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Quantum Electronics and Laser Science Conference

Quantum feedback and adaptive measurements

Hideo Mabuchi, John K. Au, J. K. Chin, Andrew C. Doherty, John K. Stockton

Published Nov 13, 2002• 0 citations
Publisher

Abstract

Summary form only given. Although real-time feedback of measured signals is an essential component of sensing and control in classical settings, models for quantum feedback that are rigorous yet useful have only become possible since the advent of measurement-based quantum trajectory theory. The quantum feedback scenario introduces new concerns of coherence and measurement backaction, but recent work has shown that these can be treated properly in a formal integration of quantum trajectory theory with standard state-space formulations of filtering and control theory. Pioneering studies by H. M. Wiseman have shown that such models can be used to design and to analyze realistic schemes for adaptive homodyne measurement and for feedback control of atomic motion. Much of the ongoing research in our group focuses on the experimental implementation of such schemes. For a broad range of quantum feedback scenarios, certain recurring technical issues arise out of the need to perform complex, high-bandwidth processing of measured signals. We are developing a "rapid-prototyping" approach to refining signal processing and feedback algorithms via quantum trajectory simulation on a PC, followed by translation of the algorithms into hardware Description language (HDL).

DOI
10.1109/qels.2001.962176

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Summary form only given. Although real-time feedback of measured signals is an essential component of sensing and control in classical settings, models for quantum feedback that are rigorous yet useful have only become possible since the advent of measurement-based quantum trajectory theory. The quantum feedback scenario introduces new concerns of coherence and measurement backaction, but recent work has shown that these can be treated properly in a formal integration of quantum trajectory theory with standard state-space formulations of filtering and control theory. Pioneering studies by H. M. Wiseman have shown that such models can be used to design and to analyze realistic schemes for adaptive homodyne measurement and for feedback control of atomic motion. Much of the ongoing research in our group focuses on the experimental implementation of such schemes. For a broad range of quantum feedback scenarios, certain recurring technical issues arise out of the need to perform complex, high-bandwidth processing of measured signals. We are developing a "rapid-prototyping" approach to refining signal processing and feedback algorithms via quantum trajectory simulation on a PC, followed by translation of the algorithms into hardware Description language (HDL).
The standard quantum formalism introduced at the undergraduate level treats measurement as an instantaneous collapse. In reality however, no physical process can occur over a truly infinitesimal time interval. A more subtle investigation of open quantum systems lead to the theory of continuous measurement and quantum trajectories, in which wave function collapse occurs over a finite time scale associated with an interaction. Within this formalism, it becomes possible to ask many new questions that would be trivial or even ill-defined in the context of the more basic measurement model. In this thesis, we investigate both theoretically and experimentally what fundamentally new capabilities arise when an experimental apparatus can resolve the continuous dynamics of a measurement. Theoretically, we show that when one can perform feedback operations on the timescale of the measurement process, the resulting tools provide significantly more control over entanglement generation, and in some settings can generate it optimally. We derive these results using a novel formalism which encompasses most known quantum feedback protocols. Experimentally, we show that continuous measurement allows one to observe the dynamics of a system undergoing simultaneous non-commuting measurements, which provides a reinterpretation of the Heisenberg uncertainty principle. Finally, we combine the theoretical focus on quantum feedback with the experimental capabilities of superconducting circuits to implement a feedback controlled quantum amplifier. The resulting system is capable of adaptive measurement, which we use to perform the first canonical phase measurement.
Recent progress in quantum physics has made it possible to perform experiments in which individual quantum systems are monitored and manipulated in real time.The advent of such new technical capabiMies provides strong motivation for the development of theoretical and experimental methodologies for quantum feedback control.The availability of such methods would enable radically new approachesto experimentalphysics in the quantum realm.Likewise, the investigationof quantumfeedback control will introduce crucialnew considerationsto control theory, such as the uniquely quantum phenomena of entanglement and measurement backaction.The extension of established ana2ysistectilques from control theory into the quantum domain may also provide new insight into the dynamics of complex quantum systems.We anticipate that the successful formulation of an input-output approach to the analysis and reduction of large quantum systems could have very general applications in non-equilibrium quantum statistical mechanics and in the nascent field quantum information theory...
Recent advances in quantum optics and atomic physics have enabled experimenters to begin exploring realtime feedback in quantum settings. In addition to the practical significance of such work for fields like nanotechnology and quantum information processing, research on quantum feedback probes the fundamental physics of conditional evolution for observed systems. Feedback in quantum settings is generally complicated by the intricacies of 'wave-function collapse' and measurement back-action, so that the proper design of quantum feedback controllers will require accurate quantitative models for the measurement process.
In this review paper, we survey the main concepts and some of the recent developments in quantum feedback control. For consistency and clarity, essential ideas and notations in the theory of open quantum systems and quantum stochastic calculus, as well as continuous measurement theory are developed. We give a general description of quantum feedback control, set up a coherent model and compare it to open-loop designs. Objectives which can be achieved by feedback, such as rapid state preparation and purification or entanglement generation are formulated and analyzed, based on the relevant literature. The connection between quantum feedback and quantum chaos is also described and unravelled which, apart from its theoretical curiosity, can shed more light on some of the intrinsic properties of this control paradigm.
Abstract This chapter discusses a novel aspect of quantum control, namely quantum feedback. It explains the crucial distinction between measurement-based feedback and autonomous feedback. In the former, a detector performs a measurement of the variable to be controlled, and information passes from the quantum system to a classical system, which processes it to produce a correction signal sent to an actuator acting back on the quantum system. In the latter, the detector-processor-actuator part of the controller is another quantum system coupled to the controlled system, and no information need pass through classical channels. The chapter treats the useful formalism of the quantum stochastic master equation, a basic element of knowledge essential to the detailed understanding of measurement-based feedback, and the design of the filters for the corresponding controller. The autonomous aspect of quantum feedback is illustrated by a discussion of analog, continuous error correction of a qubit by quantum optics elements.
Introduction In the preceding chapter we introduced quantum trajectories: the evolution of the state of a quantum system conditioned on monitoring its outputs. As discussed in the preface, one of the chief motivations for modelling such evolution is for quantum feedback control. Quantum feedback control can be broadly defined as follows. Consider a detector continuously producing an output, which we will call a current. Feedback is any process whereby a physical mechanism makes the statistics of the present current at a later time depend upon the current at earlier times. Feedback control is feedback that has been engineered for a particular purpose, typically to improve the operation of some device. Quantum feedback control is feedback control that requires some knowledge of quantum mechanics to model. That is, there is some part of the feedback loop that must be treated (at some level of sophistication) as a quantum system. There is no implication that the whole apparatus must be treated quantum mechanically. The structure of this chapter is as follows. The first quantum feedback experiments (or at least the first experiments specifically identified as such) were done in the mid 1980s by two groups [WJ85a, MY86]. They showed that the photon statistics of a beam of light could be altered by feedback. In Section 5.2 we review such phenomena and give a theoretical description using linearized operator equations. Section 5.3 considers the changes that arise when one allows the measurement to involve nonlinear optical processes.