Analytical Theory of Higher-Order Collective Spin Interactions in Cavity Quantum Electrodynamics

Abstract:Cavity-mediated collective-spin interactions are commonly described by a quadratic one-axis twisting Hamiltonian. However, the underlying atom-light interaction naturally generates nonlinearities to arbitrary order. Here, we derive a closed-form analytical expression for the complete hierarchy of cavity-mediated collective-spin interactions. We show that the nonlinear coefficients $\chi_k$ are governed by Chebyshev polynomials, with $k$ the order of nonlinearity. This yields a universal scaling $\chi_k\propto\eta^k$ with the single-atom cooperativity $\eta$ and a description of their dependence on cavity detuning. The result provides a systematic framework for determining when higher-order nonlinearities become relevant and when the quadratic approximation breaks down. We identify experimentally relevant regimes in which higher-order terms substantially modify collective-spin dynamics, accelerating the generation of quantum correlations and quantum Fisher information, and demonstrate that finite-order expansions can accurately reproduce the full cavity-mediated evolution. Our results establish a general framework for understanding higher-order nonlinearities in cavity quantum electrodynamics and their role in collective entanglement and quantum-enhanced sensing.

Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph)

arXiv:2608.14343 [quant-ph]

(or arXiv:2608.14343v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.14343 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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