Suppression of Coherent Mode Formation in Central-Spin Systems Coupled to Spin Baths: A Quantitative Dephasing Crossover Criterion
Year: 2026
Type: preprint
Abstract: We derive a quantitative, non-circular criterion for coherent-mode formation in a central spin coupled to a spin bath. The criterion compares the pre-decoherence rate to the quantum speed limit rate from the Margolus-Levitin bound, defining a crossover exactly at Gamma = 1. The characteristic energy scale depends on the finite-size regime or the gap-dominated regime. For the spin-boson model with a hard gap, the polaron transformation gives an exact initial rate of pi*J0/2, and the criterion yields a crossover at J0_crit = 0.405*Delta. For the NV/P1 system, using the measured T2, we find the system is deeply in the coherent regime for all accessible concentrations. We validate the analytical results by exact diagonalization of central-spin-bath systems with up to three bath spins. For interacting bath spins (Ising coupling J), we find a non-monotonic dependence of the central-spin coherence on J, with a maximum at intermediate coupling (J ~ 1-2), of order the bath precession frequency. This is a collective motional narrowing effect that is absent for the bosonic bath. We formulate eight falsifiable predictions. The derivation relies only on established theorems, exact solutions, and exact diagonalization; it contains no adjustable parameters and no fitting.
Author: Bourizk, Ali
Institution: École Nationale de Commerce et de Gestion de Tanger
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221600899
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