Neutrino Spin--Flavor Dynamics and Quantum Rabi Model: Spectral Correspondence and QRM Benchmarks

Abstract

We formulate a two-state neutrino spin--flavor system coupled through a transition magnetic moment to a single quantized electromagnetic mode and establish its operator-level correspondence with the quantum Rabi model (QRM). For the sector $\{|{\nu }_{iL}⟩,|{\nu }_{jR}⟩\}$, the diagonal splitting is ${\Delta }_s=(m_i^2-m_j^2)/(2E)+V_{iL}-V_{jR}$, while quantization of a transverse electromagnetic mode gives a coupling $g_{\nu }={\mu }_{ij}{B}_{\mathrm{zpf}}$. The effective Hamiltonian consequently has the QRM form $H_{\nu }={\Delta }_s{\sigma }_z/2+{\omega }_c{a}^{†}a+g_{\nu }{\sigma }_x(a+a^{†})$. We then formulate the correspondence at the level of the exact QRM spectrum, focusing on its exceptional (Juddian) states, and transfer the QRM constraint polynomials directly to neutrino variables. This yields explicit algebraic conditions on the neutrino mass splitting, energy, transition magnetic moment, zero-point magnetic field, and mode frequency. We also identify QRM phenomena that would become conditional predictions of the quantized-field neutrino model---including counter-rotating corrections, parity structure, spin--field entanglement, and occupation-dependent dynamics. The trapped-ion QRM experiments provide benchmarks for the operator family, while none of these QRM phenomena is presented as an already observed neutrino effect.