TY - JOUR
T1 - Observing the Quantum Wave Nature of Free Electrons through Spontaneous Emission
AU - Remez, Roei
AU - Karnieli, Aviv
AU - Trajtenberg-Mills, Sivan
AU - Shapira, Niv
AU - Kaminer, Ido
AU - Lereah, Yossi
AU - Arie, Ady
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/8/6
Y1 - 2019/8/6
N2 - We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.
AB - We investigate, both experimentally and theoretically, the interpretation of the free-electron wave function using spontaneous emission. We use a transversely wide single-electron wave function to describe the spatial extent of transverse coherence of an electron beam in a standard transmission electron microscope. When the electron beam passes next to a metallic grating, spontaneous Smith-Purcell radiation is emitted. We then examine the effect of the electron wave function transversal size on the emitted radiation. Two interpretations widely used in the literature are considered: (1) radiation by a continuous current density attributed to the quantum probability current, equivalent to the spreading of the electron charge continuously over space; and (2) interpreting the square modulus of the wave function as a probability distribution of finding a point particle at a certain location, wherein the electron charge is always localized in space. We discuss how these two interpretations give contradictory predictions for the radiation pattern in our experiment, comparing the emission from narrow and wide wave functions with respect to the emitted radiation's wavelength. Matching our experiment with a new quantum-electrodynamics derivation, we conclude that the measurements can be explained by the probability distribution approach wherein the electron interacts with the grating as a classical point charge. Our findings clarify the transition between the classical and quantum regimes and shed light on the mechanisms that take part in general light-matter interactions.
UR - http://www.scopus.com/inward/record.url?scp=85070567627&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.123.060401
DO - 10.1103/PhysRevLett.123.060401
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AN - SCOPUS:85070567627
SN - 0031-9007
VL - 123
JO - Physical Review Letters
JF - Physical Review Letters
IS - 6
M1 - 060401
ER -