标题： 自旋声子耦合和9.2GHz时钟跃迁在Lu(II)化合物中的弛豫时间 显示英文标题

标题： Spin Phonon Coupling and Relaxation time in Lu(II) compound with 9.2GHz clock transition

摘要： 电子自旋量子比特在原子钟跃迁下运行表现出极长的相干时间，使其成为可扩展量子信息应用的有前途的候选者。 在固态系统中，量子比特与晶格声子之间的相互作用已被证明在自旋弛豫（T1）和退相干（T2）中起关键作用。 在本工作中，我们对一个具有显著钟跃迁的Lu(II)配合物自旋量子比特进行了第一性原理计算。 通过采用先进的电子结构方法，我们定量评估了声子对超精细相互作用的影响，该相互作用作为主要的自旋-晶格耦合机制。 将这些由声子引起的变异视为一阶微扰，我们应用Redfield主方程来计算T1和T2及其温度依赖性。 对于T1，我们采用第二量子化形式来描述声子相互作用，而T2则是通过在整个布里渊区中显式积分声学声子贡献来评估的。 我们的结果再现了实验观察到的T2的磁场依赖性，包括在0.43 T附近的相干峰，尽管T1和T2的绝对值相差一到两个数量级。 分析表明，T1主要由纵向声子控制，而T2则最强烈地受到中波长、中能量的声学模式影响。 这些发现提供了对自旋量子比特相干性的钟跃迁保护效应的定量演示，并为评估其他分子自旋量子比特中的自旋-声子相互作用提供了一个可转移的计算框架。 显示英文摘要

摘要： Electron spin qubits operating at atomic clock transitions exhibit exceptionally long coherence times, making them promising candidates for scalable quantum information applications. In solid-state systems, interactions between qubits and lattice phonons are known to play a critical role in spin relaxation (T1) and decoherence (T2). In this work, we perform first-principles calculations on a Lu(II) complex spin qubit featuring a prominent clock transition. By employing advanced electronic structure methods, we quantitatively evaluate the influence of phonons on the hyperfine interaction, which serves as the primary spin-lattice coupling mechanism. Treating these phonon-induced variations as first-order perturbations, we apply the Redfield master equation to compute both T1 and T2, along with their temperature dependencies. For T1, we adopt a second quantization formalism to describe phonon interactions, while T2 is evaluated by explicitly integrating acoustic phonon contributions across the full Brillouin zone. Our results reproduce the experimentally observed magnetic field dependence of T2, including the coherence peak near 0.43 T, though the absolute values of T1 and T2 differ by one to two orders of magnitude. Analysis reveals that T1 is primarily governed by longitudinal phonons, whereas T2 is most strongly influenced by mid-wavelength, mid-energy acoustic modes. These findings provide a quantitative demonstration of the clock transition protective effect on spin qubit coherence and offer a transferable computational framework for evaluating spin-phonon interactions in other molecular spin qubits.