We present a broad summary of research involving the application of quantum feedback control techniques to optical setups, from the early enhancement of optical amplitude squeezing to the recent stabilisation of photon number states in a microwave cavity, dwelling mostly on the latest experimental advances. Feedback control of quantum optical continuous variables, quantum nondemolition memories, feedback cooling, quantum state control, adaptive quantum measurements, and coherent feedback strategies will all be touched upon in our discussion. 1. Introduction Quantum control is a broad field of study, engaging the engineering, mathematics, and physical sciences communities in an effort to analyse, design, and experimentally demonstrate techniques whereby the dynamics of physical systems operating at the quantum regime is steered towards desired aims by external, time-dependent manipulation [1, 2]. The development of advanced quantum control schemes is clearly central to the areas of quantum and nanotechnologies, whenever the main focus is on the exploitation of coherent quantum effects. Prominent among classical and quantum control techniques are the so-called feedback or closed-loop techniques [2, 3], where the manipulation applied on the system at a given time depends on its state in the past. Closed-loop quantum control is particularly well suited to fight decoherence (the nemesis of quantum information processing, whereby the system quantum coherence is lost through unwanted interaction with a large macroscopic environment) and stabilise quantum resources in the face of noise. It is therefore a very promising paradigm, which is attracting considerable attention. Due to the high degree of coherent control, to the wide availability of well-established experimental techniques, and to the relatively low technical noise and decoherence enjoyed by optical setups, the quantum optics community has been in a position to pioneer most of the quantum control techniques developed so far and is still definitely at the forefront of such research. In particular, quantum optics allows for fast and relatively efficient detections in the quantum regime, for manipulations by control fields on time scales much shorter than the system’s typical dynamical time scales, as well as for efficient input-output interfaces (as for travelling modes impinging on optical cavities). These advantages make quantum optical systems particularly well suited for the implementation of closed-loop (“feedback”) control techniques, where some (classical or quantum) information is extracted from
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