We derive the predicted time dilation of delocalized atomic clocks in an optical lattice setup in the presence of a gravitational field to leading order in quantum relativistic corrections. We investigate exotic quantum states of motion whose relativistic time dilation is outside of the realm of classical general relativity, finding a regime where 24Mg optical lattice clocks currently in development would comfortably be able to detect the special-relativistic contribution to the quantum effect (if the technical challenge of generating the necessary states can be met and the expected accuracy of such clocks can be attained). We find that the gravitational contribution, on the other hand, is negligible in this setup. We provide a detailed experimental protocol and analyse the effects of noise on our predictions. We also show that the magnitude of our predicted quantum time dilation effect remains just out of detectable reach for the current generation of 87Sr optical lattice clocks. Our calculations agree with the predicted time dilation of classical general relativity when restricting to Gaussian states.

中文翻译：

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检测光钟中相对论时间膨胀的量子离域效应的可行性


我们推导了在存在引力场的情况下光学晶格设置中离域原子钟的预测时间膨胀，以达到量子相对论校正的领先顺序。我们研究了奇特的量子运动态，其相对论时间膨胀超出了经典广义相对论的范围，找到了一种机制，目前正在开发的 24Mg 光学晶格时钟将能够轻松地检测到狭义相对论对量子效应的贡献（如果可以应对生成必要状态的技术挑战，并且可以达到此类时钟的预期精度）。另一方面，我们发现在这种设置中，引力的贡献可以忽略不计。我们提供了详细的实验方案并分析了噪声对我们预测的影响。我们还表明，我们预测的量子时间膨胀效应的幅度对于当前一代 87Sr 光学晶格时钟来说仍然超出了可检测的范围。当限制于高斯态时，我们的计算与经典广义相对论的预测时间膨胀一致。