Quantum Acoustics: A Unified Quantum Theory of Phonons Analogous to Quantum Optics
shifa liu
We develop quantum acoustics as an independent quantum discipline. The elementary bosonic quantum is the phonon, obtained by canonical quantization of the elastic displacement field of a medium. The central replacement is c → cs, ε0 → ρ0, μ0 → 1/K, ℏ → ℏ, while the Planck constant is not replaced. Phonons obey canonical commutation relations, Bose–Einstein statistics with vanishing chemical potential, and energy quantization E = ℏω. The optical–acoustic dictionary is exact at the level of canonical quantization, mode algebra, Fock, coherent, squeezed, thermal and entangled states, and at the level of linear interference in the long-wavelength, single-branch, dissipationless limit. Multi-branch, dispersive, dissipative and finite-lifetime effects are handled by the generalized dictionary stated in Chapter 56. Quantum acoustics contains a macroscopic quantum branch, but it is not identical to macro- scopic quantum mechanics. The manuscript covers classical elasticity, variational principles, canonical quantization, phonon field algebra, propagators, Green functions, wave–particle duality, Bose–Einstein statistics, blackbody radiation, Debye heat capacity, acoustic quantum constants, acoustic Bekenstein–Hawking entropy, phonon thermodynamics, phonon BEC, phonon lasers, superfluidity, Fock, coherent, squeezed, thermal, entangled and non-classical states, beam splitters, Mach–Zehnder interferometers, Fabry–Perot cavities, Hong–Ou–Mandel interference, second-order coherence, phonon qubits, single- and two-qubit gates, quantum algorithms, quantum error correction and surface-code thresholds, quantum computing architecture, quantum networks and repeaters, quantum simulation, quantum sensing, topological phononic crystals, the SSH phonon model, two-dimensional topological phononic insulators, three-dimensional phonon Weyl semimetals, non-Hermitian acoustics and the phonon skin effect, non-Bloch band theory, topological defect classification, acoustic metrics, acoustic horizons, acoustic Hawking radiation, acoustic black- hole entropy and the information paradox, acoustic cosmology, phonon–graviton mixing, gravitational-wave coupling, the phonon analogy of dark matter and dark energy, surface acoustic wave resonators, optomechanical systems, superconducting qubit–phonon hybrid systems, Bose–Einstein condensates, phononic crystals, acoustic metamaterials, gravitational-wave detectors, the complete optical–acoustic dictionary, the generalized dictionary for multi-branch, dispersive, dissipative and finite-lifetime phonons, and strong-field QED vacuum and media as an analogue of multi-refringent, dispersive and dissipative media. Acoustic Hawking radiation has been observed in Bose–Einstein condensates by Steinhauer (2016). All definitions, derivations, mathematical details, experimental proposals and comparison factors are presented with explicit assumptions and complete proofs.
•Dec 31, 2025•0 citations