Generation of multipartite entangled states based on double-longitudinal-mode cavity optomechanial system

TL;DR

The paper addresses scalable generation of multipartite continuous-variable entanglement in a double-longitudinal-mode cavity optomechanical platform. It introduces two schemes: (1) a beamsplitter network coupling outputs from multiple identical cavities to realize 2N- or 4N-partite entanglement with tunable ladder or square structures, and (2) double-pump pumping with orthogonal polarization to realize quadrapartite entanglement and extend to 4N-partite states across more cavities. Entanglement dependencies on detuning $\Delta_2$, cavity decay $\kappa$, mechanical decay $\gamma_m$, and temperature $T$ are analyzed, with maximal optical–optical and optomechanical entanglements near $\Delta_2=\omega_m$ while maintaining stability for $\Delta_2 \ge \omega_m$. The work demonstrates potential for connecting heterogeneous quantum systems and enabling large-scale quantum networks via programmable entanglement structures, with scalability through cascading, feedback, and multiplexing in frequency and polarization degrees of freedom.

Abstract

Optomechanical system is a promising platform to connect different notes of quantum networks, therefore, entanglement generated from it is also of great importance. In this paper, the parameter dependence of optomechanical and optical-optical entanglements generated from the double-longitudinal-mode cavity optomechanical system are discussed and two quadrapartite entanglement generation schemes based on such a system are proposed. Furthermore, 2N or 4N-partite entangled states can be obtained by coupling N cavities with N-1 beamsplitter(BS)s, and these schemes are scalable in increasing the partite number of entanglement. Certain ladder or linear structures are contained in the finally obtained entanglement structure, which can be applied in quantum computing or quantum networks in the future.

Figures (13)

• Figure 1: The considered double-longitudinal-mode cavity optomechanical system. (a) Schematic diagram. (b) frequency ralation.
• Figure 2: The optical-optical entanglement $E_{12}$, the optomechanical entanglements $E_{01}$ and $E_{02}$, versus $\Delta_{2}$. The relative parameters are: $L=0.01m$, $T= 0.01 K$, $\lambda=1.33\mu m$, $\gamma_{m}=0.1MHz$, $\kappa_{1}=\kappa_{2}=\kappa=1MHz$, $m=5\times10^{-9} kg$, $P=20mW$, $\Delta_{1}=\Delta_{2}-2\omega_{m}$.
• Figure 3: The optomechanical entanglements $E_{01}$ and $E_{02}$ ((a),(b),(c)), and the optical-optical entanglement $E_{12}$ ((d),(e),(f)), vary with detuning $\Delta_2$, cavity decay $\kappa$ and mechanical decay $\gamma_m$. In some regions of subgraph (a), (b) and (c), only one color is shown and the visible color stands for stronger entanglement. $\gamma_{m}=0.01MHz$. Other parameters are the same as that in Fig.2.
• Figure 4: Optomechanical entanglements $E_{01}$ and $E_{02}$ versus mechanical decay $\gamma_m$. (a) $\Delta_{2}=\omega_m$. (b)$\Delta_{2}=1.005\omega_m$. $\kappa=10MHz$. Other parameters are the same as that in Fig.2.
• Figure 5: Entanglements versus temperature $T$, with $\Delta_{2} = \omega_{m}$ and $\gamma_{m}=0.1MHz$. (a) optomechanical entanglements. (b) optical-optical entanglement. Other parameters are the same as that in Fig.2.