Nonreciprocal transmission (classical nonreciprocity) in optomechanical systems based on asymmetric Fabry-Perot (F-P) cavities has been theoretically proposed and experimentally demonstrated. However, nonreciprocal quantum effects, particularly nonreciprocal quantum entanglement, remain unexplored in such systems. Here, we propose to generate nonreciprocal optomechanical entanglement in an asymmetric F-P cavity and discuss the connection between the nonreciprocal transmission and nonreciprocal quantum entanglement. We reproduce the nonreciprocal transmission spectra by solving the quantum Langevin equations, and then discuss the optimal parameters to achieve nonreciprocal optomechanical entanglement in the system. We show that a greater and more robust optomechanical entanglement can be approached in the asymmetric F-P cavities, in comparing with the symmetric cavities. Furthermore, we find that the degrees of classical and quantum nonreciprocities do not exhibit positive correlation as expected. Our work shows that the classical and quantum nonreciprocities can be realized simultaneously in the asymmetric F-P cavities, which provide a platform to explore the connection between classical and quantum nonreciprocities.
Multipartite quantum entanglement in PT-symmetric molecular optomechanics: Nonreciprocal enhancement and thermal resilience to \SI{500}{\kelvin}
We present a theoretical framework for a PT-symmetric double-cavity molecular optomechanical system demonstrating nonreciprocal enhancement of multipartite quantum entanglement at elevated temperatures. All bipartite entanglement channels (Eac, EaB1, EcB2, EB1B2) simultaneously maximize at optimal nonreciprocal asymmetry J1/J2≈5, with entanglement persisting to $T \sim \SIrange{400}{500}{\kelvin}$ (material-limited ceiling) two orders of magnitude beyond conventional optomechanical systems. This thermal resilience and balanced enhancement across all channels arise from synergistic combination of ultra-high-frequency molecular vibrations ($ω_m/2π= \SI{30}{\tera\hertz}$), collective N coupling enhancement with $N=\num{e6}$ molecules, and directional nonreciprocal coupling shielding entanglement-generating interactions from backaction noise. Unlike optical parametric amplifier schemes where vibration-vibration enhancement suppresses optical-vibration correlations, our PT-symmetric architecture circumvents this fundamental trade-off, validated through rigorous stability analysis via Routh-Hurwitz criterion.