Quantum feedback control of levitating opto-mechanics

当面临控制物理自由度的任务时，基于这种观察的观察和调整是最自然的方法。这是反馈控制概念背后的基本思想，反馈控制是控制工程的标准范例之一。如果应用于受连续噪声影响的系统，则由连续监测驱动的反馈控制回路通常允许消除噪声的影响，并将系统稳定在期望的配置中，达到一定的精度。这种强大的控制程序是为宏观物体建立的，遵守经典力学定律。然而，越来越需要将反馈控制的应用扩展到由量子力学控制的微观自由度。由于量子力学的基本概率特性，对量子对象的观测通常会导致概率结果的分布，这表现为额外的噪声（技术上称为测量反作用）。这一特性使得量子反馈控制理论，即量子自由度被监控并引导到期望的状态，比经典的理论更加复杂。然而，量子反馈控制方案的设计和实施将是最及时和最受欢迎的，因为目前正在努力实现应用于纳米和量子技术的相干操纵。可利用的量子计算的主要障碍仍然是工程多体微观系统的问题，其中受控子系统之间的相互作用被增强，而与环境的不必要的相互作用被抑制。反馈控制方案将提供一种有效的方法来抑制这种环境噪声的影响，并有可能将系统稳定在量子态中，作为量子信息处理的资源。冷却、捕获和制造技术的最新进展正在为量子体系带来越来越多的自由度。在这些自由度中，谐振光耦合到微米或纳米机械振荡器的腔光机系统家族因其在传感、量子信息处理和作为量子到经典边界的探针（因为它们包括不同尺寸的大质量振荡器）方面的兴趣而脱颖而出。特别是，最近出现了新一代的这种系统，其中机械振荡器不是被夹在基板上，而是被光学装置捕获的悬浮珠。这些设置是特别有前途的，因为它们不受底层的热波动的影响。尽管如此，由于它们的频率相对较低，这对冷却要求要严格得多，它们还没有进入完全量子化的状态，在这种状态下，相干的纯量子态可以被操纵和观察。我们的研究项目旨在设计和实施反馈方案，用于光学机械系统的冷却和量子控制，特别是伦敦大学学院和维也纳大学（项目合作伙伴）的悬浮珠装置。我们打算实现基态冷却以及压缩态（位置不确定性低于基态不确定性的状态，与量子计量学相关），以及悬浮珠的非经典叠加（薛定谔猫）。

When confronted with the task of controlling a physical degree of freedom, observations and adjustments based on such observations are a most natural way to proceed. This is the basic idea behind the notion of feedback control, one of the standard paradigms of control engineering. If applied to systems subject to continuous noise, feedback control loops driven by continuous monitoring often allow one to cancel the effect of noise and to stabilise the system in a desirable configuration, up to a certain precision. Such powerful control routines are well established for macroscopic objects, obeying the laws of classical mechanics. However, it is becoming more and more desirable to extend the application of feedback control to microscopic degrees of freedom, governed by quantum mechanics. Due to the fundamentally probabilistic character of quantum mechanics, the observation of quantum objects typically results in a distribution of probabilistic outcomes, which manifests itself as additional noise (technically referred to as measurement back-action). This feature makes the theory of quantum feedback control, whereby quantum degrees of freedom are monitored and steered to desired states, rather more complex than its classical counterpart. Yet, the design and implementation of quantum feedback control schemes would be most timely and welcome, given the current struggle to achieve coherent manipulations for application in nano- and quantum technologies. The main obstacle standing in the way of exploitable quantum computation is still the problem of engineering multipartite microscopic systems where the interactions between the controlled subsystems are enhanced, while the unwanted interaction with their environment is suppressed. Feedback control schemes would offer an active way to suppress the effect of such environmental noise, with the possibility of stabilising the systems in quantum states useful as resources for quantum information processing.Recent advances in cooling, trapping and manifacturing techniques are bringing more and moredegrees of freedom into the quantum regime. Among such degrees of freedom the family of cavity opto-mechanical systems, where resonating light is coupled to a micro- or nano-scopic mechanical oscillator, stand out for their interest in sensing, quantum information processing and as probes of the quantum to classical boundary (as they include massive oscillators of varying size). In particular, a new generation of such systems recently emerged where the mechanical oscillator is not clamped to a substrate but is instead a levitating bead, trapped by optical means. These set-ups are particularly promising because they are not influenced by the thermal fluctuations of a substratum. Still, because of their relatively low frequencies, which set much more stringent cooling requirements, they have not yet entered a fully quantum regime, where coherent, pure quantum states can be manipulated and observed. They would hence benefit greatly from the development of bespoke feedback control techniques.Our research project is aimed at the design and implementation of feedback schemes for the cooling and quantum control of opto-mechanical systems, and in particular for the levitated bead set-ups at University College London and at the University of Vienna (project partner). We intend to achieve ground state cooling as well as squeezed states (states where the uncertainty on position is below the uncertainty of the ground state, of relevance to quantum metrology), as well as non-classical superpositions (Schroedinger cats) of the levitated beads.