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arXiv:1510.05946 · Ultramicroscopy

Designs for a quantum electron microscope

P. Kruit, Richard G. Hobbs, Chung-Soo Kim, Yujia Yang, Vitor R. Manfrinato, J. Hammer, S. Thomas, P. Weber, Brannon B. Klopfer, Christoph Kohstall, Thomas Juffmann, Mark A. Kasevich, Peter Hommelhoff, Karl K. Berggren

Published Mar 9, 2016• 161 citations

Abstract

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.

DOI: 10.1016/j.ultramic.2016.03.004

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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.

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.

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.

Free electrons provide a powerful tool for probing material properties at atomic resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free-electron wave functions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron microscopes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel concept that leverages free electrons that are coherently shaped by laser pulses to measure quantum coherence in materials. We develop the quantum theory of interactions between shaped electrons and arbitrary qubit states in materials, and show how the postinteraction electron energy spectrum enables measuring the qubit state (on the Bloch sphere) and the decoherence or relaxation times (T_{2}/T_{1}). Finally, we describe how such electrons can detect and quantify superradiance from multiple qubits. Our scheme can be implemented in ultrafast transmission electron microscopes (UTEM), opening the way toward the full characterization of the state of quantum systems at atomic resolution.