Cell-Dependent Criticality for Quantum Metrology

Quantum Physics [Submitted on 15 Apr 2026] Cell-Dependent Criticality for Quantum Metrology Zhoutao Lei, Jihao Ma, Yun Chen, Tingting Wang, Jiangbin Gong Exploiting enhanced sensitivity of a system in the vicinity of a phase transition boundary, critical quantum metrology to date still suffers from gap-closure related bottleneck effects, namely, critical slowing down of the sensing dynamics and a drastic shrinking of the parameter sensing window. To alleviate the said bottleneck inherent to any homogeneous lattice used for sensing, here we propose to leverage the intrinsic hopping inhomogeneity arising from bosonic ladder-operator matrix elements in Fock-space lattices (FSLs). Specifically, using a two-mode Jaynes--Cummings-type model, we show that the sensing parameter can be imprinted onto a topological zero-energy mode of the FSL. The key system parameters thus become cell dependent, effectively tracing out a curve in a topological phase diagram. Cell-dependent criticality emerges when this curve crosses or approaches a topological phase boundary, without globally tuning the lattice close to criticality. An external control parameter reshapes this curve, continuously tuning the scaling of the quantum Fisher information from the standard to the Heisenberg scaling while maintaining broad sensing coverage and a reduced gap cost. Furthermore, a local photon-number measurement on a single cavity saturates the quantum Fisher information. These results identify FSLs as a scalable and practical route to criticality-based quantum metrology. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.14300 [quant-ph]   (or arXiv:2604.14300v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.14300 Focus to learn more Submission history From: Zhoutao Lei [view email] [v1] Wed, 15 Apr 2026 18:00:40 UTC (3,048 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)