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

TL;DR

This work analyzes the entanglement dynamics of a double Jaynes-Cummings system under realistic imperfections. Through numerical simulations in the strong-coupling regime, it shows that Markovian noise drives monotonic entanglement decay while cavity disorder tends to wash out entanglement features, and that nonlinear driving accelerates dynamics. Notably, thermal noise can induce entanglement sudden death (ESD) and revivals even when absent in the ideal case, whereas nonlinear interactions can delay ESD and, with pumping, even generate ESD/REV without dissipation. The results illuminate the interplay of noise, disorder, and nonlinearity in open quantum systems and offer guidance for robust entanglement control in circuit QED and related technologies, with future work extending to non-Markovian dynamics.

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.

Figures (6)

• Figure 1: (Color online) Entanglement dynamics in double JC model in the single excitation case ($C$) is illustrated as (a) and (b) and the double excitation case ($\tilde{C}$) as (c) and (d). In (a) and (c), symmetric cavities are considered, i.e., $G_A=G_B$, while asymmetry in the double JC model is considered as $G_A=0.9G_B$ in (b) and (d). The rest of the parameters are assumed to be the same for both the cavities, for example, $\kappa_A = \kappa_B = \kappa$, $\gamma_A = \gamma_B = \gamma$ and $\gamma_{\phi}^A = \gamma_{\phi}^B = \gamma_{\phi}$. Here and in what follows, the effect of noises is compared by studying them independently, such as the atomic decay without leakage and dephasing, dephasing without atomic decay and leakage, and cavity leakage without atomic decay and dephasing. Further, $\alpha = \frac{\pi}{6}$ and $\omega_0 = \omega = G_B$, i.e., resonant case is considered.
• Figure 2: Entanglement dynamics in double JC model in the single excitation case ($C$) (in (a), (b), (e), and (f)) and the double excitation case ($\tilde{C}$) (in (c) and (d)). In (a), (c), (e), and (f), symmetric cavities are considered, i.e., $G_A=G_B$, while asymmetry in the double JC model is considered as $G_A=0.9G_B$ in (b) and (d). Also, $N=2$ in (e) and $N=3$ in (f). Dissipation rates are in units of $G_B$. The rest of the parameters are assumed the same as in Figure \ref{['fig:dissipative_linear']}.
• Figure 3: The evolution of concurrence in the nonlinear clean double JC case (without entanglement sudden death) with the addition of a pump. Here, $\alpha = \frac{\pi}{6}$, $G_A = G_B$, and $\epsilon(t) = 0.01$ in Eqs. \ref{['eq:doubleJC,non_lin,pump']}. In (a) $(N,M) \in \{(2,1),(2,2),(3,1)\}$ and $N=3,M=3$ in (b). It is observed that the entanglement oscillates with time in the case of $M<N$. Entanglement sudden deaths and revivals are also observed even in the absence of dissipation. All the plots are generated at resonance.
• Figure 4: Concurrence as in Figure \ref{['fig:non_linear_with_pump']} except the driving pulse is stronger at $\epsilon(t) = 0.04$. In (a) $(N,M) \in \{(2,1),(2,2),(3,1)\}$ and $N=3,M=3$ in (b). It should be noted that the symmetry between the $N=2,M=2$ and $N=3,M=3$ cases is broken when going from $\epsilon = 0.01$ in Figure \ref{['fig:non_linear_with_pump']} to $\epsilon = 0.04$.
• Figure 5: The clean double JC model with (a) uniform and (b) Gaussian disorders introduced for different values of nonlinearity ($N$ in the figure legend) with $G_A = G_B$. Also, $g_A=(1+\delta_A)G_A$ and $g_B=(1+\delta_B)G_B$ are selected independently at random for 1000 iterations according to the respective distribution of $\delta_A$ and $\delta_B$. It is seen that the dynamics of the system are faster for larger values of nonlinearity, which is consistent with earlier observations.