标题： 引力光子回波 显示英文标题

标题： Gravitational photon echo

摘要： 在地球上的8.4 eV钍-229核钟跃迁中，对重力引起的光子回波的生成、控制和存储进行了理论研究。 由于其极窄的线宽约为1 mHz，并且在$10^{19}$量级的高品质因数， 钍-229钟跃迁允许在毫米尺度高度变化下检测重力红移效应。 此外，钍-229同位素态的1740秒半衰期允许系统在其相干时间内缓慢移动。 沿着这一方向，我们探索了由单个目标或多个等距样品中旋转引起的重力频移反转所产生的光子回波的生成、控制和存储。 我们的方法为地球上的可控制重力量子光学奠定了基础。 显示英文摘要

摘要： The generation, controls, and storage of the gravitationally induced photon echo using the 8.4 eV Thorium-229 nuclear clock transition on Earth are theoretically investigated. With its exceptionally narrow linewidth of approximately 1 mHz and high quality factor in the order of $10^{19}$, the Thorium-229 clock transition allows for the potential detection of gravitational-redshift effects at millimeter-scale altitude variations. Moreover, the 1740-second half lifetime of the Thorium-229 isomeric state allows for the slow movement of the system within its coherence time. Along this line, we explore the generation, controls, and storage of photon echo arising from a rotation induced inversion of the gravitational frequency shift in a single target or in multiple equally spaced samples. Our approach lays the foundation for the controllable gravitational quantum optics on Earth.