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Physical Review Letters

Non-Gaussian State Generation from Linear Elements via Feedback

Masahiro Yanagisawa

Published Nov 11, 2009• 17 citations
Publisher

Abstract

We present a feedback scheme to produce quantum non-Gaussian states from linear optical elements. Instead of traditional additive control methods, we introduce a mutiplicative feedback control and apply it to the deterministic generation of quantum superposition states. The protocol of feedback control is based on quantum nondemolition measurement of a quadrature, multifeedback structure, and Lyapunov stability for feedback design.

DOI
10.1103/physrevlett.103.203601

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We present a feedback scheme to produce quantum non-Gaussian states from linear optical elements. Instead of traditional additive control methods, we introduce a mutiplicative feedback control and apply it to the deterministic generation of quantum superposition states. The protocol of feedback control is based on quantum nondemolition measurement of a quadrature, multifeedback structure, and Lyapunov stability for feedback design.
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In the control of classical mechanical systems, feedback has been applied to the generation of desired nonlinear dynamics, e.g., in chaos control. However, how much this can be done is still an open problem in quantum mechanical systems. This paper presents a scheme of enhancing nonlinear quantum effects via the recently developed coherent feedback techniques, which can be shown to outperform the measurement-based quantum feedback scheme that can only generate pseudo-nonlinear quantum effects. Apart from the advantages of our method, an unsolved problem is that the decoherence rate is also increased by the quantum amplifier, which may be solved by introducing, e.g., an integral device or an nonlinear quantum amplifier. Such a proposal is demonstrated via two application examples in quantum optics on chip. In the first example, we show that nonlinear Kerr effect can be generated and amplified to be comparable with the linear effect in a transmission line resonator (TLR). In the second example, we show that by tuning the gains of the quantum amplifiers in a TLR coherent feedback network, the resulting nonlinear effects can generate and manipulate non-Gaussian “light” (microwave field) which exhibits fully quantum sub-Poisson photoncount statistics and photon antibunching phenomenon. The scheme opens up broad applications in engineering nonlinear quantum optics on chip. Particularly, in this study, the concept of feedback nonlinearization which is very useful for quantum feedback control systems is introduced. This is in contrast to the feedback linearization concept used in classical nonlinear feedback control systems.