Department of Electrical and Systems Engineering, Washington University in St Louis, St Louis, MO, 63130, USA.
Departments of Mechanical and Systems Engineering, University of Texas at Dallas, Richardson, TX, 75080, USA.
Nat Commun. 2017 Sep 5;8(1):446. doi: 10.1038/s41467-017-00441-7.
Designing accurate and high-fidelity broadband pulses is an essential component in conducting quantum experiments across fields from protein spectroscopy to quantum optics. However, constructing exact and analytic broadband pulses remains unsolved due to the nonlinearity and complexity of the underlying spin system dynamics. Here, we present a nontrivial dynamic connection between nonlinear spin and linear spring systems and show the surprising result that such nonlinear and complex pulse design problems are equivalent to designing controls to steer linear harmonic oscillators under optimal forcing. We derive analytic broadband π/2 and π pulses that perform exact, or asymptotically exact, excitation and inversion over a defined bandwidth, and also with bounded amplitude. This development opens up avenues for pulse sequence design and lays a foundation for understanding the control of two-level systems.Coherent control of two-level systems is crucial for achieving fidelity in spectroscopy and quantum computing, but inherent nonlinearities and parameter variation have, to date, required an approximate, numerical approach. Here, Li et al. show how to map a spin ensemble to a spring model so analytic pulses can be designed using linear methods.
设计准确且高保真的宽带脉冲是在从蛋白质光谱学到量子光学等多个领域进行量子实验的关键组成部分。然而，由于基础自旋系统动力学的非线性和复杂性，构建精确和解析的宽带脉冲仍然是一个未解决的问题。在这里，我们展示了非线性自旋和线性弹簧系统之间的一种非平凡的动态联系，并得出了一个令人惊讶的结果，即这种非线性和复杂的脉冲设计问题等同于设计控制来在线性谐振子下引导最优力。我们推导出了在定义的带宽内执行精确或渐近精确激发和反转的解析宽带π/2 和 π 脉冲，并且具有有界的幅度。这一发展为脉冲序列设计开辟了道路，并为理解二能级系统的控制奠定了基础。在光谱学和量子计算中，实现保真度需要对二能级系统进行相干控制，但到目前为止，固有的非线性和参数变化需要采用近似的数值方法。在这里，Li 等人展示了如何将自旋系统映射到弹簧模型，以便使用线性方法设计解析脉冲。
