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We propose using highly excited cyclotron states of a trapped electron to detect meV axion and dark-photon dark matter, marking a significant improvement over our previous proposal and demonstration [One-electron quantum cyclotron as a milli-ev dark-photon detector, .]. When the axion mass matches the cyclotron frequency ${\omega }_c$, the cyclotron state is resonantly excited, with a transition probability proportional to its initial quantum number, $n_c$. The sensitivity is enhanced by taking $n_c\sim {10}^6{\left(\frac{0.1\mathrm{meV}}{{\omega }_c}\right)}^2$. By optimizing key experimental parameters, we minimize the required averaging time for cyclotron detection to $t_{\mathrm{ave}}\sim {10}^{-6}$s, permitting detection of such a highly excited state before its decay. An open–end-cap trap design enables the external photon signal to be directed into the trap, rendering our background-free detector compatible with large focusing cavities, such as the BREAD proposal, while capitalizing on their strong magnetic fields. Furthermore, the axion conversion rate can be coherently enhanced by incorporating layers of dielectrics with alternating refractive indices within the cavity. Collectively, these optimizations enable us to probe the QCD axion parameter space from 0.1 to 2.3 meV (25–560 GHz), covering a substantial portion of the predicted postinflationary QCD axion mass range. This sensitivity corresponds to probing the kinetic mixing parameter of the dark photon down to $\epsilon \approx 2\times {10}^{-16}$. Published by the American Physical Society2025 

While matrix-covariate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional matrix-valued covariates. To address these issues, this paper proposes a framework of matrix-covariate regression models based on a low-rank constraint and an additional regularization term for structured signals, with considerations of models of both continuous and binary responses. We propose an efficient Riemannian-steepest-descent algorithm for regression coefficient estimation. We prove that the consistency of the proposed estimator is in the order of O(sqrt{r(q+m)+p}/sqrt{n}), where r is the rank, p x m is the dimension of the coefficient matrix and p is the dimension of the coefficient vector. When the rank r is small, this rate improves over O(sqrt{qm+p}/sqrt{n}), the consistency of the existing work (Li et al. in Electron J Stat 15:1909-1950, 2021) that does not apply a rank constraint. In addition, we prove that all accumulation points of the iterates have similar estimation errors asymptotically and substantially attaining the minimax rate. We validate the proposed method through a simulated dataset on two-dimensional shape images and two real datasets of brain signals and microscopic leucorrhea images.