. In the white-noise limit, the fidelity decays exponentially, whereas finite noise correlation times produce nonexponential decay and slower coherence loss. We further show that the crossover between Markovian-like and non-Markovian regimes is controlled by the ratio of the noise correlation rate to the coherent coupling strength, and that decoherence increases with photon number because of the enhanced effective qubit--cavity coupling. These results provide a unified analytical framework for quantifying decoherence induced by stochastic coupling fluctuations and for evaluating the robustness of cavity-QED protocols under correlated noise.
We find that a suppression of the collapse and revival of population inversion occurs in response to insertion of Gaussian quenched disorder in atom-cavity interaction strength in the Jaynes-Cummings model. The character of suppression can be significantly different in the presence of non-Gaussian disorder, which we uncover by studying the cases when the disorder is uniform, discrete, and Cauchy-Lorentz. Interestingly, the quenched averaged atom-photon entanglement keeps displaying nontrivial oscillations even after the population inversion has been suppressed. Subsequently, we show that disorder in atom-cavity interactions helps to avoid sudden death of atom-atom entanglement in the double Jaynes-Cummings model. We identify the minimal disorder strengths required to eliminate the possibility of sudden death. We also investigate the response of entanglement sudden death in the disordered double Jaynes-Cummings model in the presence of atom-atom coupling.
We investigate the entanglement dynamics of two atoms interacting with a single-mode cavity field within the Tavis-Cummings model in the presence of noise. The atoms are initially prepared in either pure Bell states or mixed Werner states, allowing a direct comparison of pure- and mixed-state entanglement. The cavity field is described by generalized single-mode squeezed coherent thermal states, incorporating both thermal and quantum noise effects. Atom-atom and atom-field entanglement are quantified using concurrence and negativity, respectively. We analyze entanglement sudden death and revival, and examine how Ising-type coupling, dipole-dipole interaction, Kerr nonlinearity, and detuning modify the entanglement dynamics. Our results show that thermal photons generally suppress entanglement and enhance sudden death, while squeezing counteracts these effects. The influence of nonlinearities and interatomic interactions depends sensitively on the purity of the initial atomic state, leading to qualitatively different behaviors for Bell and Werner states.
How to analytically deal with the general entanglement dynamics of separate Jaynes–Cummings nodes with continuous-variable fields is still an open question, and few analytical approaches can be used to solve their general entanglement dynamics. Entanglement dynamics between two separate Jaynes–Cummings nodes are examined in this article. Both vacuum state and coherent state in the initial fields are considered through the numerical and analytical methods. The gap between two nonidentical qubit-field coupling strengths shifts the revival period and changes the revival amplitude of two-qubit entanglement. For vacuum-state fields, the maximal entanglement is fully revived after a gap-dependence period, within which the entanglement nonsmoothly decreases to zero and partly recovers without exhibiting sudden death phenomenon. For strong coherent-state fields, the two-qubit entanglement decays exponentially as the evolution time increases, exhibiting sudden death phenomenon, and the increasing gap accelerates the revival period and amplitude decay of the entanglement, where the numerical and analytical results have an excellent coincidence.