Super-resolution of two Closely-spaced Electromagnetic Fields via Walsh-Modulated Dynamical Decoupling Spectroscopy

TL;DR

This paper introduces a Walsh-modulated dynamical decoupling protocol that achieves super-resolution spectroscopy, resolving closely spaced electromagnetic fields beyond traditional limits by suppressing quantum noise, with broad applicability and rapid data acquisition.

Contribution

The authors develop and experimentally validate a broadband super-resolution spectroscopy method using Walsh modulation to encode frequency differences, surpassing conventional resolution limits.

Findings

Resolved two 100 MHz electric fields separated by 5 Hz with 1 ms measurement time

Achieved 200-fold improvement over traditional spectral resolution

Accelerated data acquisition by over 10^5 times

Abstract

Due to quantum fluctuations, non-orthogonal quantum states cannot be distinguished with complete certainty, making their underlying physical parameters difficult to resolve. Traditionally, it has been believed that the linewidth of a system behaves like these quantum fluctuations to set the ultimate limit on frequency resolution as two oscillating electromagnetic fields are applied. Consequently, the measurement time required to resolve a frequency difference $\Delta \omega$ was assumed to diverge as $\Delta \omega \rightarrow 0$. Here, we show that linewidth does not play a defining role in resolving two closely spaced frequencies. Instead, the ultimate limit is set by parameter-independent quantum fluctuations, such as shot noise in our case. We propose and experimentally demonstrate the first general broadband protocol for super-resolution spectroscopy. Specifically, our protocol uses a Walsh-modulated dynamical decoupling (WMDD) sequence to encode $\Delta \omega$ between two unknown tones into a quantum state. This leverages phase information to suppress parameter-independent shot noise, thereby enhancing the signal-to-noise ratio and enabling super-resolution spectroscopy. With this approach, we resolve two randomly chosen oscillating electric fields of order 100 MHz separated by 5 Hz, with a measured frequency difference of 5.0(1.6) Hz using a measurement time per run of just 1 ms, representing an improvement of 200 beyond the traditional resolution limit. As such, our technique accelerates data acquisition by more than $10^5$ magnitude compared to conventional methods. Crucially, as our protocol is rooted in the motional Raman (quantum vector signal analyzer) framework, it is effective across an arbitrary frequency range and thus promises to enhance broadband sensing of electromagnetic fields and improve spectral efficiency of next-generation communication systems.