Affine spin-pencil factorization of generalized driven anisotropic Rabi--Stark Hamiltonians in an inhomogeneous orthosymplectic superalgebra

Abstract:We construct a supersymmetric factorization for generalized driven anisotropic Rabi--Stark Hamiltonians using an affine factor $\hat{A}=\hat{C}+\hat{a}\hat{D}$ in an inhomogeneous orthosymplectic superalgebra, with two real invertible spin matrices $\hat{C}$ and $\hat{D}$. The six real pencil parameters constrain nine Hamiltonian frequencies and one energy offset up to an overall frequency scale. The normal product $\hat{A}^{\dagger}\hat{A}$ has an exact zero-energy ground doublet and, with its antinormal partner $\hat{A}\hat{A}^{\dagger}$, gives a Witten index of two. For distinct pencil roots with finite baseline slopes, coherent gauges define a Bargmann hierarchy and endpoint conditions for exceptional finite-polynomial states. The spin grading organizes four limiting cases, comprising two driven-oscillator families with every baseline exact and the constrained anisotropic-Rabi and Rabi--Stark sheets, which meet at the degenerate-qubit isotropic Rabi model. An aligned interior example adds direct and longitudinal drives, Stark deformation, and intensity-dependent coupling while retaining the factorization.

arXiv:2609.36511 [quant-ph]

(or arXiv:2609.36511v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.36511 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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