标题： 增强时钟转换和动态解耦在Cr$_7$Mn分子纳米磁体中的相干性 显示英文标题

标题： Enhancing Coherence with a Clock Transition and Dynamical Decoupling in the Cr$_7$Mn Molecular Nanomagnet

摘要： 分子磁体由于其化学可调性、通过电子自旋共振技术的可寻址性以及长相干时间，作为自旋量子比特具有吸引力。 时钟跃迁（CTs）使得系统在一级近似下对磁场波动的影响免疫，提供了一种增强相干时间$T_2$的方法，并揭示了不由这些波动引起的退相干机制。 在此我们研究了 Cr$_7$Mn 的两种变体，在零场时钟跃迁附近的磁场下进行研究。我们发现，在温度$\le$2 K 时，使用 Hahn-echo 脉冲序列在时钟跃迁处观察到$T_2\sim1$ $\mu$ 。 远离CT，观察到由于与核自旋耦合而产生的电子自旋回波包络调制（ESEEM）振荡，其$T_2$高达$1.35$ $\mu$ s，表明存在不同的相干性保持机制。 在CPMG脉冲序列下的动态解耦在CT处产生$T_2\sim\!2.8$ $\mu$ s，并在ESEEM区域内达到高达$\sim\!3.6$ $\mu$ s，同时伴随着振荡行为的解调。 $T_2$ 的实验值在很大程度上与分子在溶剂中的稀释程度或溶剂是否为氘代无关，这表明大部分退相干和 ESEEM 源自分子本身。 为了解释退相干，我们建立了一个模型，该模型不仅包含场涨落，还包含 CT 跃迁频率本身的涨落。 通过将环境视为核拉莫尔进动频率的噪声和横向各向异性参数 $E$ 的 $1/f$ 噪声的组合，我们的结果可以得到很好的解释。 这些关于退相干微观起源的信息有助于合理设计基于分子的自旋量子比特。 显示英文摘要

摘要： Molecular magnets are attractive as spin qubits due to their chemical tunability, addressability through electron-spin resonance techniques, and long coherence times. Clock transitions (CTs), for which the system is immune to the effect of magnetic-field fluctuations to first order, provide a method to enhance the coherence time $T_2$, and to reveal mechanisms of decoherence that are not due to such fluctuations. Here we investigate two variants of Cr$_7$Mn, a spin-1 molecular nanomagnet, at fields near a zero-field CT. We find that at temperatures $\le$2 K, $T_2\sim1$ $\mu$s at the CT using a Hahn-echo pulse sequence. Away from the CT, electron-spin-echo envelope modulation (ESEEM) oscillations due to coupling to nuclear spins are observed and have a $T_2$ as high as $1.35$ $\mu$s, indicating a distinct mechanism of coherence preservation. Dynamical decoupling with the CPMG pulse sequence yields $T_2\sim\!2.8$ $\mu$s at the CT and up to $\sim\!3.6$ $\mu$s in the ESEEM regime along with a demodulation of the oscillatory behavior. The experimental values of $T_2$ are largely independent of the degree of dilution of the molecules in solvent or whether the solvent is deuterated, indicating that much of the decoherence and ESEEM arises from sources within the molecules themselves. To account for decoherence, we develop a model that includes not only field fluctuations but also fluctuations in the CT transition frequency itself. Our results can be well explained by treating the environment as a combination of noise at the nuclear Larmor precession frequency and $1/f$ noise in the transverse anisotropy parameter $E$. Such information about the microscopic origins of decoherence can aid the rational design of molecular-based spin qubits.