引力子浴导致的相干性丢失与相干性保护
Loss of coherence and coherence protection from a graviton bath
AI总结：
本文研究了量子谐振子与引力子浴耦合导致的相干性丢失，通过量子场论框架推导出主方程，发现退相干率与陷俘频率立方成正比，且数态叠加态永不退相干，揭示了引力子相互作用下的相干性保护机制。
摘要：
我们考虑了一个与引力子浴耦合的量子谐振子，并讨论了由于物质-引力子顶点相互作用导致的物质部分相干性丢失。在量子场论框架下，通过在领头阶$\mathcal{\sim O}(G)$和$\sim\mathcal{O}(c^{-2})$处对引力场求迹，我们得到了一个主方程。我们发现退相干率与谐振子陷俘频率的立方成正比，并且对于自由粒子该退相干率为零，这与无质量四极矩系统的预期一致。此外，我们的引力子发射量子模型在具有大占据数的相干态下，恢复了经典谐振子引力辐射的已知经典公式。另外，我们发现量子谐振子最终会稳定在一个具有基态和第一激发态残余相干性的稳态。尽管引力波的经典发射会使谐振系统失去所有能量，但我们的量子场论模型不允许数态$\vert 1\rangle$和$\vert 0\rangle$通过引力子发射而衰变。特别地，数态叠加态$\frac{1}{\sqrt{2}}\left[\vert0\rangle+\vert1\rangle\right]$是一个稳态，且永远不会退相干。
英文摘要：
We consider a quantum harmonic oscillator coupled with a graviton bath and discuss the loss of coherence in the matter sector due to the matter-graviton vertex interaction. Working in the quantum-field-theory framework, we obtain a master equation by tracing away the gravitational field at the leading order $\mathcal{\sim O}(G)$ and $\sim\mathcal{O}(c^{-2})$. We find that the decoherence rate is proportional to the cube of the harmonic trapping frequency and vanishes for a free particle, as expected for a system without a mass quadrupole. Furthermore, our quantum model of graviton emission recovers the known classical formula for gravitational radiation from a classical harmonic oscillator for coherent states with a large occupation number. In addition, we find that the quantum harmonic oscillator eventually settles in a steady state with \emph{a remnant coherence} of the ground and first excited states. While classical emission of gravitational waves would make the harmonic system loose all of its energy, our quantum field theory model does not allow the number states $\vert 1\rangle$ and $\vert 0\rangle$ to decay via graviton emission. In particular, the superposition of number states $\frac{1}{\sqrt{2}}\left[\vert0\rangle+\vert1\rangle\right]$ is a steady state and never decoheres.
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