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arXiv:2211.16704

Fundamental limit of linear bosonic sensors and the Schawlow-Townes laser linewidth limit

Geng, Qi, Ka-Di Zhu

Published Nov 30, 2022• 0 citations
arXivHTMLPDF

Abstract

In recent years, many peculiar sensors have been proposed, such as the sensors based on exceptional points, Parity-Time symmetric structures or non-reciprocal systems. It is crucial to evaluate the fundamental limit of these sensing schemes and to judge whether there is an enhanced performance. Several papers have already investigated the fundamental limits based on different aspects and criteria, some led to different conclusions. In this paper, we suggest that for linear bosonic sensors that can be modeled as coupled oscillators below threshold, a measurement of the mode frequency $w_0$ can not has a precision beyond $\frac{\sqrt{κ_0}}{2\sqrt{nτ}}$, in which $κ_{0}$ is the intrinsic loss, $n$ is the average particle number at that mode and $τ$ is the measurement time. Such a precision limit can already be achieved for a single mode passive sensor, and we have proved that it can not be exceeded by adding gain components, or by coupling it to other modes to form a n-mode linear sensor. Further more, we recognize that the above limit is comparative to the frequency uncertainty ($\frac{\sqrt{κ_0}}{\sqrt{2 nτ}}$) for an above-threshold oscillation mode (e.g. a laser cavity above threshold), which is related to the Schawlow-Townes laser linewidth limit. This observation makes us conjecture that the limit we proposed for linear sensors may be a basic general limit which restricts most, if not all, sensors.

DOI
10.48550/arxiv.2211.16704

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We study a class of feedback oscillators realized by a phase-insensitive amplifier in positive feedback, where either the amplifier or the feedback element may determine the oscillator's linewidth. The spectral purity of the output of such a device originates from basic demands of quantum mechanics and causality. The resulting expression generalizes the Schawlow-Townes limit, which is itself one component of a standard quantum limit for feedback oscillators. Recently realized bad-cavity oscillators, such as superradiant lasers and solid-state masers, can saturate this generalized Schawlow-Townes limit. This limit can be surpassed through appropriate quantum engineering, for example, by atomic spin squeezing in a superradiant laser.
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Abstract : We demonstrated that an optical laser can operate with less than 1 photons on average inside the cavity while also obtaining significant spectral narrowing of the emitted light relative to the single atom transition linewidth. We further explored the power output properties and threshold conditions of this laser. We made direct measurements that showed that the lasing frequency can be made greater than 10000 times less sensitive to the resonance frequency of the optical cavity than is the case for normal lasers or for passive optical reference cavities. Such a large reduction in sensitivity would essentially remove both thermal and technical mirror vibrations as a limitation on laser linewidth. Other studies included how phase information can be stored and manipulated inside of our laser, such that it may be possible to have both an active laser and a passive Ramsey-like sensor in the same setup. We considered the fundamental limits on the atomic quantum information that can be extracted from the laser light and found that it corresponded closely to the fundamental atomic standard quantum limit on phase estimation.
Feedback oscillators, consisting of an amplifier whose output is partially fed back to its input, provide stable references for standardization and synchronization. Notably, the laser is such an oscillator whose performance can be limited by quantum fluctuations. The resulting frequency instability, quantified by the Schawlow-Townes formula, sets a limit to laser linewidth. Here, we show that the Schawlow-Townes formula applies universally to feedback oscillators beyond lasers. This is because it arises from quantum noise added by the amplifier and out-coupler in the feedback loop. Tracing the precise origin of quantum noise in an oscillator informs techniques to systematically evade it: we show how squeezing and entanglement can enable sub-Schawlow-Townes linewidth feedback oscillators. Our analysis clarifies the quantum limits to the stability of feedback oscillators in general, derives a standard quantum limit (SQL) for all such devices, and quantifies the efficacy of quantum strategies in realizing sub-SQL oscillators.