开放量子系统中的随机调控和噪声模拟

As open systems, quantum memory and quantum information processing device are subject to the quantum noise generated by the surrounding environment. The understanding, simulation, application of quantum noise shed a new light on the theory of decoherence and the protocols of quantum control and measurement. Quantum noise is indeed relevant to many fields. In quantum optics, it describes spontaneous fluctuations of the relative phase between the probe and reference lasers. In atomic and molecular physics, it induces spontaneous emission of excited states and fluctuations of levels. In solid systems, it arises from the stochastic response to the materials impurity and the collective effect by phonons or nuclear spins. To trace the environmental noise and control the open quantum system in a consistent manner, it is desirable to achieve novel dynamical approaches beyond the Markovian and Born approximations because in reality, the noise could be strong and also non-trivially correlated in either time or spatial domain. Our purpose in this subject is to develop random control protocols based on the nonperturbative quantum control theory in various physical realizations of qubit and quantum memory or storage. In particular, the fast random signal control is independent on the pulse design and robust to the errors induced in the experiments. It is expected to provide a prevailing strategy aimed at suppressing decoherence, preventing the target systems from the leakage or diffusion, and engineering adiabatic or diabatic passage of a quantum state. Random control could provide the phase diagram of pulse strength, during time and period as well as their fluctuations. In theory, it will illustrate the microscopic mechanism for dynamical decoupling. Also, it will optimize experimental resources in quantum manipulation to a great deal.

作为开放系统，任何量子存储和信息处理器都要受到外界环境噪声的干扰。理解、模拟和利用量子噪声将为退相干理论和量子随机调控方案带来重要启发。量子噪声在量子光学中描述探测光与基准光之间相对位相的自发涨落；在原子分子物理中造成自发辐射和能级涨落；在固态系统里，它由于杂质随机响应以及声子或核自旋的集体效应而产生。在现实物理实现中，环境噪声可能强度较大并且在时域和空域上关联，我们应该超越马尔科夫近似和玻恩近似，发展新的开放量子系统动力学方法，从而能够自洽描述环境噪声并对系统进行调控。本项目旨在发展基于非微扰论的量子随机调控方案。非微扰的随机激光脉冲调制不依赖于脉冲序列的设计、不受实验误差的干扰，将成为抑制退相干和操控量子态绝热或非绝热演化的重要手段。随机调控将为量子调控实验提供脉冲强度、时间、周期及这些物理量随机涨落的相图，有助于在微观理论上澄清动力学解耦等物理机制，在实验上优化资源。

本项目旨在研究非马尔科夫噪声对开放量子系统动力学及其调控的影响，发展非微扰的量子态调控方案，进一步加深对开放量子系统理论模型的认识。在过去四年中，我们基本上遵循项目原始设计的方案、技术路线、研究计划，主要在非马尔科夫动力学方程、开放量子系统的退相干、作为调控手段的量子测量、量子与经典噪声、开放量子系统的绝热过程等方面做出努力和贡献。其中部分成果涉及得量子计算或量子调控在物理上的限制。值得一提的成果包括：（1）在多量子点系统中，我们得到了由局域环境对电子自旋超精细作用引起的多体退相干过程的标度行为；（2）在共同环境下，我们用非马尔可夫量子轨迹刻画并估算了双比特系统的退纠缠动力学；（3）我们将量子绝热定理推广到开放量子系统，并通过我们的系统性的微扰理论得到非卷积形式的主方程；（4）我们用量子速度极限方法刻画了开放量子系统非经典性产生的时间尺度；（5）我们分析了不同参量的经典涨落或噪声对非阿贝尔和乐量子门的影响；（6）我们发现了经典噪声对量子冷却方案的原理性限制；（7）我们首次利用马尔科夫退相位噪声减缓了非马尔科夫耗散噪声对系统相干度的影响；（8）我们得到了一种特殊情况下的自旋环境中的量子比特精确主方程；（9）我们得到了零温环境下量子芝诺与反芝诺效应的简单判据，而无需计算系统动力学；（10）我们将有限温度下量子耗散过程的二阶微扰主方程推广到含时调控的情况，并由此利用量子测量实现量子冷却。这些工作拓展了开放量子系统动力学方程的应用范围，一方面与量子调控、量子计算相结合，进一步夯实这些未来应用的理论基础；另一方面帮助我们对量子力学基本原理有了更深刻的认知。