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arXiv:2211.06050 · Physical Review A

Ultimate limits of exoplanet spectroscopy: A quantum approach

Zixin Huang, Christian Schwab, Cosmo Lupo

Published Feb 8, 2023• 18 citations
arXivHTMLPDF

Abstract

One of the big challenges in exoplanet science is to determine the atmospheric makeup of extrasolar planets and to find biosignatures that hint at the existence of biochemical processes on another world. The biomarkers we are trying to detect are gases in the exoplanet atmosphere such as oxygen or methane, which have deep absorption features in the visible and near-infrared spectrum. Here we establish the ultimate quantum limit for determining the presence or absence of a spectral absorption line, for a dim source in the presence of a much brighter stellar source. We characterize the associated error exponent in both the frameworks of symmetric and asymmetric hypothesis testing. We found that a structured measurement based on spatial demultiplexing allows us to decouple the light coming from the planet and achieve the ultimate quantum limits. If the planet has intensity $\ensuremath{\epsilon}\ensuremath{\ll}1$ relative to the star, we show that this approach significantly outperforms direct spectroscopy yielding an improvement of the error exponent by a factor $1/\ensuremath{\epsilon}$. We find the optimal measurement, which is a combination of interferometric techniques and spectrum analysis.

DOI
10.1103/physreva.107.022409

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One of the big challenges in exoplanet science is to determine the atmospheric makeup of extrasolar planets and to find biosignatures that hint at the existence of biochemical processes on another world. The biomarkers we are trying to detect are gases in the exoplanet atmosphere such as oxygen or methane, which have deep absorption features in the visible and near-infrared spectrum. Here we establish the ultimate quantum limit for determining the presence or absence of a spectral absorption line, for a dim source in the presence of a much brighter stellar source. We characterize the associated error exponent in both the frameworks of symmetric and asymmetric hypothesis testing. We found that a structured measurement based on spatial demultiplexing allows us to decouple the light coming from the planet and achieve the ultimate quantum limits. If the planet has intensity \ensuremathϵ\ensuremath≪1\ensuremath{\epsilon}\ensuremath{\ll}1\ensuremathϵ\ensuremath≪1 relative to the star, we show that this approach significantly outperforms direct spectroscopy yielding an improvement of the error exponent by a factor 1/\ensuremathϵ1/\ensuremath{\epsilon}1/\ensuremathϵ. We find the optimal measurement, which is a combination of interferometric techniques and spectrum analysis.
Discovering exoplanets in orbit around distant stars via direct imaging is fundamentally impeded by the combined effect of optical diffraction and photon shot noise under extreme star-planet contrast. Coronagraphs strive to increase the signal-to-noise ratio of exoplanet signatures by optically suppressing light from the host star while preserving light from the exoplanet. However, it is unclear whether direct-imaging coronagraphs constitute an optimal strategy for attaining fundamental limits relevant to exoplanet discovery. In this work, we first review the quantum information limits of exoplanet detection and localization characterized by (1) the quantum Chernoff exponent for symmetric hypothesis testing, (2) the quantum relative entropy for asymmetric hypothesis testing, and (3) the quantum Fisher information matrix for multiparameter estimation. We demonstrate that coronagraphs designed to completely suppress light in the fundamental mode of the telescope, while perfectly transmitting higher-order orthogonal modes, indeed achieve these limits in the regime of high star-planet contrasts. Furthermore, we formulate coronagraphs as quantum channels, thus generalizing the classical framework of coronagraphy to the quantum setting. Using this framework, we compare the information-theoretic performance of leading coronagraph designs against the quantum limits. Our analysis indicates that quantum-optimal coronagraphs offer enhanced information efficiency in the subdiffraction regime compared to leading coronagraph designs and may significantly expand the domain of accessible exoplanets.
Detecting the faint emission of a secondary source in the proximity of the much brighter one has been the most severe obstacle for using direct imaging in searching for exoplanets. Using quantum state discrimination and quantum imaging techniques, we show that one can significantly reduce the probability of error for detecting the presence of a weak secondary source, especially when the two sources have small angular separations. If the weak source has intensity ε≪1 relative to the bright source, we find that the error exponent can be improved by a factor of 1/ε. We also find linear-optical measurements that are optimal in this regime. Our result serves as a complementary method in the toolbox of optical imaging, with applications ranging from astronomy to microscopy.
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