Shaped microwave pulses for measuring hybrid quantum devices

研究混合量子器件的动机是将自然自旋系统的长相干时间与电路量子电动力学的可扩展性结合起来，用于固态量子信息处理[1]。电子自旋共振（ESR）是测量自旋系统的一种标准技术，它使用电感耦合微波谐振器用脉冲辐射激发自旋并检测其特征磁场响应[2]。它已被进一步用于探测存在于量子器件表面的自旋，由此可以将化学指纹归因于退相干[3]的来源。在其他条件相同的情况下，具有高Q因子的谐振器产生更好的ESR灵敏度（随Q的平方缩放）。然而，能量从谐振器中消散所花费的衰铃时间可能会超过自旋的特征衰减时间，从而掩盖了它们的信号[2]。高Q也会扭曲施加于自旋的激励信号。为了克服这些问题，并从高q谐振器中开发实用的ESR，我们将环衰抑制和控制理论结合起来，应用形状微波脉冲，在短时间尺度上有效地操纵和检测自旋系综。振铃抑制使用一个相位反转的能量脉冲来驱动谐振器振荡到零b[4]。对谐振频率为8.7 GHz的高q介质谐振腔的初步结果表明，通过使用方形补偿脉冲，环衰抑制了65%。为了改变脉冲在频域的分布，还考虑了扫频脉冲和相位调制点周围的脉冲整形。我们进一步讨论了形脉冲和最优控制理论在高q超导平面微谐振器中的应用，这是将实际ESR扩展到少量自旋的自然候选者。

Research into hybrid quantum devices is motivated by the potential to combine the long coherence times of natural spin systems with the scalability of circuit quantum electrodynamics for applications in solid state quantum information processing [1]. Electron Spin Resonance (ESR) is a standard technique for the measurement of a spin system, using an inductively-coupled microwave resonator to excite the spins with pulsed radiation and detect their characteristic magnetic field response [2]. It has further been used to probe the spins present on the surface of quantum devices, from which it is possible to attribute chemical fingerprints to sources of decoherence [3]. All else being equal, resonators with high-Q factors yield better ESR sensitivity (which scales with Q squared). However, the ringdown time taken for the energy to dissipate from the resonator might then exceed the characteristic decay time of the spins, concealing their signal [2]. The high Q also distorts the excitation signal applied to the spins. To try to overcome these issues, and develop practical ESR which benefits from high-Q resonators, we combine ringdown suppression and control theory to apply shaped microwave pulses, to enable efficient manipulation and detection of spin ensembles on short timescales. Ringdown suppression uses a phase-inverted pulse of sucient energy to drive the resonator oscillations to zero [4]. Preliminary results from a high-Q dielectric resonator of resonant frequency 8.7 GHz show the ringdown suppressed by 65 percent through the use of a square-shaped compensation pulse. To alter the pulse distribution in the frequency domain, frequency-swept pulses and pulse shaping around the point of phase modulation are also considered. We further discuss the application of shaped pulses and optimal control theory to high-Q superconducting planar micro-resonators, which are natural candidates for extending practical ESR to small numbers of spins.