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arXiv:1912.05870 · Physical Review Research

Approaching the quantum limit of precision in absorbance estimation using classical resources

Euan J. Allen, Javier Sabines-Chesterking, Alex R. McMillan, Siddarth Koduru Joshi, Peter S. Turner, Jonathan C. F. Matthews

Published Aug 12, 2020• 15 citations
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Abstract

This work investigates precision bounds in absorbance sensing via the Beer-Lambert law for quantum and classical sources of light. The authors find that by optimizing the length of the sample, classical sources of light are able to reach within 83% of the absolute quantum limit in precision. A bulk optical experiment is used to demonstrate optimization of thermal and Fock states of light

DOI
10.1103/physrevresearch.2.033243

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This work investigates precision bounds in absorbance sensing via the Beer-Lambert law for quantum and classical sources of light. The authors find that by optimizing the length of the sample, classical sources of light are able to reach within 83% of the absolute quantum limit in precision. A bulk optical experiment is used to demonstrate optimization of thermal and Fock states of light
Optical quantum sensing strategies that utilise features of quantum states of light have implications for precision measurement in areas as wide ranging as such as gravitational wave sensing [1] and biological imaging [2]. Optical absorption estimation is the task of estimating the transmission parameter η which is defined by the ratio of input, Iin, to output, Iout, intensity of light from a sample of interest (Iout= ηIιη). The optimal quantum strategy provides a quantum advantage (per incident photon) of 1/(1-η) over the best classical strategy [3]. This technique has been demonstrated experimentally in single parameter estimation and imaging scenarios [4,5].
The field of quantum sensing aims at improving the detection and estimation of classical parameters that are encoded in physical systems by resorting to quantum sources of light and quantum detection strategies.The same approach can be used to improve the current classical measurements that are performed on biological systems.Here we consider the scenario of two bacteria (E. coli and Salmonella) growing in a Luria-Bertani broth and monitored by classical spectrophotometers.Their concentration can be related to the optical transmissivity via the Beer-Lambert-Bouguer's law and their growth curves can be described by means of Gompertz functions.Starting from experimental data points, we extrapolate the growth curves of the two bacteria and we study the theoretical performance that would be achieved with a quantum setup.In particular, we discuss how the bacterial growth can in principle be tracked by irradiating the samples with orders of magnitude fewer photons, identifying the clear superiority of quantum light in the early stages of growth.We then show the superiority and the limits of quantum resources in two basic tasks: (i) the early detection of bacterial growth and (ii) the early discrimination between two bacteria species.
Understanding the fundamental limits on the precision to which an optical phase can be estimated is of key interest for many investigative techniques utilized across science and technology. We study the estimation of a fixed optical phase shift due to a sample which has an associated optical loss, and compare phase estimation strategies using classical and nonclassical probe states. These comparisons are based on the attainable (quantum) Fisher information calculated per number of photons absorbed or scattered by the sample throughout the sensing process. We find that for a given number of incident photons upon the unknown phase, nonclassical techniques in principle provide less than a 2020%20 reduction in root-mean-square error (RMSE) in comparison with ideal classical techniques in multipass optical setups. Using classical techniques in a different optical setup that we analyze, which incorporates additional stages of interference during the sensing process, the achievable reduction in RMSE afforded by nonclassical techniques falls to only $\ensuremath{\simeq}4%$. We explain how these conclusions change when nonclassical techniques are compared to classical probe states in nonideal multipass optical setups, with additional photon losses due to the measurement apparatus.
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.
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.