Generation of optomicrowave and optomagnonic entanglements in cascaded optomagnomechanical systems

TL;DR

Addressing the challenge of distributing quantum entanglement across heterogeneous platforms, the paper proposes a cascaded optomagnomechanical system to generate and elevate optomicrowave and optomagnonic entanglement and to realize quadripartite entanglement. The authors model two cascaded hybrid nodes, derive the linearized quantum Langevin equations, and compute the steady-state covariance matrix by solving the Lyapunov equation $\mathcal{A}V+V\mathcal{A}^T=-\mathcal{D}$, quantifying entanglement with logarithmic negativity $E_N$. They analyze how detunings, decay rates, coupling strengths, and transmission efficiencies affect entanglement, and identify parameter regions that maximize cascaded enhancement. The results show substantial entanglement boost in the second cavity and the emergence of multipartite entanglement across the cascade, offering a theoretical blueprint for building hybrid quantum networks that couple microwave, optical, and magnon degrees of freedom.

Abstract

The optomagnomechanical system, which involves flexible nonlinearities, is one of the promising physical platforms for studying the preparation and manipulation of quantum entanglements, as well as the construction of hybrid quantum networks. A scheme for entanglement enhancement and quadripartite entanglement generation is proposed, based on a cascaded optomagnomechanical system. On the one hand, optomicrowave and optomagnonic entanglements within the two subsystems are investigated, and their parameter dependence, such as detuning, decay, coupling strength, and transmission efficiency, is discussed. On the other hand, the parameter conditions for achieving optimal optomicrowave and optomagnonic quadripartite entanglements are also obtained. The results show that significant enhancement of optomicrowave and optomagnonic entanglements in the second cavity can be obtained in a certain range of parameters. Under optimized parameter conditions, optomicrowave and optomagnonic quadripartite entanglements can be generated throughout the entire cascaded system. This research provides a theoretical basis for the manipulation of quantum entanglement, the transmission of the magnon's state, and the construction of hybrid quantum networks involving different physical systems.

Figures (7)

• Figure 1: (a) Schematic diagram of the cascaded optomagnomechanical system for generating optomagnonic and optomicrowave entanglements. (b) frequency relation. (c) interaction between various modes.
• Figure 2: The optomicrowave entanglements ($E_{a_1c_1}$ and $E_{a_2c_2}$) and the optomagnonic entanglements ($E_{m_1c_1}$ and $E_{m_2c_2}$) versus the effective detuning of magnon mode (a,d), the detuning of microwave mode (b,e), and the effective detuning of optical mode (c,f), respectively. The related parameters are: $\kappa_{a_i}=\kappa_a=2\pi\times1.5MHz$, $\kappa_{m_i}=\kappa_m=2\pi\times1.5MHz$, $\gamma_{b_i}=\gamma_b=2\pi\times100Hz$, $\kappa_{c_i}=\kappa_c=2\pi\times2MHz$, $\omega_{a_i}=\omega_a=2\pi\times10GHz$, $\omega_{m_i}=\omega_m=2\pi\times10GHz$, $\omega_{b_i}=\omega_b=2\pi\times40MHz$, $\lambda_{c}=1550nm$, $G_{c_1b_1}=2\pi\times8MHz$, $G_{m_ib_i}=2\pi\times2MHz$, $T=10mK$, $\eta_i=0.75$. $g_{am}=2\pi\times4MHz$ for subgraphs (a), (b) and (c); $g_{am}=2\pi\times6MHz$ for subgraphs (d), (e) and (f). The unchanged detunings are: $\Delta_{a_i}=\Delta_a=-\omega_b$, $\widetilde{\Delta}_{m_i}=\widetilde{\Delta}_m=-\omega_b$, $\widetilde{\Delta}_{c_i}=\widetilde{\Delta}_c=\omega_b$.
• Figure 3: The optomicrowave entanglement ($E_{a_1c_1}$ and $E_{a_2c_2}$) and the optomagnonic entanglement ($E_{m_1c_1}$ and $E_{m_2c_2}$) versus the decay of microwave mode (a,d), magnon mode (b,e), and optical mode (c,f), respectively. All parameters being consistent with those in Fig.2, except the variables.
• Figure 4: The optomicrowave entanglement ($E_{a_1c_1}$ and $E_{a_2c_2}$) and the optomagnonic entanglement ($E_{m_1c_1}$ and $E_{m_2c_2}$) versus the microwave-magnon coupling strength $g_{am}$ (a,d), the effective magnonmechanical coupling strength $G_{mb}$ (b,e), and the effective optomechanical coupling strength $G_{c_1b_1}$ (c,f), respectively. All parameters being consistent with those in Fig.2, except the variables.
• Figure 5: The optomicrowave entanglement $E_{a_2c_2}$ (a) and the optomagnonic entanglement $E_{m_2c_2}$ (b) versus the ratio of the single-photon optomechanical coupling strengths $g_{c_2b_2}/g_{c_1b_1}$, respectively. Except for $G_{c_2b_2}$, the remaining parameters are consistent with those in Fig.2.