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IEEE Conference on Decision and Control (CDC)

Quantum back-action evasion via coherent feedback control: A geometric control approach

Yu Yokotera, Naoki Yamamoto

Published Dec 1, 2016• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cdc.2016.7798644

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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.
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.
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) 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).].
Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by 2.8\textbf{2.8}2.8 dB, corresponding to a reduction in the noise power by 72±5.1\textbf{72}\pm\textbf{5.1}72±5.1 \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe.
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.
Continuous quantum displacement measurements are fundamentally limited by a trade-off between readout imprecision and measurement back-action, constrained by the Heisenberg uncertainty principle. In the Laser Interferometric Gravitational-Wave Observatory (LIGO), these two quantum noise components dominate much of the observation band, making it an excellent testbed. We induce a sub-Hz-linewidth optomechanical mode by trapping the differential motion of the 40-kg mirrors in a band where radiation-pressure back-action dominates the motion. Engineering the quantum state entering the dark port creates correlations between imprecision and back-action that partially cancel their contributions, reducing observed motion near resonance by ~47%. A framework resolving the imprecision, back-action, and correlation terms identifies the origin of this suppression. These results demonstrate quantum back-action evasion and quantum reservoir engineering in a macroscopic optomechanical system.