Quantum Čerenkov Radiation: Spectral Cutoffs and the Role of Spin and Orbital Angular Momentum

Abstract

We show that the well-known Čerenkov effect contains new phenomena arising from the quantum nature of charged particles. The Čerenkov transition amplitudes allow coupling between the charged particle and the emitted photon through their orbital angular momentum and spin, by scattering into preferred angles and polarizations. Importantly, the spectral response reveals a discontinuity immediately below a frequency cutoff that can occur in the optical region. Near this cutoff, the intensity of the conventional Čerenkov radiation (ČR) is very small but still finite, while our quantum calculation predicts exactly zero intensity above the cutoff. Below that cutoff, with proper shaping of electron beams (ebeams), we predict that the traditional ČR angle splits into two distinctive cones of photonic shockwaves. One of the shockwaves can move along a backward cone, otherwise considered impossible for conventional ČR in ordinary matter. Our findings are observable for ebeams with realistic parameters, offering new applications including novel quantum optics sources, and opening a new realm for Čerenkov detectors involving the spin and orbital angular momentum of charged particles.

Quantum calculation of the Vavilov-Cherenkov radiation by twisted electrons

“…Although the quantum theory of Vavilov-Cherenkov radiation was worked out more than half a century ago, new theoretical publications on this topic still appear, see for example the very recent papers [10,11]. These works are in part driven by new experimental achievements which make it possible to observe and investigate the V-Ch radiation under unusual circumstances.…”

“…[12], vortex electron beams were experimentally demonstrated [13,14] and a number of remarkable effects they produce was investigated [15]. Electromagnetic radiation of vortex electrons has not yet been investigated experimentally, but theoretical works suggest that it should display interesting effects in transition radiation [16,17] and Vavilov-Cherenkov radiation [10].…”

“…We undertook this study despite there exists a very recent publication [10] on the same topic, because we were not fully satisfied with its results and presentation. First, the formalism itself presented in the Supplementary materials of Ref.…”

“…First, the formalism itself presented in the Supplementary materials of Ref. [10] is very far from optimal and obscures the physics. In the present paper, we develop a much more concise, convenient, and physically transparent formalism, based on the standard technology of helicity amplitude calculation and on the exact description of vortex electrons.…”

“…[10]. We also describe new effects produced by radiating vortex electrons, namely, the diagnostic power of the V-Ch radiation from vortex state superpositions, the spiraling pattern of the radiation of such electrons in the longitudinal magnetic fields, and the peculiar phenomenon of V-Ch light concentration along the forward direction under an appropriate parameter choice.…”