Interaction-Free Measurement with Electrons

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 $14\pm 1\%$. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.

Figure 1

Schematic of an optical Mach-Zehnder interferometer (a),(b) juxtaposed with the electron two-grating interferometer (c). The first two schematics (a),(b) illustrate the effect of an opaque sample on the output of a Mach-Zehnder interferometer.

Figure 2

Schematic of an electron two-grating interferometer in a TEM (not to scale) with the object removed (a) and inserted (b), overlayed with ray diagrams. The detector coloring illustrates the selectable regions on the camera that define the bright and dark output ports. The interferometer relies on nanofabricated diffraction gratings as beam splitters, both blazed (c),(d) and binary (e),(f). The full gratings (i) and capped cross sections (ii) are shown; the red lines highlight the profiles muddled by the platinum cap. All scale bars represent 400 nm. (d),(f) Raw images of the diffracted outputs of the two gratings used in the interferometer and their diffraction efficiencies below. The two-path interferometer is constructed by inserting an aperture, as shown in (d).

Figure 3

Simulated (a),(b) and experimental (c),(d) output diffraction profiles of a two-grating interferometer as the second grating is moved relative to the projection of the top grating. The relative grating shift is reported as a fraction of the blazed grating pitch, $\delta x_2/p_1$. The left column (a),(c) shows the output currents for the object removed—the two-path case. The right column (b),(d) shows the output currents for the object inserted—the one-path case. The colored regions on the left illustrate the defined dark port (pink) and bright port (gray) regions of the detector. The dashed pink line illustrates an interaction-free measurement alignment. All values are normalized to the maximum pixel current in the two-path case. (e) The normalized dark port current as a function of the relative grating shift. (f) The experimental diffraction profile along the dashed pink line with the dark port highlighted.

Figure 4

Normalized output currents of a properly aligned two-grating interferometer with the object (a) removed and (b) inserted. The top row contains raw images of the interaction plane with a mock aperture to illustrate the object’s position. The bar chart displays the DP, BP, and total (Tot) current in each configuration, normalized to the maximum output of the two-path configuration [Tot in (a)]. The light gray bars show the expected outputs from simulation. The error bars are the standard deviation of multiple measurements in distinct alignments.