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Recovering the dynamics of optical frequency combs from phase-amplitude noise correlations measurements

Matthieu Ansquer, Valérian Thiel, Syamsundar De, Bérengère Argence, Grégory Gredat, Fabien Bretenaker, Nicolas Treps

Published Jun 25, 2018• 0 citations
OpenAlex

Abstract

Controlling the noise properties of optical frequency combs (OFC) is of great importance as most OFC-based precision measurements are limited by their intrinsic stability. It has been found that OFC noise manifests itself as fluctuations of only a few global parameters, which indicates strong correlations between the fluctuations of individual frequency lines. However, the physical processes underneath such correlations are still not completely understood. We introduce a novel measurement scheme that allows us to measure simultaneously and in real time the whole Fourier spectrum of phase and amplitude fluctuations of the OFC field as well as its amplitude-phase correlations in many frequency bands spanning the laser spectrum. This enables us to determine the full quadrature covariance matrices in the frequency band mode basis, and this for various Fourier frequencies, to find their principal modes in time and frequency domain, and to associate them with global physical parameters.

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Controlling the noise properties of optical frequency combs (OFC) is of great importance as most OFC-based precision measurements are limited by their intrinsic stability. It has been found that OFC noise manifests itself as fluctuations of only a few global parameters, which indicates strong correlations between the fluctuations of individual frequency lines. However, the physical processes underneath such correlations are still not completely understood. We introduce a novel measurement scheme that allows us to measure simultaneously and in real time the whole Fourier spectrum of phase and amplitude fluctuations of the OFC field as well as its amplitude-phase correlations in many frequency bands spanning the laser spectrum. This enables us to determine the full quadrature covariance matrices in the frequency band mode basis, and this for various Fourier frequencies, to find their principal modes in time and frequency domain, and to associate them with global physical parameters.
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.
Cavity-based noise detection schemes are combined with ultrafast pulse shaping as a means to diagnose the spectral correlations of both the amplitude and phase noise of an ultrafast frequency comb. The comb is divided into ten spectral regions, and the distribution of noise as well as the correlations between all pairs of spectral regions are measured against the quantum limit. These correlations are then represented in the form of classical noise matrices, which furnish a complete description of the underlying comb dynamics. Their eigendecomposition reveals a set of theoretically predicted, decoupled noise modes that govern the dynamics of the comb. These matrices also contain the information necessary to deduce macroscopic noise properties of the comb.
Optical clocks and their associated frequency comparison networks are exceptionally sensitive to microscopic physical variations and thus capable of measuring fundamental physical quantities across diverse applications. In frequency comparison networks, the optical frequency combs (OFCs) act as accurate frequency sensors designed to translate terahertz optical signals down to radio frequency signals for accurate frequency counting. The number of OFC's comb modes that beat with clock and transfer lasers during remote frequency comparison is indispensable for the calculation of their frequency difference. In this work, with the assistance of a 1542 nm cavity-stabilized laser at Changping campus, the number of comb modes is locally determined with sufficient uncertainty by stepping the comb's repetition rate. This approach bypasses the technical challenges of simultaneous operation of optical clocks, OFC and fiber-link noise cancelation during long-distance comparison, providing a reliable prerequisite for remote optical clock comparisons.
Abstract Measuring the spectral properties of an optical frequency comb is among the most fundamental tasks of precision metrology. In contrast to general single-parameter measurement schemes, we demonstrate here single shot multi-parameter estimation of an optical frequency comb at and beyond the standard quantum limit. The mean energy and the central frequency as well as the spectral bandwidth of ultrafast pulses are simultaneously determined with a multi-pixel spectrally resolved (MPSR) apparatus, without changing the photonics architecture. Moreover, using a quantum frequency comb that intrinsically consists of multiple squeezed states in a family of Hermite–Gaussian spectral/temporal modes, the signal-to-noise ratios of the multiple spectral parameters estimation can surpass the standard quantum limit. Combining our multi-pixel detection scheme and the multimode entangled resource could find applications in ultrafast quantum metrology and multimode quantum information processing.