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In contrast to interferometry-based quantum sensing, where interparticleinteraction is detrimental, quantum many-body probes exploit such interactionsto achieve quantum-enhanced sensitivity. In most of the studied quantummany-body probes, the interaction is considered to be short-ranged. Here, weinvestigate the impact of long-range interaction at various filling factors onthe performance of Stark quantum probes for measuring a small gradient field.These probes harness the ground state Stark localization phase transition whichhappens at an infinitesimal gradient field as the system size increases. Ourresults show that while super-Heisenberg precision is always achievable in allranges of interaction, the long-range interacting Stark probe reveals twodistinct behaviors. First, by algebraically increasing the range ofinteraction, the localization power enhances and thus the sensitivity of theprobe decreases. Second, as the interaction range becomes close to a fullyconnected graph its effective localization power disappears and thus thesensitivity of the probe starts to enhance again. The super-Heisenbergprecision is achievable throughout the extended phase until the transitionpoint and remains valid even when the state preparation time is incorporated inthe resource analysis. As the probe enters the localized phase, the sensitivitydecreases and its performance becomes size-independent, following a universalbehavior. In addition, our analysis shows that lower filling factors lead tobetter precision for measuring weak gradient fields.

Long-range interacting Stark many-body probes with Super-Heisenberg precision