Subensemble correlations as a covariance geometry
Phys. Rev. A 113, 042821 – Published 27 April, 2026
DOI: https://doi.org/10.1103/5s4b-kw34
Abstract
Conventional practice of spatially resolved detection in diffusion-coupled thermal atomic vapors implicitly treats localized responses as mutually independent. However, in this study, it is shown that observable correlations are governed by the intrinsic spatiotemporal covariance of a global spin-fluctuation field, such that spatial separation specifies only overlapping statistical projections rather than independent physical components. A unified field theoretic description is established in which subensembles are defined as measurement-induced statistical projections of a single stochastic field. Within this formulation, subensemble correlations are determined by the covariance operator, inducing a natural geometry in which statistical independence corresponds to orthogonality of the measurement functionals. For collective spin fluctuations described by a diffusion-relaxation Ornstein-Uhlenbeck stochastic field, the covariance spectrum admits only a finite set of fluctuation modes in a bounded domain, imposing an intrinsic, field-level limit on the number of statistically distinguishable subensembles. The loss of subensemble independence is formalized through the notion of spatial sampling overlap, which quantifies the unavoidable statistical coupling arising from shared access to common low-order fluctuation modes. While multichannel atomic magnetometry provides a concrete physical setting in which these constraints become explicit, the framework applies generically to diffusion-coupled stochastic fields.
