Magnetoplasmon Engineering in Microchannel-Confined Electrons on Helium: Edge Modes, Derivation of Spectra, and Quantitative Coherence Analysis

Abstract

We present a comprehensive theoretical framework for engineering magnetoplasmons in microchannel-confined electrons on superfluid helium under perpendicular magnetic field control. By extending established magnetoplasmon theory to realistic confined geometries, we rigorously derive the dispersion relations incorporating finite-size effects, smooth electrostatic boundary conditions, and the exact Coulomb kernel for channel geometry. Applied magnetic fields transform gapless plasmons into structured magnetoplasmon spectra with tunable frequencies spanning 5–40 GHz. We specifically address the nature of edge magnetoplasmons in the non-degenerate regime characteristic of electrons on helium, distinguishing them from their semiconductor counterparts through the analysis of soft-wall confinement potentials. Our quantitative decoherence analysis explicitly defines the coupling to the electromagnetic environment and evaluates five primary damping channels. We show that while environmental coupling dominates (\(T_2=2.1\)–35 \(\mu \)s), optimized impedance engineering can enhance coherence times toward the intrinsic limit (\({\sim }100~\mu \)s), establishing a robust foundation for collective-mode quantum devices.