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

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.