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arXiv:2001.05603 · Physical Review A

Resilient quantum electron microscopy

Hiroshi Okamoto

Published Aug 5, 2022• 3 citations
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Abstract

We investigate the fundamental limit of biological quantum electron microscopy, which is designed to go beyond the shot noise limit. Inelastic scattering is expected to be the main obstacle in this setting, especially for thick specimens of actual biological interest. Here we describe a measurement procedure that, in principle, significantly neutralizes the effect of inelastic scattering.

DOI
10.1103/physreva.106.022605

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We investigate the fundamental limit of biological quantum electron microscopy, which is designed to go beyond the shot noise limit. Inelastic scattering is expected to be the main obstacle in this setting, especially for thick specimens of actual biological interest. Here we describe a measurement procedure that, in principle, significantly neutralizes the effect of inelastic scattering.
The major resolution-limiting factor in cryoelectron microscopy of unstained biological specimens is radiation damage by the very electrons that are used to probe the specimen structure. To address this problem, an electron microscopy scheme that employs quantum entanglement to enable phase measurement precision beyond the standard quantum limit has recently been proposed [H. Okamoto, Phys. Rev. A 85, 043810 (2012)]. Here we identify and examine in detail measurement errors that will arise in the scheme. Emphasis is given to considerations concerning inelastic scattering events because, in general, schemes assisted with quantum entanglement are known to be highly vulnerable to lossy processes. We find that the amount of error due to both elastic and inelastic scattering processes is acceptable provided that the electron beam geometry is properly designed and the specimen is sufficiently thin.
New-generation transmission electron microscopes (TEMs) are equipped with detectors that approach the shot-noise limit. Hence it is pertinent to ask: What are the quantum limits of electron scattering experiments in the TEM? For example, for a given electron dose, what is the ultimate accuracy allowed by quantum mechanics for the atomic structure of a material? We provide quantitative answers based on quantum estimation theory. We also show that, for an arbitrary set of sample parameters, the quantum limit is achievable under conditions of weak scattering, but not strong multiple scattering (this conclusion extends to scattering of other types of radiation). Implications for structure determination of radiation-sensitive materials are discussed.
Quantum enhanced optical measurement protocols aim at reducing the uncertainty in the estimation of some physical quantities of a system below the shot-noise limit, classically unavoidable. In particular when small number of photons is used the shot noise can be the main source of uncertainty, in these cases the use of quantum light is of great interest. Note that there are several situations where the number of photons in the probe can not be increased arbitrarily, as when fragile biological samples are under investigation. Two different imaging protocols are discussed in the following.
Quantum metrology experiments in atomic physics and quantum optics have demonstrated measurement accuracy beyond the shot-noise limit via multi-particle entanglement. At the same time, electron microscopy, an essential tool for high-resolution imaging of biological systems, is severely constrained in its signal-to-noise ratio (SNR) by shot noise, due to the dose limit imposed by electron beam-induced damage. Here, we show theoretically that spin squeezing, a form of quantum metrology based on entanglement, is a natural fit for improving the SNR in electron microscopy. We investigate the generation of the necessary entangled states through electron-electron Coulomb interactions and quantum non-demolition measurements. Our results connect the fields of quantum metrology and electron interferometry, paving the way toward electron microscopy with SNR beyond the shot-noise limit.
Quantum metrology allows high sensitivity measurements to proceed with a lower light intensity than classically possible [1]. An important frontier for this technology is in biological measurements, where photochemical interactions often disturb biological processes and can damage the specimen [2]. Here we report the first demonstration of biological measurement with precision surpassing the quantum noise limit [3]. This was enabled through the development of a new microscopy system which extended previous methods used to track the motion of highly reflective mirrors with non-classical light to measurements of microscopic particles with non-paraxial fields (see Fig. 1). Biological dynamics in the critical Hz-kHz frequency range were made accessible by applying a quantum optical lock-in technique for the first time. This straightforward technique allowed quantum enhancement over a frequency range which reached as low as the range reported for squeezed light sources developed for gravity wave interferometers [4].