Approaching the Heisenberg Limit Without Single-Particle Detection

Achieving Heisenberg-limited measurements with ensembles of more than a few particles remains a major outstanding challenge. The problem is two-fold: one must not only prepare a sufficiently sensitive state, but also be able to detect it. While it is commonly assumed that Heisenberg-limited measurement demands single-particle-resolved detection, we propose an alternative approach that bypasses this requirement. We show that the “one-axis twisting” interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout [1]. Even in the presence of dissipation, the protocol significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit, and achieves near-Heisenberg-limited precision in a $\sqrt{N}$-times shorter evolution than is required to reach the GHZ state.\\ \vspace{0.5cm} [1] E. Davis, G. Bentsen, M. Schleier-Smith, arXiv:1508.04110 (2015)