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The proceedings of the IEEE Conference on Control Applications/The proceedings of the ... IEEE Conference on Control Applications

Optimal amplitude quadrature control of an optical squeezer using an integral LQG approach

S. Z. Sayed Hassen, Ian R. Petersen

Published Sep 1, 2010• 5 citations
Publisher

Abstract

Squeezed states of light possess an asymmetric noise distribution whereby the uncertainty in one quadrature is less than the standard quantum noise limit. These states can be generated through a nonlinear optical process in an optical parametric oscillator (OPO). In this paper, we model such an optical squeezer and design an LQG controller which includes integral action to optimize the level of squeezing achieved in one of the quadratures of the fundamental optical field.

DOI
10.1109/cca.2010.5611273

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Squeezed states of light possess an asymmetric noise distribution whereby the uncertainty in one quadrature is less than the standard quantum noise limit. These states can be generated through a nonlinear optical process in an optical parametric oscillator (OPO). In this paper, we model such an optical squeezer and design an LQG controller which includes integral action to optimize the level of squeezing achieved in one of the quadratures of the fundamental optical field.
In this paper, we consider the application of linear quadratic Gaussian (LQG) control to the problem of optimizing the level of squeezing in one of the quadratures of an optical field. Squeezed states of light can be generated when two optical fields (at fundamental and second-harmonic frequencies) interact in an optical cavity in the presence of a second-order nonlinear crystal. Our system is an optical squeezer which is modelled as a nonlinear quantum system. Suitable models for the quantum and classical noises present in the system are used and laser phase noise which arises due to mechanical vibration of the mirror(s) in the beam path is modeled as (approximately) integrated white noise. An LQG controller is synthesized and the closed loop system is simulated to validate our design.
This paper studies feedback quantum control of a class of linear quantum optical systems by means of squeezing and phase modulation. A new quadrature representation of such systems is introduced, which includes explicitly phase modulation of light fields involved. Some fundamental relations are derived in terms of the new quadrature representation. The coherent quantum LQG control studied in is re-investigated base on controller parametrization and a two-stage optimization approach. Examples are given to illustrate the effectiveness of the results in the paper.
The purpose of this paper is to present a theoretic and numerical study of utilizing squeezing and phase shift in coherent feedback control of linear quantum optical systems. A quadrature representation with built-in phase shifters is proposed for such systems. Fundamental structural characterizations of linear quantum optical systems are derived in terms of the new quadrature representation. These results reveal considerable insights into the issue of the physical realizability of such quantum systems. The problem of coherent quantum linear quadratic Gaussian (LQG) feedback control studied in H. I. Nurdin, M. R. James, and I. R. Petersen, Automatica, IFAC, 45 (2009), pp. 1837--1846; G. Zhang and M. R. James, IEEE Trans. Automat. Control, 56 (2011), pp. 1535--1550 is reinvestigated in depth. First, the optimization methods in these papers are extended to a multistep optimization algorithm which utilizes ideal squeezers. Second, a two-stage optimization approach is proposed on the basis of controller parametrization. Numerical studies show that closed-loop systems designed via the second approach may offer LQG control performance even better than that when the closed-loop systems are in the vacuum state. When ideal squeezers in a closed-loop system are replaced by (more realistic) degenerate parametric amplifiers, a sufficient condition is derived for the asymptotic stability of the resultant new closed-loop system; the issue of performance convergence is also discussed in the LQG control setting.
Squeezed light is a nonclassical state of electro-magnetic field and has noise suppressed below the standard quantum limit in one quadrature component while increased in the other. One of the important applications of squeezed lights is quantum enhanced sensing such as gravitational wave detector with ultimate resolution. Another important application is continuous variables quantum teleportation which utilizes two mode squeezed lights as an essential resource for quantum entanglement. In these applications the final outcome is limited by squeezing level. So it is important to generate highly squeezed light. Over the past few decades a considerable number of the experiments have been performed to generate highly squeezed lights. One of the successful methods is utilization of a sub-threshold optical parametric oscillator (OPO) which includes a nonlinear optical crystal. In this article we will introduce current development of experimental investigation of continuous-wave highly squeezed light by utilizing the OPO and current topics about applications of squeezed light.
The squeezed state is important in quantum metrology and quantum information. The most effective generation tool known is the optical parametric oscillator (OPO). Currently, only the squeezed states of lower-order spatial modes can be generated by an OPO. However, the squeezed states of higher-order complex spatial modes are more useful for applications such as quantum metrology, quantum imaging and quantum information. A major challenge for future applications is efficient generation. Here, we use cascaded phase-only spatial light modulators to modulate the amplitude and phase of the incident fundamental mode squeezed state. This efficiently generates a series of squeezed higher-order Hermite-Gauss modes and a squeezed arbitrary complex amplitude distributed mode. The method may yield new applications in biophotonics, quantum metrology and quantum information processing.
The squeezed state is important in quantum metrology and quantum information. The most effective generation tool known is the optical parametric oscillator (OPO). Currently, only the squeezed states of lower-order spatial modes can be generated by an OPO. However, the squeezed states of higher-order spatial modes are more useful for applications such as quantum metrology, quantum imaging, and quantum information. A major challenge for future applications is efficient generation. Here we use cascaded phase-only spatial light modulators to modulate the amplitude and phase of the incident fundamental mode squeezed state. This efficiently generates a series of squeezed higher-order Hermite–Gauss modes and a squeezed arbitrary complex amplitude distributed mode. The method may yield new applications in biophotonics, quantum metrology, and quantum information processing.