Coherent Amplification of Vacuum Fluctuations in Multi-Walled Carbon Nanotubes: A Quantum Optomechanical Approach to Stimulated Phonon Emission under Crossed Electromagnetic Fields

This paper presents a theoretical framework for the stimulated emission of coherent optomechanical modes within the concentric van der Waals gaps of Multi-Walled Carbon Nanotubes (MWCNTs). Treating the inter-wall spacing (d≈0.34 nm) as a nanoscale Fabry-Pérot Casimir cavity, we model the system using cavity quantum electrodynamics (cQED). We propose that applying crossed electric and magnetic (E×B) fields induces a transverse Hall drift velocity. When this drift exceeds the phase velocity of the confined acoustic modes, it triggers an acoustoelectric-like amplification of zero-point vacuum fluctuations. We derive the critical electric field threshold (Ecrit) required to overcome cavity dissipation, initiating a Dicke superradiant phase transition. Furthermore, we demonstrate that inducing a macroscopic superconducting state within the MWCNT eliminates thermal acoustic scattering, effectively phase-locking the stimulated emission. This architecture acts as a quantum "phonon laser" (Saser), generating a highly directional, coherent beam of localized metric perturbations, offering novel pathways for precision mass spectrometry, quantum information shielding, and advanced metric engineering.