Abstract
Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.
Highlights
Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years
At the end of an interrogation cycle, the collective atomic spin is measured along a projection, which we take as Sy, providing information about the deviation of the laser from the atomic transition frequency, see Fig. 1c
What is meant by thispiffisffi that we look for the pre-factor to the asymptotic σyðτÞ / 1= τ scaling, found e.g., by extrapolating the Allan deviation from a regime with τ ≫ TC back to τ = 1 s
Summary
Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. Spin squeezed states can be generated with trapped ions[18,19] and in cold atomic gases[20,21,22], and have already been used in proof-of-principle experiments to demonstrate a reduction of quantum projection noise (QPN) in measurements of small phases on microwave transitions[23,24,25,26] The realization of such tailored entangled states on optical clock transitions is a major challenge for experiment[26,27,28] and theory[29,30,31,32,33,34]. In atomic clocks based on platforms whose atomic number cannot be scaled, such as multi-ion traps[48,49,50,51] or tweezer arrays[52,53,54,55], spin squeezing can offer a relevant advantage
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