Differential Frequency Comparison of Conditionally and Unconditionally Spin‐Squeezed States of an Optical Lattice Clock

Abstract Optical lattice clocks are the world's most accurate and stable timepieces. Thus far, the differential clock comparison has reached a stability limited by the quantum projection noise of uncorrelated atoms. Overcoming this limit relies on using spin squeezing, where quantum fluctuations of the collective spin undergo a strong suppression in one direction while being enhanced in the conjugation direction. The recent differential comparison of spin‐squeezed clocks mainly employs multiple atomic clouds or sub‐ensembles within one cloud, complicating the clock operation. Here, it is numerically investigated the differential comparison of conditionally and unconditionally spin‐squeezed states of one lattice‐trapped cloud of neutral atoms. The simulation results in a comparison stability of at the averaging time for atoms. The metrological gain reaches dB, primarily limited by the decoherence induced by quantum jumps of intracavity probe photons during quantum non‐demolition measurements. Besides the quantum precision enhancement, our scheme paves the way to using one spin squeezing protocol to appraise the other.