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arXiv:1609.04524 · EPJ Quantum Technology

Geometric control theory for quantum back-action evasion

Yu Yokotera, Naoki Yamamoto

Published Oct 28, 2016• 4 citations
arXivHTMLPDF

Abstract

Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present.

DOI
10.1140/epjqt/s40507-016-0053-5

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Engineering a sensor system for detecting an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle to this goal is that, in a simple detection setup, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic mechanical back-action noise. Hence, the sensor system has to be carefully engineered so that it evades the back-action noise and eventually beats the SQL. In this paper, based on the well-developed geometric control theory for classical disturbance decoupling problem, we provide a general method for designing an auxiliary (coherent feedback or direct interaction) controller for the sensor system to achieve the above-mentioned goal. This general theory is applied to a typical opto-mechanical sensor system. Also, we demonstrate a controller design for a practical situation where several experimental imperfections are present.
Engineering a detector for sensing an extremely tiny signal such as the gravitational-wave force is a very important subject in quantum physics. A major obstacle towards this goal is that, in the standard detection scheme, the measurement noise is lower bounded by the so-called standard quantum limit (SQL), which is originated from the intrinsic measurement back-action. Hence the detector system has to be carefully engineered so that it evades the back-action and eventually beats the SQL; feedback control is, of course, expected to be a very effective method to achieve this goal. In this paper, we show that this engineering problem can be formulated and solved within the framework of well-developed geometric control theory, for a specific opto-mechanical system.
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing devices, such as sensors and atomic clocks. Here we show that by engineering the dynamics of coupled quantum systems, it is possible to construct a subsystem that evades the measurement back action of quantum mechanics, at all times of interest, and obeys any classical dynamics, linear or nonlinear, that we choose. We call such a system a quantum-mechanics-free subsystem (QMFS). All of the observables of a QMFS are quantum-nondemolition (QND) observables; moreover, they are dynamical QND observables, thus demolishing the widely held belief that QND observables are constants of motion. QMFSs point to a new strategy for designing classical information-processing devices in regimes where quantum noise is detrimental, unifying previous approaches that employ QND observables, back-action evasion, and quantum noise cancellation. Potential applications include gravitational-wave detection, optomechanical force sensing, atomic magnetometry, and classical computing. Demonstrations of dynamical QMFSs include the generation of broad-band squeezed light for use in interferometric gravitational-wave detection, experiments using entangled atomic spin ensembles, and implementations of the quantum Toffoli gate.
The Standard Quantum Limit (SQL) in classical force detection using mechanical systems arises from quantum back-action, which disturbs the oscillator’s evolution during measurement. We present a theoretical analysis of a scheme that enables broadband back-action evading (BAE) force sensing by employing a multidimensional optical transducer. The proposed system consists of a mechanical oscillator coupled to an optical structure supporting three distinct optical modes, with mode spacing approximately matched to the mechanical resonance. The central mode is coherently pumped, and the signal is extracted by monitoring the light emitted from the adjacent sideband modes. By selecting appropriate optical quadratures for detection and applying tailored post-processing to the measurement data, our approach suppresses back-action noise across a wide frequency range, enabling sensitivity beyond the SQL. The architecture can be interpreted as a composite system hosting quantum-mechanics-free subsystems (QMFS), which effectively isolate the measured observable from quantum fluctuations by exploiting correlations akin to those found in systems with engineered “negative mass” response. We also show that the adjacent sideband modes are entangled and discuss possible methods for detecting this entanglement. This configuration opens a promising route toward high-precision quantum metrology without being constrained by quantum measurement noise.
The standard quantum limit (SQL) of a classical mechanical force detection results from quantum back action perturbing evolution of a mechanical system. In this paper we show that usage of a multidimensional optical transducer may enable a broadband quantum back action evading measurement. We study theoretically a corresponding technique of measurement of a resonant signal force acting on a linear mechanical oscillator coupled to a generic optical system with three optical modes with separation nearly equal to the mechanical frequency. The measurement is performed by optical pumping of the central optical mode and analyzing the light escaping the two other modes. By detecting optimal quadrature components of the optical modes and postprocessing the measurement results we are able to exclude the back action in a broad frequency band and characterize the force with sensitivity better than the SQL. We show that the proposed scheme is similar to the multidimensional system containing quantum-mechanics-free subsystems which can evade the SQL using the idea of the so-called negative mass [M. Tsang and C. M. Caves, Phys. Rev. X 2, 031016 (2012).].
In many optical and atomic systems it is now possible to monitor an individual quantum system with high signal to noise and feed back by altering the system dynamics in real time. This motivates further development of quantum mechanical descriptions of feedback control. We discuss recent work on closed loop control of open quantum systems, focusing on general linear systems for which the statistics of the problem are Gaussian. Such systems may be realized with linear optics, parametric amplifiers and homodyne detection. This problem allows a direct comparison with the classical linear, quadratic cost, Gaussian noise (LQG) optimal control problem. This highlights the key distinction between the quantum and classical theories for linear systems: that increased measurement sensitivity may run counter to the control objectives since it increases the backaction noise. While in an idealized classical control problem it is always preferable to obtain a better sensor, quantum mechanical problems generically have an optimal sensitivity since quantum mechanical measurements irreducibly disturb the system. The general theory will be illustrated by reference to specific simple examples.
Today's mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself—the quantum-mechanical backaction of measurement—and go below this ‘standard’ limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme—voltage or current—for each mechanical detector configuration implies access to either the position or velocity of the mechanical subsystem. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles. Published by the American Physical Society 2024