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

TL;DR

This paper explores how long-range interactions affect the sensitivity of Stark quantum probes, revealing that interaction range influences localization and precision, with super-Heisenberg scaling achievable across various regimes.

Contribution

It demonstrates that long-range interactions can enhance or diminish probe sensitivity, providing new insights into quantum sensing with many-body systems.

Findings

Super-Heisenberg precision is achievable across all interaction ranges.

Localization power and sensitivity vary with interaction range, peaking near fully connected graphs.

Lower filling factors improve measurement precision for weak fields.

Abstract

In contrast to interferometry-based quantum sensing, where interparticle interaction is detrimental, quantum many-body probes exploit such interactions to achieve quantum-enhanced sensitivity. In most of the studied quantum many-body probes, the interaction is considered to be short-ranged. Here, we investigate the impact of long-range interaction at various filling factors on the performance of Stark quantum probes for measuring a small gradient field. These probes harness the ground state Stark localization phase transition which happens at an infinitesimal gradient field as the system size increases. Our results show that while super-Heisenberg precision is always achievable in all ranges of interaction, the long-range interacting Stark probe reveals two distinct behaviors. First, by algebraically increasing the range of interaction, the localization power enhances and thus the sensitivity of the probe decreases. Second, as the interaction range becomes close to a fully connected graph its effective localization power disappears and thus the sensitivity of the probe starts to enhance again. The super-Heisenberg precision is achievable throughout the extended phase until the transition point and remains valid even when the state preparation time is incorporated in the resource analysis. As the probe enters the localized phase, the sensitivity decreases and its performance becomes size-independent, following a universal behavior. In addition, our analysis shows that lower filling factors lead to better precision for measuring weak gradient fields.