ar X iv : q ua nt - p h / 05 09 12 5 v 1 19 S ep 2 00 5 Feedback cooling of a single trapped ion

Quantum optics, and more recently mesoscopic condensed matter physics, have taken a leading role in realizing individual quantum systems, which can be monitored continuously in quantum limited measurements, and at the same time can be controlled by external fields on time scales fast in comparison with the system evolution. Examples include cold trapped ions and atoms [1], cavity QED [2, 3, 4, 5] and nanomechanical systems [6]. This setting opens the possibility of manipulating individual quantum systems by feedback, a problem which is not only of a fundamental interest in quantum mechanics, but also promises a new route to generating interesting quantum states in the laboratory. First experimental efforts to realize quantum feedback have been reported only recently. While not all of them may qualify as quantum feedback in a strict sense, feedback has been applied to various quantum systems [5, 7, 8, 9, 10, 11]. On the theory side, this has motivated during the last decade the development of a quantum feedback theory [12, 13], where the basic ingredients are the interplay between quantum dynamics and the back-action of the measurement on the system evolution. In this letter we report a first experiment to demonstrate quantum feedback control, i.e. quantum feedback cooling, of a single trapped ion by monitoring the fluorescence of the laser driven ion in front of a mirror. We establish a continuous measurement of the position of the ion which allows us to act back in a feedback loop demonstrating “cold damping” [14, 15]. We will show that quantum control theory based on a quantum optical modelling of the system dynamics and continuous measurement theory of photodetection provides a quantitative understanding of the experimental results.