Advantages of interaction-based readout for quantum sensing

Detection noise poses a challenge for achieving Heisenberg-limited phase estimation. We discuss a "twisting echo" protocol1 that addresses this problem by using interactions to amplify a spectroscopic signal. The echo protocol enables phase sensitivity near the Heisenberg limit while permitting detection noise on the order of the quantum noise of an unentangled state. For comparison with conventional schemes requiring direct detection of entangled states, we calculate the dependence of metrological gain on detection noise in Ramsey spectroscopy with squeezed, twin Fock, and GHZ states. The twisting echo outperforms all of these alternatives if the detection uncertainty is at or above the single-atom level.