Description
Precision metrology underpins scientific and technological advancements. Quantum metrology offers a pathway to surpass classical sensing limits by leveraging both quantum states and measurement strategies. However, measuring multiple incompatible parameters suffers from a fundamental limit, exemplified by Heisenberg's uncertainty principle for two non-commuting observables, such as position and momentum.
Here, we demonstrate single-probe measurements of two incompatible parameters where the uncertainties are simultaneously reduced below the standard quantum limit (SQL). This is achieved by measuring modular observables using tailored, highly non-classical states that are designed to evade measurement backactions. Our experiment uses grid states prepared in the mechanical motion of a trapped ion to measure small displacements in position and momentum and shows a metrological gain of up to 5.1(5) dB over the simultaneous SQL for the two parameters. We demonstrate a phase estimation algorithm with Bayesian inference and achieve a combined variance of 2.6(11) dB below the SQL using an adaptive strategy. Furthermore, we investigate simultaneously estimating number and phase which are the polar counterparts of position and momentum. This is performed by preparing a novel quantum resource---number-phase states---and we demonstrate a metrological gain over their SQL. This work presents new resources for quantum sensing and marks a significant step towards multi-parameter quantum metrology, unlocking pathways to unprecedented precision in applications ranging from fundamental physics to advanced quantum technologies.
| I am the presenting author | Yes |
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