Sub-Fourier characteristics of a $\delta$-kicked rotor resonance

TL;DR

This paper experimentally demonstrates sub-Fourier scaling in a $ ext{delta}$-kicked rotor resonance using a Bose-Einstein condensate, revealing a $1/N^3$ dependence that could enhance precision in gravity measurements.

Contribution

It provides the first experimental verification of a $1/N^3$ sub-Fourier scaling in a quantum resonance, supported by theoretical analysis.

Findings

Fidelity resonance peak width scales as $1/N^3$

Mean energy width scales as $1/N^2$

Sub-Fourier effect observed in acceleration space

Abstract

We experimentally investigate the sub-Fourier behavior of a $\delta$-kicked rotor resonance by performing a measurement of the fidelity or overlap of a Bose-Einstein condensate (BEC) exposed to a periodically pulsed standing wave. The temporal width of the fidelity resonance peak centered at the Talbot time and zero initial momentum exhibits an inverse cube pulse number ($1/N^{3}$) dependent scaling compared to a $1/N^{2}$ dependence for the mean energy width at the same resonance. A theoretical analysis shows that for an accelerating potential the width of the resonance in acceleration space depends on $1/N^{3}$, a property which we also verify experimentally. Such a sub-Fourier effect could be useful for high precision gravity measurements.