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arXiv:2002.07644 · Physical Review A

Direct approach to realizing quantum filters for high-precision measurements

J. D. Bentley, Hendra I. Nurdin, Yanbei Chen, Haixing Miao

Published Jan 7, 2021• 7 citations
arXivHTMLPDF

Abstract

Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using nonclassical states and quantum filters, which modify both the noise and signal response. We find an approach to realizing quantum filters directly from their frequency-domain transfer functions, utilizing techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show an optical realization of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.

DOI
10.1103/physreva.103.013707

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Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using nonclassical states and quantum filters, which modify both the noise and signal response. We find an approach to realizing quantum filters directly from their frequency-domain transfer functions, utilizing techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show an optical realization of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.
We present a new quantum control strategy for increasing the shot-noise-limited sensitivity of optical interferometers. The strategy utilizes active phase-insensitive quantum filtering of the signal inside the interferometer and does not rely on optical squeezing. On the example of the coupled-cavity resonators, employed in the gravitational-wave detectors, we show that fully causal and stable phase-insensitive filters can improve the interferometer sensitivity by more than an order of magnitude. The role of the phase-insensitive component in such systems is to provide frequency-dependent compensation for the unwanted dispersion introduced by the position-sensing optical cavity. The system's stability is achieved by limiting the frequency band of this compensation. We demonstrate that stable optomechanical Parity-time-symmetric (PT-symmetric) filters comprise a special subclass of such phase-insensitive devices and find entirely new solutions which overcome the sensitivity of PT-symmetric filters. This scheme is robust against optical loss at the output of the detectors and in the cavities.
Quantum sensors represent a revolutionary technology with the potential to surpass the limits of classical sensors across a wide range of applications, including precision measurement, navigation, and medical diagnostics. However, the realization of this potential is significantly hindered by the pervasive presence of noise. This work addresses the critical need for accurate noise modeling and effective suppression techniques within quantum sensors. We introduce a novel noise model that incorporates both thermal and coherent noise sources, explicitly accounting for the quantum mechanical nature of these sensors. This model is then utilized to design and analyze various noise suppression strategies, including feedback control algorithms and advanced filtering methods. The theoretical framework presented here provides a foundation for improved sensor design and operation, ultimately driving advancements in quantum sensing technology. The core claim of this work is that precise noise modeling and effective suppression techniques are paramount for enhancing the precision of quantum sensors. This is achieved through the establishment of a new noise model and the subsequent design of suppression techniques such as feedback control and filtering. The novelty lies in the detailed and accurate representation of noise sources within the quantum sensor system.
Resolving signals with closely spaced frequencies is central to applications in communications, spectroscopy and sensing. Recent results have shown that quantum sensing protocols can exhibit superresolution, the ability to discriminate between spectral lines with arbitrarily small frequency separation. Here, we revisit this problem from the perspective of quantum control theory, utilizing the filter function formalism to derive general, analytic conditions on quantum control protocols for achieving superresolution. Building on these conditions, we develop an optimal control framework, the utility of which is demonstrated through numerical identification of superresolution control protocols in the presence of realistic, experimentally-relevant constraints. We further extend our results to entangled initial states and assess their potential advantage. Our approach is broadly applicable to a wide variety of quantum sensing platforms, and it provides a systematic path to discover novel protocols that surpass conventional resolution limits in these systems.
Quantum systems can be used to measure various quantities in their environment with high precision. However, their sensitivity is limited by the decohering effects of this same environment. Quantum error correction has recently emerged as a tool to separate these two external contributions, and thus filter noise from signal in quantum sensors. However, this strategy has been commonly thought to be useful only for reducing noise which couples to a sensor differently than the signal, greatly limiting its practical utility. Here we show that this is not the case, and present a method through which an error-corrected quantum sensor can measure a signal while also suppressing background noise in the same direction. Our result opens the possibility of correcting for noise in all directions on a quantum sensor without also correcting away the signal.
Abstract The sensitivity of the second generation ground-based gravitational-wave detectors is mostly limited by quantum noise (QN). The injection of frequency-dependent squeezed vacuum states into the output port of the interferometer has been shown to reduce QN across the entire detector bandwidth. Frequency dependent squeezed states are generated by reflecting a frequency independent squeezed states off a detuned optical cavity: the phase response of the cavity rotates the squeeze angle as a function of frequency. The precision of the longitudinal control of the such cavity, known as filter cavity, is one of the key parameters affecting the QN suppression factor. The target longitudinal control precision was achieved by simultaneously acting on both the cavity length and the frequency of the squeezing main laser. In this scenario, the analysis of this system requires a Multiple-Input Multiple-Output (MIMO) system model. In this work, we demonstrate that a MIMO model is required and show that a MIMO system identification technique is effective to characterize the system and improve its robustness. Ultimately we show that these techniques allow the design of robust filters that can keep the cavity residual length fluctuations below 1 pm, allowing for a QN reduction of 4.5 dB at high frequencies and 2 dB at low frequencies in the Advanced Virgo interferometer.
We present a general transfer-function approach to noise filtering in open-loop Hamiltonian engineering protocols for open quantum systems. We show how to identify a computationally tractable set of fundamental filter functions, out of which arbitrary transfer filter functions may be assembled up to arbitrary high order in principle. Besides avoiding the infinite recursive hierarchy of filter functions that arises in general control scenarios, this fundamental filter-function set suffices to characterize the error suppression capabilities of the control protocol in both the time and the frequency domain. We prove that the resulting notion of filtering order reveals conceptually distinct, albeit complementary, features of the controlled dynamics as compared to the order of error cancellation, traditionally defined in the Magnus sense. Examples and implications are discussed.