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arXiv:1102.4691 · Physical Review A

Possible use of a Cooper-pair box for low-dose electron microscopy

Hiroshi Okamoto

Published Apr 9, 2012• 25 citations
arXivHTMLPDF

Abstract

A transmission electron microscope that takes advantage of superconducting quantum circuitry is proposed. The microscope is designed to improve the image contrast of radiation-sensitive weak-phase objects, in particular, biological specimens. The objective in this setting is to measure the phase shift of the probe electron wave to a precision \ensuremath{\Delta}\ensuremath{\theta} within the number of electrons $N$ that does not destroy the specimen. In conventional electron microscopy \ensuremath{\Delta}\ensuremath{\theta} scales as \ensuremath{\sim}1/${N}^{1/2}$, which falls short of the Heisenberg limit \ensuremath{\sim}1/$N$. To approach the latter by using quantum entanglement, we propose a design that involves a Cooper-pair box placed on the surface of an electrostatic electron mirror in the microscope. Significant improvement could be attained if inelastic scattering processes are sufficiently delocalized.

DOI
10.1103/physreva.85.043810

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A transmission electron microscope that takes advantage of superconducting quantum circuitry is proposed. The microscope is designed to improve the image contrast of radiation-sensitive weak-phase objects, in particular, biological specimens. The objective in this setting is to measure the phase shift of the probe electron wave to a precision \ensuremath{\Delta}\ensuremath{\theta} within the number of electrons NNN that does not destroy the specimen. In conventional electron microscopy \ensuremath{\Delta}\ensuremath{\theta} scales as \ensuremath{\sim}1/N1/2{N}^{1/2}N1/2, which falls short of the Heisenberg limit \ensuremath{\sim}1/NNN. To approach the latter by using quantum entanglement, we propose a design that involves a Cooper-pair box placed on the surface of an electrostatic electron mirror in the microscope. Significant improvement could be attained if inelastic scattering processes are sufficiently delocalized.
A notorious problem in high-resolution biological electron microscopy is radiation damage caused by probe electrons. Hence, acquisition of data with minimal number of electrons is of critical importance. Quantum approaches may represent the only way to improve the resolution in this context, but all proposed schemes to date demand delicate control of the electron beam in highly unconventional electron optics. Here we propose a scheme that involves a flux qubit based on a radio-frequency superconducting quantum interference device, inserted in a transmission electron microscope. The scheme significantly improves the prospect of realizing a quantum-enhanced electron microscope for radiation-sensitive specimens.
We show that quantum computational imaging is advantageous in the setting of low-dose electron microscopy of beam-sensitive specimens. Two qudits placed near the electron beam enable full transfer of quantum information between the electron microscope and a quantum computer in the proposed scheme, providing the specimen is a phase object. We present a quantum algorithm that identifies the correct image among n candidate images, where n is larger than the effective dimension of the Hilbert space of the imaging electron.
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.
One of the astounding consequences of quantum mechanics is that it allows the detection of a target using an incident probe, with only a low probability of interaction of the probe and the target. This 'quantum weirdness' could be applied in the field of electron microscopy to generate images of beam-sensitive specimens with substantially reduced damage to the specimen. A reduction of beam-induced damage to specimens is especially of great importance if it can enable imaging of biological specimens with atomic resolution. Following a recent suggestion that interaction-free measurements are possible with electrons, we now analyze the difficulties of actually building an atomic resolution interaction-free electron microscope, or "quantum electron microscope". A quantum electron microscope would require a number of unique components not found in conventional transmission electron microscopes. These components include a coherent electron beam-splitter or two-state-coupler, and a resonator structure to allow each electron to interrogate the specimen multiple times, thus supporting high success probabilities for interaction-free detection of the specimen. Different system designs are presented here, which are based on four different choices of two-state-couplers: a thin crystal, a grating mirror, a standing light wave and an electro-dynamical pseudopotential. Challenges for the detailed electron optical design are identified as future directions for development. While it is concluded that it should be possible to build an atomic resolution quantum electron microscope, we have also identified a number of hurdles to the development of such a microscope and further theoretical investigations that will be required to enable a complete interpretation of the images produced by such a microscope.
We propose a simple design of a quantum electron microscope that ``queries'' a beam-sensitive phase object, such as a biological specimen, as part of quantum computation. Lower quantum query complexity, not the time complexity, of a quantum algorithm means less specimen damage, which translates to more data extracted from the specimen. Hence small-scale quantum computing offers provable quantum advantage in this context. A possible application of the proposed microscope is the Grover search for a true structure, out of a set of candidate structures.
In electron microscopy, the pursuit of atomic-scale resolution for imaging biological [1] samples and soft-matter systems [2] is perpetually constrained by beam-induced sample degredation. While classical approaches attempt to optimize the trade-off between dose efficiency and image quality, they remain fundamentally limited by the physical interactions between electrons and the sample. Quantum technologies, however, present a transformative opportunity by enhancing information extraction per electron without increasing exposure [3], thereby breaking through classical constraints. In this work, we integrate for the first time a trapped-ion qubit into a transmission electron microscope, leveraging the strong Coulomb interaction between swift electrons and Ca⁺ ions [4], along with the precise control and readout capabilities of trapped Ca⁺ ions [5]. By harnessing quantum coherence and controlled interactions, this hybrid approach seeks to advance the capabilities of low-dose imaging, improving the analysis of radiation-sensitive samples while minimizing damage. For this purpose, we customize a transmission electron microscope to provide the required ultra-high-vacuum integrity and adapt the Ca⁺ trap design, including laser cooling and state readout/manipulation, to the geometric constraints of the microscope’s pole-piece gap.