## Feedback and quantum systems

### Wed May 3 08:57:19 BST 2006

- [quant-ph/0605015]
- Title: Applications of Feedback Control in Quantum Systems
- Authors: Kurt Jacobs
- Abstract: We give an introduction to feedback control in quantum systems, as well as an overview of the variety of applications which have been explored to date. This introductory review is aimed primarily at control theorists unfamiliar with quantum mechanics, but should also be useful to quantum physicists interested in applications of feedback control. We explain how feedback in quantum systems differs from that in traditional classical systems, and how in certain cases the results from modern optimal control theory can be applied directly to quantum systems. In addition to noise reduction and stabilization, an important application of feedback in quantum systems is adaptive measurement, and we discuss the various applications of adaptive measurements. We finish by describing specific examples of the application of feedback control to cooling and state-preparation in nano-electro-mechanical systems and single trapped atoms.
- Comment:
- Quantum systems display different dynamics to classical systems because measuring the state of the system changes it, and the measurement itself introduces randomness.
- Evolution of a classical system is given by the Kushner-Stratonovich (K-S) equation, which leads to the equations for the Kalman-Bucy filter.
- Quantum systems with Hamiltonians containing terms at most quadratic in the dynamical variables are linear, as the equations of motion of the dynamical variables are linear. These linear equations are the same as for the classical system subjected to the same forces.
- Measurement of the system allows feedback but also adds randomness, so there is an optimum measurement strength for optimum control of the system.

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