Breaking Rayleigh’s curse: broadband frequency super-resolution via a quantum harmonic oscillator

Abstract

Non-orthogonal quantum states cannot be distinguished with complete certainty, making their underlying physical parameters difficult to resolve. In frequency spectroscopy of two closely spaced electromagnetic fields, this challenge has traditionally been associated with the Fourier-transform-limited linewidth, implying that the measurement time required to resolve a frequency difference Δω diverges as Δω → 0. Here, we show that this linewidth does not fundamentally limit the resolution of two closely spaced frequencies when each signal has sufficient amplitude for efficient detection. We propose and experimentally demonstrate a broadband quantum harmonic oscillator protocol for super-resolution spectroscopy in the radio-frequency and microwave domains. A Quantum Fluctuation Suppression (QFS) sequence encodes Δω into the oscillator state while suppressing parameter-independent shot noise. We resolve two randomly chosen electric fields near 100 MHz separated by 5 Hz, measuring 5.0(1.6) Hz with a 1ms probe time, 200 × beyond the conventional spectral-resolution limit. The method reduces acquisition time by more than five orders of magnitude and, through the motional Raman framework, is applicable across a broad frequency range.