arXiv subjects

Beibei Sun

Publications and source records attributed to Beibei Sun.

3 recordsLinked to original sources

arXiv2025

MEMS Vapor Cells-based Rydberg-atom Electrometry Toward Miniaturization and High Sensitivity

Rydberg-atom electrometry, as an emerging cutting-edge technology, features high sensitivity, broad bandwidth, calibration-free operation, and beyond. However, until now the key atomic vapor cells used for confining electric field-sensitive Rydberg atoms nearly made with traditional glass-blown techniques, hindering the miniaturization, integration, and batch manufacturing. Here, we present the wafer-level MEMS atomic vapor cells with glass-silicon-glass sandwiched structure that are batch-manufactured for both frequency stability and electric field measurement. We use specially customized ultra-thick silicon wafers with a resistivity exceeding 10,000 cm, three orders of magnitude higher than that of typical silicon, and a thickness of 6 mm, providing a 4-fold improvement in optical interrogation length. With the as-developed MEMS atomic vapor cell, we configured a high-sensitivity Rydberg-atom electrometry with the minimal detectable microwave field to be 2.8 mV/cm. This combination of miniaturization and sensitivity represents a significant advance in the state-of-the-art field of Rydberg-atom electrometry, paving the way for chip-scale Rydberg-atom electrometry and potentially opening up new applications in a wider variety of fields.

physics.atom-ph↗

arXiv2025

Open dynamical systems with a moving hole

Given an integer $b\ge 3$, let $T_b: [0,1)\to [0,1); x\mapsto bx\pmod 1$ be the expanding map on the unit circle. For any $m\in\mathbb{N}$ and $\omega=\omega^0\omega^1\ldots\in(\left\{0,1,\ldots,b-1\right\}^m)^\mathbb{N_0}$ let \[ K^\omega=\left\{x\in[0,1): T_b^n(x)\notin I_{\omega^n}~\forall n\geq 0\right\},\] where $I_{\omega^n}$ is the $b$-adic basic interval generated by $\omega^n$. Then $K^\omega$ is called the survivor set of the open dynamical system $([0,1),T_b,I_\omega)$ with respect to the sequence of holes $I_\omega=\left\{I_{\omega^n}: n\geq 0\right\}$. We show that the Hausdorff and lower box dimensions of $K^\omega$ always conincide, and the packing and upper box dimensions of $K^\omega$ also coincide. Moreover, we give sharp lower and upper bounds for the dimensions of $K^\omega$, which can be calculated explicitly. For any admissible $\alpha\leq \beta$ there exist infinitely many $\omega$ such that $\dim_H K^\omega=\alpha$ and $\dim_P K^\omega=\beta$. As applications we study badly approximable numbers in Diophantine approximation. For an arbitrary sequence of balls $\left\{B_n\right\}$, let $K\left(\left\{B_n\right\}\right)$ be the set of $x\in[0,1)$ such that $T_b^n(x)\notin B_n$ for all but finitely many $n\geq 0$. Assuming $\lim_{n\to\infty}\operatorname{diam} \left(B_n\right)$ exists, we show that $\dim_H K\left(\left\{B_n\right\}\right)=1$ if and only if $\lim_{n\to\infty}\operatorname{diam} \left(B_n\right)=0$. For any positive function $\phi$ on $\mathbb{N}$, let $E\left(\phi\right)$ be the set of $x\in[0,1)$ satisfying $|T_b^n (x)-x|\geq \phi(n)$ for all but finitely many $n$. If $\lim_{n\to\infty}\phi(n)$ exists, then $\dim_H E(\phi)=1$ if and only if $\lim_{n\to\infty}\phi(n)=0$. Our results can be applied to study joint spectral radius of matrices. We show that the finiteness property for the joint spectral radius of associated adjacency matrices holds true.

math.DS↗

arXiv2022

Projections of four corner Cantor set: total self-similarity, spectrum and unique codings

Given $\rho\in (0,1/4]$, the four corner Cantor set $E\subset \mathbb{R}^{2}$ is a self-similar set generated by the iterated function system \[ \left\{(\rho x, \rho y), \quad(\rho x, \rho y+1-\rho),\quad (\rho x+1-\rho, \rho y),\quad(\rho x+1-\rho,\rho y+1-\rho)\right\}. \] For $\theta\in[0,\pi)$ let $E_\theta$ be the orthogonal projection of $E$ onto a line with an angle $\theta$ to the $x$-axis. In this paper we give a complete characterization on which the projection $E_\theta$ is totally self-similar. We also study the spectrum of $E_\theta $, which turns out that the spectrum of $E_\theta$ achieves its maximum value if and only if $E_\theta $ is totally self-similar. Furthermore, when $E_\theta$ is totally self-similar, we calculate its Hausdorff dimension and study the subset $U_\theta $ which consists of all $x\in E_\theta $ having a unique coding. In particular, we show that $\dim_H U_\theta=\dim_H E_\theta$ for Lebesgue almost every $\theta \in[0,\pi)$. Finally, for $\rho=1/4$ we describe the distribution of $\theta $ in which $E_\theta$ contains an interval. It turns out that the possibility for $E_\theta$ to contain an interval is smaller than that for $E_\theta$ to have an exact overlap.

math.DS↗