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

• URL: http://arxiv.org/abs/2608.14343v2
• Date: Mon, 17 Aug 2026 14:38:12 GMT
• Title: Analytical Theory of Higher-Order Collective Spin Interactions in Cavity Quantum Electrodynamics
• Abstract summary: Cavity-mediated collective-spin interactions are commonly described by a quadratic one-axis twisting Hamiltonian.<n>We show that the nonlinear coefficients $_k$ are governed by Chebyshevs, with $k$ the order of nonlinearity.<n>We identify experimentally relevant regimes in which higher-order terms substantially modify collective-spin dynamics.
• Score: 0.5696201935316318
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $χ_k$ are governed by Chebyshev polynomials, with $k$ the order of nonlinearity. This yields a universal scaling $χ_k\proptoη^k$ with the single-atom cooperativity $η$ 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.

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