Beating the Fourier Limit: Ultranarrow Field Sensing at Arbitrary Frequency via Motional Floquet Engineering*

Despite unprecedented control over Quantum Harmonic Oscillators (QHOs) and their ubiquity in precision metrology, frequency sensing on QHOs remain largely subjugated by the Fourier Transform Limit (FTL), which dictates minimum achievable linewidths and resolutions via relaxation and dephasing times.

 

While existing work has sought to overcome this challenge by exploiting the metrological properties of quantum states to improve the efficiency of frequency estimation, the FTL problem has in fact been exacerbated due to the more fragile coherences of quantum states.

 

In contrast, we present a novel protocol for electric-field frequency sensing that not only achieves beyond-FTL linewidths, but also operates at arbitrary frequency within the microwave band.

By applying a combination of dipolar and quadrupolar microwave fields on a trapped ion, we engineer a set of motional Floquet states that interact with a microwave field of interest to generate an ultranarrow resonance.

 

We demonstrate our protocol using the motional modes of a trapped 40Ca+ ion and show linewidth narrowing over 6x beyond the FTL, as well as a frequency sensitivity up to 12.3 dB beyond the FTL, yielding sub-Hz resolution with an 80 MHz field.

 

Our scheme is general and requires no apparatus beyond the trapping infrastructure of the QHO, and is thus easily extendable to other QHO platforms.