[Paper Review] Enhanced metrology at the critical point of a many-body Rydberg atomic system

Dong-Sheng Ding, Zong-Kai Liu+4 more|arXiv (Cornell University)|Jul 25, 2022

Cold Atom Physics and Bose-Einstein Condensates4 citations

TL;DR

This paper demonstrates enhanced microwave electric field metrology using a many-body Rydberg atomic system near a critical point, where collective interactions amplify sensitivity. By exploiting the divergent susceptibility and steep transmission response at criticality, the Fisher information increases by over 1000× compared to non-interacting systems, achieving a measured sensitivity of 49 nV/cm/Hz^{1/2}.

ABSTRACT

The spectral properties of an interacting many-body system may display critical character and have potential applications in precision metrology. Here, we demonstrate such many-body enhanced metrology for microwave (MW) electric fields in a non-equilibrium Rydberg atomic gas. Near criticality the high sensitivity of Rydberg atoms to external MW electric fields, combined with many-body enhancement induces significant changes in the optical transmission. We quantify this behavior using the Fisher information. For continuous optical transmission at the critical point, the Fisher information is three orders of magnitude larger than in independent particle systems, the measured data provides an equivalent sensitivity of 49 nV/cm/$ extrm{Hz}^{1/2}$. The reported results constitute a milestone towards the application of many-body effects in precision metrology.

Motivation & Objective

• To explore how many-body criticality in Rydberg atomic systems enhances sensitivity for precision metrology.
• To demonstrate that criticality enables extreme sensitivity to external microwave electric fields.
• To quantify the metrological advantage using Fisher information in a non-equilibrium many-body system.
• To analyze the non-adiabatic dynamics near criticality and its impact on measurement sensitivity scaling.

Proposed method

• Modeling the Rydberg system using a mean-field approximation where the effective detuning includes a population-dependent interaction shift $\Delta_{\text{eff}} = \Delta - V\rho_{rr}$.
• Deriving the steady-state Rydberg population $\rho_{rr}$ from the optical Bloch equations under mean-field approximation, leading to a cubic equation for $\rho_{rr}$.
• Calculating the derivative $\mathrm{d}\rho_{rr}/\mathrm{d}\Delta$ to quantify sensitivity, with criticality defined by $\mathrm{d}\rho_{rr}/\mathrm{d}\Delta \to \infty$.
• Using the Fisher information $\mathcal{F}$ as a figure of merit to compare metrological performance between interacting and non-interacting systems.
• Performing experimental measurements of optical transmission during detuning scans, with data acquired via a differencing photodetector and calibrated using photon number conversion.
• Analyzing the non-integer power-law dependence of Fisher information on scan duration due to critical slowing down, deviating from adiabatic assumptions.

Experimental results

Research questions

• RQ1 How does many-body criticality in a Rydberg atomic gas enhance sensitivity to external microwave electric fields?
• RQ2 What is the scaling of Fisher information with measurement time near the critical point, and how does it differ from adiabatic behavior?
• RQ3 To what extent can collective interactions in a Rydberg ensemble improve metrological sensitivity compared to independent particles?
• RQ4 How does non-adiabatic dynamics near the critical point affect the measurement resolution and signal response?
• RQ5 What is the achievable sensitivity limit in terms of electric field resolution, and how does it compare to existing benchmarks?

Key findings

• The Fisher information at the critical point exceeds that of non-interacting systems by a factor of over 1000, demonstrating a strong many-body enhancement.
• The measured sensitivity of the system reaches 49 nV/cm/Hz^{1/2}, significantly surpassing typical single-particle limits.
• The derivative $\mathrm{d}\rho_{rr}/\mathrm{d}\Delta$ reaches a maximum at the critical point, indicating maximal sensitivity to external field-induced shifts.
• Non-adiabatic dynamics near criticality lead to a non-integer power-law dependence of Fisher information on scan duration, deviating from standard scaling.
• Theoretical simulations confirm that the critical point corresponds to a divergence in susceptibility and a sharp transition in Rydberg population.
• The experimental setup achieves high-precision transmission measurements via a differencing photodetector with calibrated photon number conversion, enabling accurate sensitivity quantification.