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arXiv:1808.03363 · Physical Review A

Efficient two-port electron beam splitter via a quantum interaction-free measurement

Yujia Yang, Chung-Soo Kim, Richard G. Hobbs, Pieter Kruit, Karl K. Berggren

Published Oct 17, 2018• 11 citations
arXivHTMLPDF

Abstract

Semitransparent mirrors are standard elements in light optics for splitting light beams or creating two versions of the same image. Such mirrors do not exist in electron optics, although they could be beneficial in existing techniques such as electron interferometry and holography and could enable alternative electron imaging and spectroscopy techniques. We propose a design for an electron beam splitter using the concept of quantum interaction-free measurement (IFM). The design combines an electron resonator with a weak phase grating. Fast switching gates allow electrons to enter and exit the resonator. While in the resonator, the phase grating transfers intensity from the direct beam into one of the weakly diffracted beams at each pass. To make the beam splitter an efficient two-port splitter, the intensity in all other diffracted beams is blocked by an aperture. The IFM principle minimizes the loss of total intensity by this aperture. We use a scattering matrix method to analyze the performance of the beam splitter, including the effects of inelastic scattering in the phase grating. This design can be generalized to beam splitters for not only electrons, but also photons, neutrons, atoms, and other quantum mechanical systems.

DOI
10.1103/physreva.98.043621

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Semitransparent mirrors are standard elements in light optics for splitting light beams or creating two versions of the same image. Such mirrors do not exist in electron optics, although they could be beneficial in existing techniques such as electron interferometry and holography and could enable alternative electron imaging and spectroscopy techniques. We propose a design for an electron beam splitter using the concept of quantum interaction-free measurement (IFM). The design combines an electron resonator with a weak phase grating. Fast switching gates allow electrons to enter and exit the resonator. While in the resonator, the phase grating transfers intensity from the direct beam into one of the weakly diffracted beams at each pass. To make the beam splitter an efficient two-port splitter, the intensity in all other diffracted beams is blocked by an aperture. The IFM principle minimizes the loss of total intensity by this aperture. We use a scattering matrix method to analyze the performance of the beam splitter, including the effects of inelastic scattering in the phase grating. This design can be generalized to beam splitters for not only electrons, but also photons, neutrons, atoms, and other quantum mechanical systems.
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.
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Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.
In this paper, we study the quantum computation realized by an interaction-free measurement (IFM). Using the interferometer of Kwiat et al., we construct a two-qubit quantum gate that changes one particle's trajectory according to whether or not the other particle exists in the interferometer. We propose a method for distinguishing Bell-basis vectors, each of which consists of a pair of an electron and a positron, by this gate. (This is called the Bell-basis measurement.) This method succeeds with probability 111 in the limit of $N\ensuremath{\rightarrow}\ensuremath{\infty}$, where NNN is the number of beam splitters in the interferometer. Moreover, we can carry out a controlled-NOT gate operation by the above Bell-basis measurement and the method proposed by Gottesman and Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM. This means that we can execute any quantum algorithm by the IFM.
The state of the quantum system will inevitably be disturbed and changed in the testing process. Using interaction-free measurement (IFM), the information can be extracted without any interaction between objects and photons or particles. Here we present a novel approach that the refractive index can be measured accurately with "no-touch" measurement between testing materials and light beam. The design system is a non-traditional model of interaction-free measurement with an unbalanced Mach-Zehnder interferometer (UMZI), which is combined with the chain quantum Zeno effect and the technique for spatial separation of light field. We select two beams with different intensity distribution in cross-section and different frequency as the transmission source, and the refractive index of samples can be obtained from the contrast degree of two beams under the condition of a few beam splitters existing. The scheme could prevent the damage to the radiation-sensitive optical materials, and provide a new idea for the research and application of precision measurement.
The quantum properties of matter and radiation can be leveraged to surpass classical limits of sensing and detection. Quantum optics does so by creating and measuring nonclassical light. However, better performance requires higher photon-number states, which are challenging to generate and detect. Here, we combine photons and free electrons to solve the problem of generating and detecting high-number states well beyond those reachable with light alone and further show that an unprecedented level of sensitivity and resolution is gained based on the measurement of free-electron currents after suitably designed electron-light interactions. Our enabling ingredient is the strong electron-light coupling produced by aloof electron reflection on an optical waveguide, leading to the emission or absorption of a high number of guided photons by every single electron. We establish through rigorous theory that, by combining electron-beam splitters with two electron-waveguide interactions, the sensitivity to detect optical-phase changes can be enhanced dramatically using currently attainable technology. These results inaugurate a disruptive quantum technology relying on free electrons and their strong interaction with waveguided light.