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

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 ${}^{171}\text{Yb}$ atoms. The simulation results in a comparison stability of $3.5\times {10}^{-17}/\sqrt{\tau }$ at the averaging time $\tau$ for ${10}^2$ atoms. The metrological gain reaches $-4.9$ 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.