Toward Heisenberg-Limited Spectroscopy with Multiparticle Entangled States

TLDR

Spectroscopy is fundamentally limited by the Heisenberg uncertainty relation, and for N systems reaching this limit requires quantum entanglement. The authors propose a scalable spectroscopy method that exploits entanglement to achieve the Heisenberg limit while protecting information against readout noise. The method is implemented on three beryllium ions, transferring spectroscopic information to states that are optimally protected against readout noise. The technique achieves a 1.45‑fold increase in sensitivity over an ideal non‑entangled three‑particle experiment.

Abstract

The precision in spectroscopy of any quantum system is fundamentally limited by the Heisenberg uncertainty relation for energy and time. For N systems, this limit requires that they be in a quantum-mechanically entangled state. We describe a scalable method of spectroscopy that can potentially take full advantage of entanglement to reach the Heisenberg limit and has the practical advantage that the spectroscopic information is transferred to states with optimal protection against readout noise. We demonstrate our method experimentally with three beryllium ions. The spectroscopic sensitivity attained is 1.45(2) times as high as that of a perfect experiment with three non-entangled particles.