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arXiv:0906.1933 · Physical Review A

Enhancement of field squeezing using coherent feedback

John Edward Gough, Sebastian Wildfeuer

Published Oct 14, 2009• 81 citations
arXivHTMLPDF

Abstract

The theory of quantum feedback networks has recently been developed with the aim of showing how quantum input-output components may be connected together so as to control, stabilize, or enhance the performance of one of the subcomponents. In this paper, we show how the degree to which an idealized component (a degenerate parametric amplifier in the strong-coupling regime) can squeeze input fields may be enhanced by placing the component in loop in a simple feedback mechanism involving a beam splitter. We study the spectral properties of output fields, placing particular emphasis on the elastic and inelastic components of the power density.

DOI
10.1103/physreva.80.042107

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The theory of quantum feedback networks has recently been developed with the aim of showing how quantum input-output components may be connected together so as to control, stabilize, or enhance the performance of one of the subcomponents. In this paper, we show how the degree to which an idealized component (a degenerate parametric amplifier in the strong-coupling regime) can squeeze input fields may be enhanced by placing the component in loop in a simple feedback mechanism involving a beam splitter. We study the spectral properties of output fields, placing particular emphasis on the elastic and inelastic components of the power density.
The purpose of this article is to present an efficient coherent feedback control technique for squeezing enhancement of degenerate parametric amplifiers (DPAs). The feedback controllers to be designed are in the form of linear quantum stochastic systems which can be described by quantum feedback networks theory recently developed. The problem of squeezing enhancement is formulated as a non-convex constrained nonlinear programming problem, whose solution yields the coherent feedback controllers to be designed. Compared with the previous study, the proposed approach reveals clear advantage when DPAs are lossy, as is always the case in practice. Based on the recently developed quantum network synthesis theory, we show how the designed coherent feedback controllers can be implemented by means of quantum optical devices.
Classical feedback control and system theory are playing an important role in modelling, controlling and analysing complex devices in many branches of engineering. Recent developments like quantum computers and miniaturisation of existing applications and devices are increasing the importance of the ability to control systems with quantum effects. Efforts have been made recently to extent the simplicity and power of the language of classical control theory to quantum mechanical systems. Within this framework of “Quantum Feedback Networks” we are investigating two problems. The first problem concerns the enhancement of squeezed states. It has been observed that the squeezing effect of squeezing devices can be enhancement by measurement based feedback techniques or use of optical cavities. We are investigating the possibility of feedback enhanced squeezing using coherent feedback control. Considered is a static ideal squeezing devices interacting with a single mode cavity undergoing coherent feedback using a beam splitter. We show that the overall squeezing of the output depends on the beam-splitter’s reflectivity and that we are thus able to enhance the squeezing by choosing an appropriate configuration of the beam-splitter. In the second part we investigate the question of compatibility of a rigorous approach to the adiabatic elimination of some degrees of freedom of a quantum mechanical systems and instantaneous feed-forward and feedback limits for quantum mechanical networks. The commutativity of both limits is not obvious but frequently assumed in quantum optics. We show that both limit procedures are instances of Schur complements and prove the commutativity of both limits by generalising a statement about successive Schur complements.
The purpose of this paper is to present an efficient coherent feedback control technique for squeezing enhancement of degenerate parametric amplifiers (DPAs). The feedback controllers to be designed are in the form of linear quantum stochastic systems which can be described by quantum feedback network theory recently developed. The problem of squeezing enhancement is formulated as a non-convex constrained nonlinear programming problem. Compared with previous study, the proposed approach reveals clear advantage when DPAs are lossy, as is always the case in practice.
A coherent feedback scheme is used to enhance the degree of squeezing of the output field in a cavity optomechanical system. In the feedback loop, a beam splitter (BS) plays the roles of both a feedback controller and an input-output port. To realize effective enhancement, the output quadrature should take the same form as the input quadrature, and the system should operate at the deamplification situation in the meantime. This can be realized by choosing an appropriate frequency-dependent phase angle for the generalized quadrature. Additionally, both the transmissivity of the BS and the phase factor induced by time delays in the loop affect optical squeezing. For the fixed frequency, the optimal values of transmissivity and phase factor can be used to achieve the enhanced optical squeezing. The effect of optical losses on squeezing is also discussed. Optical squeezing is degraded by the introduced vacuum noise owing to the inefficient transmission in the loop. We show that the enhancement of squeezing is achievable with the parameters of the current experiments.
We present squeezing and anti-squeezing spectra of the output from a degenerate optical parametric oscillator (OPO) network arranged in different coherent quantum feedback configurations. One OPO serves as a quantum plant, the other as a quantum controller. The addition of coherent feedback enables shaping of the output squeezing spectrum of the plant, and is found to be capable of pushing the frequency of maximum squeezing away from the optical driving frequency and broadening the spectrum over a wider frequency band. The experimental results are in excellent agreement with the developed theory, and illustrate the use of coherent quantum feedback to engineer the quantum-optical properties of the plant OPO output.