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Applied Physics Letters

Generation of tripartite entanglement among optical modes in a single multimode nanobeam

Tijjani Abdulrazak, Qizhi Cai, Boyu Fan, Guangwei Deng

Published Apr 13, 2026• 0 citations
Publisher

Abstract

We theoretically demonstrate genuine steady-state tripartite entanglement in a monolithic optomechanical nanobeam integrating one transverse electric (TE) and two transverse magnetic (TM) optical modes coupled to a single mechanical mode. The system achieves strong coupling rates of g1/2π≈6.99×105 Hz for the TE mode, and g2,3/2π≈5.92×104 Hz and 4.91×104 Hz for the TM modes, with a mechanical quality factor Qm≈2.15×109, ensuring thermal stability up to 350 mK. Our analysis reveals that while bipartite entanglement persists across various regimes, genuine tripartite entanglement requires strong coupling, confirming the optimal operating point of our design. Telecom-band compatibility at 1549 nm is achieved through width-dependent tuning. Using finite element simulations and quantum Langevin analysis, we identify parameter regimes where the three optical modes exhibit verifiable tripartite entanglement (Rτmin>0), stable under cryogenic conditions with milliwatt-level pump powers.

DOI
10.1063/5.0315067

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We theoretically demonstrate genuine steady-state tripartite entanglement in a monolithic optomechanical nanobeam integrating one transverse electric (TE) and two transverse magnetic (TM) optical modes coupled to a single mechanical mode. The system achieves strong coupling rates of g1/2π≈6.99×105 Hz for the TE mode, and g2,3/2π≈5.92×104 Hz and 4.91×104 Hz for the TM modes, with a mechanical quality factor Qm≈2.15×109, ensuring thermal stability up to 350 mK. Our analysis reveals that while bipartite entanglement persists across various regimes, genuine tripartite entanglement requires strong coupling, confirming the optimal operating point of our design. Telecom-band compatibility at 1549 nm is achieved through width-dependent tuning. Using finite element simulations and quantum Langevin analysis, we identify parameter regimes where the three optical modes exhibit verifiable tripartite entanglement (Rτmin>0), stable under cryogenic conditions with milliwatt-level pump powers.
We theoretically propose a scheme to generate strong genuine tripartite entanglement among three mechanical oscillators in a multimode optomechanical system. In our setup, each mechanical oscillator is independently coupled to three optical modes supported by a single optical cavity, with each optical mode driven by a six-tone driving field. By appropriately tailoring the amplitudes of the driving fields, the mechanical steady state can be engineered into a three-mode squeezed vacuum state exhibiting significant genuine tripartite entanglement. We further investigate the effects of mechanical thermal reservoirs and demonstrate that the entanglement generated by our scheme persists at a significant level even at dilution refrigerator temperatures. Our results offer a feasible route toward the generation and utilization of multipartite entanglement in quantum optomechanical platforms, with potential applications in quantum devices.
A scheme for the generation of steady-state entanglement between optical and mechanical cavity modes in an optomechanical crystal nanobeam is proposed. Based on finite element simulation and the quantum Langevin equation, we explore the evolution of entanglement with optomechanical properties in various device configurations, and demonstrate the ability of optimal entanglement generation in both blue and red detuned optical pumps. The intrinsic relationship between optomechanical cooperativity and entanglement is further clarified for depicting a clear physical picture of optomechanical interaction. Our work expands the understanding of macroscopic quantum mechanics and is an important step for developing novel quantum optomechanical devices.
We propose a scheme to generate one-way steering, bipartite, and genuine tripartite entanglement in a five-mode hybrid cavity electro-optomechanical system consisted of an optical cavity, a mechanical resonator, and three microwave cavity modes with the help of a squeezed vacuum field. The optical cavity is pumped by a squeezed vacuum field. The mechanical resonator is formed by a freely vibrating silicon nitride membrane, which is a part of a capacitor in an inductor–capacitor circuit forming three microwave resonators. We find that there is robust entanglement and one-way steering between the optical cavity mode and microwave cavity modes in the presence of the squeezed vacuum field. Particularly, there is steady-state genuine tripartite entanglement between three microwave cavity modes, which is robust against thermal fluctuations. Our scheme could be useful for various quantum tasks based on hybrid electro-optomechanical systems fabricated on chips.
We provide analytic insight into the generation of stationary itinerant photon entanglement in a three-mode optomechanical system. We identify the parameter regime of maximal entanglement and show that strong entanglement is possible even for weak many-photon optomechanical couplings. We also show that strong tripartite entanglement is generated between the photonic and phononic output fields; unlike the bipartite photon-photon entanglement, this tripartite entanglement diverges as one approaches the boundary of system stability.
This study investigates the generation and enhancement of quantum entanglement in an electro-optomechanical ring cavity system. The setup integrates two Coulomb-coupled mechanical resonators, which serve as the fundamental mechanism for the generation of bipartite and tripartite entanglement via charge mediated coupling. We then demonstrate the significant enhancement of this entanglement via a nonlinear parametric drive (an optical parametric amplifier, OPA), which injects a controllable nonlinearity into the cavity. We derive the system's Hamiltonian and the corresponding quantum Langevin equations, which are linearized around steady-state solutions to analyze Gaussian quantum fluctuations. Employing the covariance matrix formalism, we quantify bipartite entanglement via logarithmic negativity and tripartite entanglement via the minimum residual contangle. Our results unequivocally show that while the Coulomb interaction is indispensable for creating entanglement, the OPA acts as a powerful control tool, dramatically amplifying the degree of quantum correlations for all subsystems. We find that the strength of entanglement is highly sensitive to several parameters and can be optimized through the strategic selection of the OPA's gain and phase, the laser detuning, and the input power. A key finding is the existence of a trade-off, where parameters that maximize entanglement also constrain the stable operating regime of the system. Furthermore, thermal noise is shown to progressively degrade all quantum correlations, underscoring the necessity for low-temperature operation. These findings provide comprehensive guidance for parameter optimization, outlining a clear path from generation to enhancement, and highlight the potential of such hybrid systems as versatile platforms for controlling multipartite entanglement in quantum technologies.
Abstract Nano-optomechanical systems, capable of supporting enhanced light-matter interactions, have wide applications in studying quantum entanglement and quantum information processors. Yet, preparing optical telecom-band entanglement within a single optomechanical nanobeam remains blank. We propose and design a triply resonant optomechanical nanobeam to generate steady-state entangled propagating optical modes and present its quantum-enhanced performance for teleportation-based quantum state transfer under realistic conditions. Remarkably, the entanglement quantified by logarithmic negativity can obtain E N = 1. Furthermore, with structural imperfections induced by realistic fabrication processes considered, the device still shows great robustness. Together with quantum interfaces between mechanical motion and solid-state qubit processors, the proposed device potentially paves the way for versatile nodes in long-distance quantum networks.