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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Ultimate Quantum Noise Limit of Frequency Comb Measurements

Ruoyu Liao, Youjian Song, Günter Steinmeyer

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Frequency comb measurements have enormously progressed in the last decade, with 10-18precisions coming into reach [1]. Similar to Moore's law, the precision in frequency metrology measurements has improved by about 3 orders of magnitude in a little bit more than a decade. Along these lines, the question may arise whether there will be continuous improvements for decades to come - or whether, at one point, an ultimate limitation to further improvement arises. Moreover, frequency metrology has proven superior to other methods to evince a drift of fundamental physical constants, e.g., the fine-structure constants, yet no such drift has ever been convincingly proven using either optical [2] or cosmological methods [3]. So the question is: how low can we go before quantum effects impose an ultimate limit for precision frequency metrology?

DOI
10.1109/cleoe-eqec.2019.8872941

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Frequency comb measurements have enormously progressed in the last decade, with 10-18precisions coming into reach [1]. Similar to Moore's law, the precision in frequency metrology measurements has improved by about 3 orders of magnitude in a little bit more than a decade. Along these lines, the question may arise whether there will be continuous improvements for decades to come - or whether, at one point, an ultimate limitation to further improvement arises. Moreover, frequency metrology has proven superior to other methods to evince a drift of fundamental physical constants, e.g., the fine-structure constants, yet no such drift has ever been convincingly proven using either optical [2] or cosmological methods [3]. So the question is: how low can we go before quantum effects impose an ultimate limit for precision frequency metrology?
Precision metrology is one application of optical frequency combs. Classical noise in their properties typically limits achievable measurement sensitivity. Amplitude and phase noise in optical frequency combs have already been studied extensively. So far, noise sidebands close to the carrier of either individual optical frequencies or of the mean field have been considered. This thesis develops methods to precisely characterize amplitude and phase noise down to the quantum limit. To this aim a transmissive, broadband passive cavity is developed. It filters and inter-converts amplitude and phase noise. The analysis of its signal by the use of homodyne detection provides a quantum limited measurement of phase noise. The application of ultrafast pulse shaping enables the measurement of the spectral correlations of amplitude and phase noise. Being represented by the use of covariance matrices, the entire noise correlations over the optical spectrum are characterized on the example of a Ti:Sapph oscillator. The measured noise correlations exhibit spectral structures, so-called modes. Their shape matches with the theoretical prediction. This concept known from multi-partite optical quantum systems is consequently applicable to classical noise in frequency combs. The knowledge of the intrinsic noise modes is likely provide an improvement of precision metrology experiments with combs.
Frequency combs enable precision measurements across timekeeping, spectroscopy, ranging and astronomy, and are now extending to integrated and field-deployable platforms. Realizing their full performance demands a comprehensive account of the quantum noise that arises when broadband optical fields are converted into finite-bandwidth electrical signals. Here we present a rigorous first-principles quantum-mechanical framework for optical frequency-comb metrology based on continuous-mode field quantization and a comb-line-resolved description of quantum fluctuations. The theory describes how quantum fluctuations of the comb field are transduced into electrical measurement noise. Formulated at the level of the comb field, the framework unifies the standard quantum limits of optical frequency division (OFD) and dual-comb spectroscopy (DCS) within a single treatment, and provides a general recipe for other comb-based measurements. On this footing, we identify practical, resource-efficient routes to quantum enhancement through engineered comb states, laying a foundation for the design of next-generation frequency combs operating at and beyond standard quantum limits.
While it is true that quantum mechanics imposes strict limits on the precision of measurements, we can sometimes improve measurement precision without violating the uncertainty principle. The rub is that this improvement may be formidable to achieve in practice—and always comes at the expense of a loss in the precision of a complementary measurement. Last October a team at AT&T Bell Labs succeeded in reducing the noise observed from an optical cavity below the “shot noise”—the level of fluctuations associated with variations in the vacuum fields, which is the ultimate limit to accuracy that would be predicted by semiclassical models. Although the Bell Labs experiment reduced the noise below this level by only 7 to 10%, it bolstered hopes that continued progress might eventually yield reductions in noise by factors of ten. Manipulation of the quantum noise limitations might be absolutely critical to such precision measurements as detection of gravity waves, whose faint signals are likely to be near the measurement limit of laser interferometers or mechanical oscillators. The phenomenon might possibly find applications in optical communication or optical memory systems.
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as 1/N21/N^21/N2 with the number of particles involved---substantially surpassing the 1/N1/N1/N-scaling characteristic to classical statistics. A natural question arises, whether such an impressive enhancement persists when one takes into account the decoherence effects that are unavoidable in any real-life implementation. In this thesis, we resolve a major part of this issue by describing general techniques that allow to quantify the attainable precision in metrological schemes in the presence of uncorrelated noise. We show that the abstract geometrical structure of a quantum channel describing the noisy evolution of a single particle dictates then critical bounds on the ultimate quantum enhancement. Our results prove that an infinitesimal amount of noise is enough to restrict the precision to scale classically in the asymptotic NNN limit, and thus constrain the maximal improvement to a constant factor. Although for low numbers of particles the decoherence may be ignored, for large NNN the presence of noise heavily alters the form of both optimal states and measurements attaining the ultimate resolution. However, the established bounds are then typically achievable with use of techniques natural to current experiments. In this work, we thoroughly introduce the necessary concepts and mathematical tools lying behind metrological tasks, including both frequentist and Bayesian estimation theory frameworks. We provide examples of applications of the methods presented to typical qubit noise models, yet we also discuss in detail the phase estimation tasks in Mach-Zehnder interferometry both in the classical and quantum setting---with particular emphasis given to photonic losses while analysing the impact of decoherence.