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Chinese Physics B

Quantum noise of a harmonic oscillator under classical feedback control*

Feng Tang, Nan Zhao

Published Jul 15, 2020• 5 citations
Publisher

Abstract

Quantum sensing has been receiving researcher’s attention these years due to its ultrahigh sensitivity and precision. However, the bandwidth of the sensors may be low, thus limiting the scope of their practical applications. The low-bandwidth problem is conquered by feedback control methods, which are widely utilized in classic control fields. Based on a quantum harmonic oscillator model operating near the resonant point, the bandwidth and sensitivity of the quantum sensor are analyzed. The results give two important conclusions: (a) the bandwidth and sensitivity are two incompatible performance parameters of the sensor, so there must be a trade-off between bandwidth and sensitivity in practical applications; (b) the quantum white noise affects the signal to be detected in a non-white form due to the feedback control.

DOI
10.1088/1674-1056/aba5fb

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Quantum sensing has been receiving researcher’s attention these years due to its ultrahigh sensitivity and precision. However, the bandwidth of the sensors may be low, thus limiting the scope of their practical applications. The low-bandwidth problem is conquered by feedback control methods, which are widely utilized in classic control fields. Based on a quantum harmonic oscillator model operating near the resonant point, the bandwidth and sensitivity of the quantum sensor are analyzed. The results give two important conclusions: (a) the bandwidth and sensitivity are two incompatible performance parameters of the sensor, so there must be a trade-off between bandwidth and sensitivity in practical applications; (b) the quantum white noise affects the signal to be detected in a non-white form due to the feedback control.
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.
Realistic quantum sensors face a trade-off between the number of sensors measured in parallel and the control and readout fidelity (F)(F)(F) across the ensemble. We investigate how the number of sensors and fidelity affect sensitivity to continuous and intermittent signals. For continuous signals, we find that increasing the number of sensors by 1/F21/{F}^{2}1/F2 for F<1F<1F<1 always recovers the sensitivity achieved when F=1F=1F=1. However, when the signal is intermittent, more sensors are needed to recover the sensitivity achievable with one perfect quantum sensor. We also demonstrate the importance of near-unity control fidelity and readout at the quantum projection noise limit by estimating the frequency components of a stochastic, intermittent signal with a single trapped ion sensor. Quantum sensing has historically focused on large ensembles of sensors operated far from the standard quantum limit. The results presented in this paper show that this is insufficient for quantum sensing of intermittent signals and reemphasizes the importance of the unique scaling of quantum projection noise near an eigenstate.
We study measurement-based feedback control of a damped harmonic oscillator, motivated by optomechanical and interferometric position measurements, in which feedback is synthesized from a displacement measurement. For a band-limited derivative controller, the loop shapes the mechanical susceptibility and reinjects measurement noise, creating a tradeoff between stabilization and noise amplification. We present a compact classical formulation that isolates this tradeoff in the closed-loop displacement spectrum and identifies the parameters governing resonance suppression versus noise-driven actuation. We then extend the same topology to a quantum-limited position detector, enforcing the imprecision-backaction constraint and introducing finite measurement bandwidth that regularizes high-frequency noise reinjection and adds phase lag in the feedback path. In the high-QQQ regime we obtain an analytic design rule for the optimal feedback gain at fixed controller and measurement bandwidths and compare it with full-spectrum calculations. The comparison shows that a high mechanical quality factor alone does not guarantee quantitative agreement: the accuracy of the near-resonant approximation depends strongly on the controller and measurement bandwidths. Because finite measurement bandwidth changes both the magnitude and phase of the feedback loop, the analysis separates the near-resonant damping contribution from imprecision-noise reinjection and shows that positive near-resonant feedback damping requires the product of the controller cutoff and measurement bandwidth to exceed the square of the mechanical resonance frequency. Finally, we present a dimensionless map of the gain-optimized high-QQQ occupation and compare its predictions with full-spectrum optimization. All analytical gains evaluated in this map satisfy the full closed-loop stability criterion for these parameters.
Characterization and suppression of noise are essential for the control of harmonic oscillators in the quantum regime. We measure the noise spectrum of a quantum harmonic oscillator from low frequency to near the oscillator resonance by sensing its response to amplitude modulated periodic drives with a qubit. Using the motion of a trapped ion, we experimentally demonstrate two different implementations with combined sensitivity to noise from 500 Hz to 600 kHz. We apply our method to measure the intrinsic noise spectrum of an ion trap potential in a previously unaccessed frequency range.
Abstract Quantum systems are promising candidates for sensing of weak signals as they can be highly sensitive to external perturbations, thus providing excellent performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. Using numerical techniques, we further generalize these results to the case of background noise with a Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences, such as CPMG, are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.
The extraordinary sensitivity of plasmonic sensors is well-known in the optics and photonics community. These sensors exploit simultaneously the enhancement and the localization of electromagnetic fields close to the interface between a metal and a dielectric. This enables, for example, the design of integrated biochemical sensors at scales far below the diffraction limit. Despite their practical realization and successful commercialization, the sensitivity and associated precision of plasmonic sensors are starting to reach their fundamental classical limit given by quantum fluctuations of light-known as the shot-noise limit. To improve the sensing performance of these sensors beyond the classical limit, quantum resources are increasingly being employed. This area of research has become known as "quantum plasmonic sensing", and it has experienced substantial activity in recent years for applications in chemical and biological sensing. This review aims to cover both plasmonic and quantum techniques for sensing, and it shows how they have been merged to enhance the performance of plasmonic sensors beyond traditional methods. We discuss the general framework developed for quantum plasmonic sensing in recent years, covering the basic theory behind the advancements made, and describe the important works that made these advancements. We also describe several key works in detail, highlighting their motivation, the working principles behind them, and their future impact. The intention of the review is to set a foundation for a burgeoning field of research that is currently being explored out of intellectual curiosity and for a wide range of practical applications in biochemistry, medicine, and pharmaceutical research.