Bounded Dyson maps and cavity-driven transitions in a time-dependent non-Hermitian spin-boson model

2026/05/31 by Andreas Fring, Marta Reboiro
Physics and Astronomy · Mathematics · #quant-ph #math-ph #math.MP

paper · pdf

20 pages, 3 figure, substantially revised version

arxiv created 2026/08/04 · arxiv updated 2026/08/05

Abstract

We study a time-dependent non-Hermitian extension of the Schütte-Da Providência spin-boson Hamiltonian with complex couplings. A time-dependent Dyson map relates the model to a Hermitian counterpart and induces a positive physical metric. Separating the positive and unitary parts of the map, we prove a no-go result for a natural Gaussian number-squeeze-number class: for a nonvanishing linear spin-boson interaction, Hermiticity and bounded invertibility force the entire bosonic part of the Dyson map to be unitary. The squeezing parameter therefore selects a time-dependent Hermitian frame rather than contributing to the metric. The squeezed and non-squeezed Hamiltonians are related exactly by a time-dependent unitary transformation. The conserved quantity formed from the boson number and spin projection is replaced by a transported dynamical invariant, so a closed squeezing-frame protocol cannot generate transitions between distinct invariant sectors. We then introduce an independently driven single-mode cavity with quadratic term iχ(t)(b^†2-b²)/2. This physical drive breaks the corresponding continuous symmetry while preserving parity and couples dressed sectors differing by two bosonic quanta. The non-Hermitian asymmetry parameter, which also determines the bounded metric, tunes the effective Hermitian coupling, transition strengths and resonance conditions. Direct numerical propagation confirms the distinction between passive frame-induced mixing and genuine cavity transitions, the asymmetry-controlled resonance shift, and the validity of the first-order transition formula in the weak-driving regime.

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