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arXiv:0904.3745 · New Journal of Physics

Feedback control using only quantum back-action

Kurt A. Jacobs

Published Apr 1, 2010• 40 citations
arXivHTMLPDF

Abstract

The traditional approach to feedback control is to apply deterministic forces to a system by modifying the Hamiltonian. Here we show that finite-dimensional quantum systems can be controlled purely by exploiting the random quantum back-action of a continuous weak measurement. We demonstrate that, quite remarkably, the quantum back-action of such an adaptive measurement is just as effective at controlling quantum systems as traditional feedback.

DOI
10.1088/1367-2630/12/4/043005

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The traditional approach to feedback control is to apply deterministic forces to a system by modifying the Hamiltonian. Here we show that finite-dimensional quantum systems can be controlled purely by exploiting the random quantum back-action of a continuous weak measurement. We demonstrate that, quite remarkably, the quantum back-action of such an adaptive measurement is just as effective at controlling quantum systems as traditional feedback.
In the conventional picture of quantum feedback control, sensors make measurements on a quantum system, a classical controller processes the results of the measurements, and semi-classical actuators act back on the system to alter its behavior. Quantum measurements are well known to yield probabilistic results and to introduce unavoidable disturbances in the system measured. Accordingly, quantum feedback is traditionally considered to be both probabilistic and destructive. This paper proposes and provides an experimental demonstration of an alternative method for quantum feedback control, in which sensors, controller, and actuators are themselves quantum systems that interact coherently with the system to be controlled. The resulting feedback loop preserves quantum coherence. Such coherent quantum feedback control is deterministic, non-destructive, and can be used to perform actions such as transferring quantum entanglement that are not possible using conventional feedback control of quantum systems. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Measuring a quantum system can randomly perturb its state. The strength and nature of this back-action depend on the quantity that is measured. In a partial measurement performed by an ideal apparatus, quantum physics predicts that the system remains in a pure state whose evolution can be tracked perfectly from the measurement record. We demonstrated this property using a superconducting qubit dispersively coupled to a cavity traversed by a microwave signal. The back-action on the qubit state of a single measurement of both signal quadratures was observed and shown to produce a stochastic operation whose action is determined by the measurement result. This accurate monitoring of a qubit state is an essential prerequisite for measurement-based feedback control of quantum systems.
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.
We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical linear-quadratic-Gaussian control theory with residual feedback.