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arXiv:2107.07888 · Physical Review A

Maximizing precision in saturation-limited absorption measurements

Jake Biele, Sabine Wollmann, Joshua W. Silverstone, Jonathan C. F. Matthews, Euan J. Allen

Published Nov 22, 2021• 5 citations
arXivHTMLPDF

Abstract

Quantum fluctuations in the intensity of an optical probe is noise which limits measurement precision in absorption spectroscopy. Increased probe power can offer greater precision; however, this strategy is often constrained by sample saturation. Here, we analyze measurement precision for a generalized absorption model in which we account for saturation and explore its effect on both classical and quantum probe performance. We present a classical probe-sample optimization strategy to maximize precision and find that optimal probe powers always fall within the saturation regime. We apply our optimization strategy to two examples, high-precision Doppler broadened thermometry and an absorption spectroscopy measurement of chlorophyll a. We derive a limit on the maximum precision gained from using a nonclassical probe and find a strategy capable of saturating this bound. We evaluate amplitude-squeezed light as a viable experimental probe state and find it capable of providing precision that reaches to within $>85%$ of the ultimate quantum limit with currently available technology.

DOI
10.1103/physreva.104.053717

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Quantum fluctuations in the intensity of an optical probe is noise which limits measurement precision in absorption spectroscopy. Increased probe power can offer greater precision; however, this strategy is often constrained by sample saturation. Here, we analyze measurement precision for a generalized absorption model in which we account for saturation and explore its effect on both classical and quantum probe performance. We present a classical probe-sample optimization strategy to maximize precision and find that optimal probe powers always fall within the saturation regime. We apply our optimization strategy to two examples, high-precision Doppler broadened thermometry and an absorption spectroscopy measurement of chlorophyll a. We derive a limit on the maximum precision gained from using a nonclassical probe and find a strategy capable of saturating this bound. We evaluate amplitude-squeezed light as a viable experimental probe state and find it capable of providing precision that reaches to within >85>85%>85 of the ultimate quantum limit with currently available technology.
Absorption spectroscopy is routinely used to characterise chemical and biological samples. For the state-of-the-art in laser absorption spectroscopy, precision is theoretically limited by shot-noise due to the fundamental Poisson-distribution of photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use wavelength-correlated and tuneable photon pairs to demonstrate how absorption spectroscopy can be performed with precision beyond the shot-noise limit and near the ultimate quantum limit by using the optimal probe for absorption measurement—single photons. We present a practically realisable scheme, which we characterise both the precision and accuracy of by measuring the response of a control feature. We demonstrate that the technique can successfully probe liquid samples and using two spectrally similar types of haemoglobin we show that obtaining a given precision in resolution requires fewer heralded single probe photons compared to using an idealised laser.
The optical shot-noise limit of a laser beam represents the classical limit in precision and signal to noise ratio achievable in optical sensors and imaging systems. It is known that quantum states of light, such as squeezed light and quantum correlated twin beams can be used to enhance precision and signal to noise ratio to beyond this limit. This promises optical sensors with fundamentally superior performance to the state of the art. While quantum-enhanced signal to noise ratio has been demonstrated with macroscopic powers of squeezed probe beam, demonstrations of quantum enhanced precision have remained at extremely low powers of light (femto-Watts). Here we will give examples where increasing SNR with quantum light is not sufficient to increase precision and we will review proof of principle experiments that have demonstrated sub shot noise precision, including for absorption spectroscopy and imaging. We will also report our efforts to achieve this sub-shot-noise precision performance for transmission measurement with ~0.1mW of average probe power, equating to ~10W peak power in a pulsed experiment. Time permitting, we will discuss how integrated optics and integrated electronics enables 10s GHz bandwidth in the detection of squeezed light, for integrated quantum sensor technology.
Engineering apparatus that harness quantum theory promises to offer practical advantages over current technology. A fundamentally more powerful prospect is that such quantum technologies could out-perform any future iteration of their classical counterparts, no matter how well the attributes of those classical strategies can be improved. Here, for optical direct absorption measurement, we experimentally demonstrate such an instance of an absolute advantage per photon probe that is exposed to the absorbative sample. We use correlated intensity measurements of spontaneous parametric downconversion using a commercially available air-cooled CCD, a new estimator for data analysis and a high heralding efficiency photon-pair source. We show this enables improvement in the precision of measurement, per photon probe, beyond what is achievable with an ideal coherent state (a perfect laser) detected with 100% efficient and noiseless detection. We see this absolute improvement for up to 50% absorption, with a maximum observed factor of improvement of 1.46. This equates to around 32% reduction in the total number of photons traversing an optical sample, compared to any future direct optical absorption measurement using classical light.
Squeezed light has lower quantum noise in amplitude or phase than the quantum noise limit (QNL) of classical light. This enables enhancing sensitivity -- quantified by the signal-to-noise ratio (SNR) -- to beyond the QNL in optical techniques such as spectroscopy, gravitational wave detection, magnetometry and imaging. Precision -- the variance of repeated estimates -- has also been enhanced beyond the QNL using squeezed vacuum to estimate optical phase and transmission. However, demonstrations have been limited to femtowatts of probe power. Here we demonstrate simultaneous precision and sensitivity beyond the QNL for estimating modulated transmission using a squeezed amplitude probe of 0.2 mW average (25 W peak) power. This corresponds to 8 orders of magnitude above the power limitations of previous sub-QNL precision measurements. Our theory and experiment show precision enhancement scales with the amount of squeezing and increases with the resolution bandwidth of detection. We conclude that quantum enhanced precision in estimating a modulated transmission increases when observing dynamics at ∼\sim∼ kHz and above. This opens the way to performing measurements that compete with the optical powers of current classical techniques, but have superior precision and sensitivity beyond the classical limit.
Abstract Nonlinear optics plays a crucial role in science and technology, with applications ranging from spectroscopy to quantum information processing. Therefore, precise estimation of their nonlinear optical parameters is of fundamental importance. Here, we investigate quantum-enhanced sensitivity in the estimation of nonlinear absorption parameters, including saturable absorption (SA) and reverse saturable absorption (RSA). By employing the quantum Fisher information, we quantify the enhancement in sensitivity for estimating transmission ( T ), linear absorption coefficient ( α0\alpha _0α0​ ), saturable intensity ( IsI_sIs​ ), and two-photon absorption coefficient ( β\beta β ) using bright two-mode squeezed states (bTMSS) and applied it to analyze the nonlinear parameters of Pt nanoparticle samples as an example. In addition, we propose an experimental scheme based on an open-aperture Z-scan with bTMSS to realize quantum-enhanced sensitivity. Our findings establish a pathway toward quantum-enhanced estimation of nonlinear optical parameters.