According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom's emission spectrum.

中文翻译：

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引力场中的量子时间膨胀

根据相对论，理想时钟的读数被解释为沿着时空经典轨迹流逝的固有时间。相比之下，量子理论允许将许多同时轨迹与单个量子时钟关联起来，每个轨迹都进行适当的加权。在这里，我们研究叠加原理如何影响简单时钟（衰变的二能级原子）观察到的引力时间膨胀。将这样的原子放置在位置的叠加中，使我们能够分析量子对自发发射中表现出的经典时间膨胀的贡献。特别是，我们表明，在引力场中分离波包的相干叠加中制备的原子的发射率不同于这些包的经典混合物中原子的发射率，这产生了量子引力时间扩张效应。我们证明，这种非经典效应也体现在当前原子钟分辨率范围内的原子内能的分数频移中。此外，我们还展示了空间相干性对原子发射光谱的影响。