Quantum Magnomechanics at the Nanoscale

The present work offers a comprehensive theoretical analysis of hybrid magnon-phononphoton systems operating in the nanocavity magnomechanical regime, where magnetostrictive coupling, microwave cavity fields, and mechanical vibrations interact
coherently within a single engineered platform. The promising potential of these
systems for quantum transduction, phonon-state engineering, and hybrid quantum
networks motivates the development of a unified open-quantum-system framework
grounded in Heisenberg-Langevin equations and input-output theory, which is applied
across a hierarchy of increasingly complex physical regimes.
The analysis begins with the derivation of magnon-photon and magnon-phonon coupling
strengths for a thin-film device geometry using the Euler-Bernoulli principle, thereby
establishing experimentally accessible parameter targets. Under red-detuned microwave
driving, beam-splitter-type magnomechanical interactions enable sideband cooling of
the mechanical mode and facilitate coherent quantum-state transfer between magnon
and phonon subsystems, with quantitative predictions provided for cooperativity and
cooling performance.
Beyond the linear regime, the intrinsic Kerr nonlinearity of the magnon mode is incorporated, revealing a power-dependent renormalization of the effective magnon detuning.
This results in phonon frequency shifts and a pronounced transient enhancement of the
phonon damping rate at intermediate drive powers, effects that may be exploited to
maximize cooling performance without increasing cavity photon occupation.
Finally, a covariance-matrix formalism is developed for evaluating continuous-variable
entanglement between the magnon and phonon modes, quantified by the logarithmic
negativity. Sideband-selective driving generates robust stationary entanglement that
persists against thermal noise across experimentally realized systems. Collectively,
these findings establish nanocavity magnomechanics as a versatile platform for coherent
quantum control, nonlinear sensing, and the generation of quantum correlations in
solid-state hybrid systems.