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$1/N^2$ Precision Interferometry with Collectively Enhanced Atomic Mirror

Yuan Liu, Ke-Mi Xu, Hong-Bo Sun, Linhan Lin

Abstract

Quantum metrology exploits quantum resources to enhance measurement precision beyond the classical limit. Conventional protocols normally rely on the preparation of delicate quantum states to acquire these resources, posing a major challenge for scaling and robustness. Here we introduce a paradigm that circumvents this requirement with a collectively enhanced quantum mirror (CEAM), i.e., a mesoscopic array of $N$ atoms coupled to a semi-infinite waveguide. When injecting single photons into the waveguide and estimating the CEAM-boundary distance from the reflection phase, a $1/N^2$ precision scaling can be obtained, which surpasses the Heisenberg limit. In this protocol, the quantum resource stems from the cooperative optical response, requiring no entangled state preparation. Our scheme is robust against positional and coupling disorder, offering a practical route to ultra-sensitive quantum metrology in integrated photonic systems.

$1/N^2$ Precision Interferometry with Collectively Enhanced Atomic Mirror

Abstract

Quantum metrology exploits quantum resources to enhance measurement precision beyond the classical limit. Conventional protocols normally rely on the preparation of delicate quantum states to acquire these resources, posing a major challenge for scaling and robustness. Here we introduce a paradigm that circumvents this requirement with a collectively enhanced quantum mirror (CEAM), i.e., a mesoscopic array of atoms coupled to a semi-infinite waveguide. When injecting single photons into the waveguide and estimating the CEAM-boundary distance from the reflection phase, a precision scaling can be obtained, which surpasses the Heisenberg limit. In this protocol, the quantum resource stems from the cooperative optical response, requiring no entangled state preparation. Our scheme is robust against positional and coupling disorder, offering a practical route to ultra-sensitive quantum metrology in integrated photonic systems.

Paper Structure

This paper contains 24 equations, 3 figures.

Figures (3)

  • Figure 1: Schematic of the system. $N$ atoms (blue dots) coupled to a semi-infinite waveguide terminated by a perfect reflective boundary at distance $x$. The incident single photons ($a_\mathrm{in}$) are reflected from the system.
  • Figure 2: Phase sensitivity of the system under different number of atoms and different atom-photon frequency detunings. The inset shows the same data on an expanded $x$‑axis scale.
  • Figure 3: Robustness of the phase sensitivity under imperfections for detunings $\Delta=\gamma$ (left) and $\Delta=0.5\gamma$. We considered $N=10$ transmon qubits ($f_0=6$ GHz) coupled to a common waveguide, with $\gamma=2\pi\times100$ MHz, $\gamma'=2\pi\times0.5$ MHz. Imperfections include atom-waveguide coupling variations ($3\sigma=0.03\gamma$), positional disorder ($3\sigma=500$ nm), and transition frequency fluctuations ($3\sigma=100$ MHz), each modeled by a truncated Gaussian distribution within $\pm3\sigma$. For each subplot, 20 random combinations of these imperfections are generated, and the resulting phase sensitivity curves are overlaid. The ideal case (black dashed line) is reserved for comparison.