TY - JOUR

T1 - Vavilov-Cherenkov emission with twisted electrons: A study of the final entangled state

AU - Chaikovskaia, A. D.

AU - Karlovets, D. V.

AU - Serbo, V. G.

N1 - We are thankful to I. Ivanov for useful discussions. The studies in Sec. are supported by the Russian Science Foundation (Project No. 21-42-04412 ). The studies in Sec. are supported by the Government of the Russian Federation through the ITMO Fellowship and Professorship Program. The studies in Sec. are supported by the Russian Science Foundation (Project No. 23-62-10026 ). The studies in Sec. are supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement No. 075-15-2021-1349).

PY - 2024/1

Y1 - 2024/1

N2 - We present a theoretical investigation of Vavilov-Cherenkov (VC) radiation by a plane wave or twisted electron. Special emphasis is put on the question of whether and at what conditions the emitted VC photons can be twisted. For this aim we obtain a general expression in the coordinate and momentum representations for the quantum state of the final electron-photon system that is a result of the radiation process itself and does not depend on the properties of a detector. It is shown that this evolved state is an entangled state of an electron and a photon, and both particles can be twisted. A direct consequence of this result follows: if one uses a detector sensitive to the twisted electron (photon) with the definite projection of the total angular momentum (TAM), then the final photon (electron) also will be in the twisted state with a definite TAM projection. Further, we investigate the polarization properties of the final twisted photon in more general conditions than have been calculated before. Finally, we exploit a close similarity between the discussed VC radiation and the process of the equivalent photon emission in the Weizsäcker-Williams method and find the corresponding final state.

AB - We present a theoretical investigation of Vavilov-Cherenkov (VC) radiation by a plane wave or twisted electron. Special emphasis is put on the question of whether and at what conditions the emitted VC photons can be twisted. For this aim we obtain a general expression in the coordinate and momentum representations for the quantum state of the final electron-photon system that is a result of the radiation process itself and does not depend on the properties of a detector. It is shown that this evolved state is an entangled state of an electron and a photon, and both particles can be twisted. A direct consequence of this result follows: if one uses a detector sensitive to the twisted electron (photon) with the definite projection of the total angular momentum (TAM), then the final photon (electron) also will be in the twisted state with a definite TAM projection. Further, we investigate the polarization properties of the final twisted photon in more general conditions than have been calculated before. Finally, we exploit a close similarity between the discussed VC radiation and the process of the equivalent photon emission in the Weizsäcker-Williams method and find the corresponding final state.

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85184025340&origin=inward&txGid=d1ac993224ca15d2e065b5270501dcb2

UR - https://www.mendeley.com/catalogue/e60562e3-1b95-33f4-8b7f-098464e72030/

U2 - 10.1103/PhysRevA.109.012222

DO - 10.1103/PhysRevA.109.012222

M3 - Article

VL - 109

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 012222

ER -