Higher order spin noise spectroscopy of coherently interacting quan- tum systems

我们希望通过超越标准的自旋噪声光谱学来研究耦合量子力学系统。推进自旋噪声光谱学超越二阶噪声光谱开辟了一个新的领域的可能性，包括均匀和非均匀加宽之间的区别，量子相干性的证明，并测试时间反演不变性。我们将为二阶和高阶自旋噪声谱奠定量子力学理论基础，并对半导体中合适的强耦合核和电子自旋对（所谓的混合核量子比特）进行测量。我们计划（i）首次使用连续量子测量理论，从量子力学传播子的第一性原理推导高阶自旋噪声谱的解析表达式。完整的量子力学理论基于Lindblad主方程的随机版本，其中包括阻尼和温度。(ii)测量了ZnO中与9/2铟核自旋强耦合的In施主电子的标准和高阶自旋噪声谱。(iii)将该谱与本课题组先前发表的用主方程技术数值计算得到的理论谱进行比较，初步工作表明，我们的理论方法恢复了已知的二阶功率谱的表达式。此外，测量过程对系统的扰动自然地出现在方程中，并且可以用于量化由于高探测光束强度引起的扰动与对于弱强度增加的测量时间之间的权衡。

We want to study coupled quantum mechanical systems by going beyond standard spin noise spectroscopy. Advancing spin noise spectroscopy beyond second order noise spectra opens up a new realm of possibilities including the distinction between homogenous and inhomogeneous broadening, proof of quantum coherence, and testing time-reversal invariance. We will lay a quantum mechanical theoretical foundation for second and higher order spin noise spectroscopy and perform measurements on suitable strongly coupled pairs of nuclear and electron spins in semiconductors (so-called hybrid nuclear qubits).We plan to(i) derive analytical expressions for higher order spin noise spectra from first principles in terms of quantum mechanical propagators using for the first time continuous quantum measurement theory. The full quantum mechanical theory is based on a stochastic version of the Lindblad master equation which includes damping and temperature.(ii) measure standard and higher order spin noise spectra of the In-donor electron in ZnO which is strongly coupled to the 9/2 indium nuclear spin.(iii) compare the spectra with theoretical spectra that we numerically obtain by master equation techniques published earlier by our group.Preliminary work shows that our theoretical approach recovers known expressions for the 2nd order power spectrum. In addition, the perturbation of the system by the measurement process appears naturally in the equations and can be used to quantify the trade-off between perturbation due to high probe beam intensities and increased measurement time for weak intensities.