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Quantum 2.0 Conference and Exhibition

Defining the Standard Quantum Limit of Heterodyne between a Continuous Wave Laser and an Optical Frequency Comb

Eugene Tsao, Noah Lordi, Alexander J. Lind, Matthew Heyrich, Josh Combes, Scott A. Diddams

Published Jan 1, 2023• 0 citations
Publisher

Abstract

Optical clocks employ heterodyne between a laser and a frequency comb, yet the quantum description of this measurement is unknown. We define measurement operators and the standard quantum limit, and demonstrate progress reaching this limit.
DOI
10.1364/quantum.2023.qw3b.4

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The measurement and manipulation of coherent optical fields have been transformed by the optical frequency comb. Today, the optical frequency comb grants measurements precise enough to count individual cycles of light as well as the generation of nearly any coherent electromagnetic field from the ultraviolet through the infrared. These capabilities have enabled the most precise realizations and comparisons of time, precision spectroscopy over broad bandwidths, and the ability to convert stable signals between optical and microwave fields–seamlessly connecting the entire electromagnetic spectrum from hertz (100 ) to petahertz (1015). These applications involve the interference of a frequency comb with another coherent light source, such as another frequency comb or a single-frequency continuous-wave laser. However, coherent light represents only one type of light. The vast majority of light emanates from “black bodies” such as stars, which is in a thermal state as opposed to a coherent state, and carries profound information about the universe and humanity’s place within it. Other types of light defy classical electromagnetism and are known as non-classical or quantum light. Such quantum light may play central roles in quantum communication, quantum computation, and quantum-enhanced metrology. In this thesis, the use of the optical frequency comb in the interferometric measurement of thermal and quantum light is investigated, with a focus on assessing fundamental limits to the sensitivity of such measurements. In order to measure thermal light, a technique called dual-comb correlation spectroscopy is explored. This technique entails heterodyne measurement of the field of thermal light and subsequent correlation of the field in time. This process reveals the spectrum of thermal light at high resolution and across broad bandwidths. New theoretical work uncovers previously unknown fundamental limits on sensitivity when measuring realistically weak thermal light. Experimental investigation verifies this scaling and is accompanied by a demonstration of spectroscopy at the equivalent power spectral density of our Sun, realizing a greater than 1000-fold sensitivity increase over past demonstrations of this technique. These insights pave the way for expansion of this technique to comb-based spatial correlation of thermal fields. This advancement would allow for extended baseline synthetic aperture hyperspectral imaging throughout the optical spectrum, facilitating novel and profound observations of the universe. The use of frequency combs for the measurement of quantum light is also investigated. This scenario breaks typical quantum optics assumptions, such as large, mode-matched local oscillators, and necessitates new quantum measurement operators. Such measurement operators are derived, which not only describe homodyne measurements on any quantum state of light with a frequency comb local oscillator, but also indicate that the shot noise limit generally reached in comb-based measurements of coherent light (such as in continuous-wave laser heterodyne and dual-comb spectroscopy) does not correspond to the quadrature or coherent state-overlap description standard in quantum optics. Efforts to experimentally reach this “standard” quantum limit demonstrate a significant improvement in the signal-to-noise ratio over the conventional comb-based shot noise limit, paving the way for lower-power portable optical clocks and quantum-enhanced frequencycomb metrology.
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?
Optical frequency combs, named for their comblike peaks in the spectrum, are essential for various sensing applications. As the technology develops, its performance has reached the standard quantum limit dictated by the quantum fluctuations of coherent light field. Quantum combs, with their quantum fluctuation engineered via squeezing and entanglement, are the necessary ingredient for overcoming such limits. We develop the theory for designing and analyzing quantum combs, focusing on dual-comb interferometric measurement. Our analyses cover both squeezed and entangled quantum combs with division receivers and heterodyne receivers, leading to four protocols with quantum advantages scalable with squeezing/entanglement strength. In the spectroscopy of a single absorption line, the division receiver with the squeezed comb suffers from entanglement-mismatching-induced amplified noise, while the other three protocols demonstrate a surprising robustness to loss at a few comb lines. Such a unique loss-robustness of a scalable quantum advantage has not been found in any traditional quantum sensing protocols.