Imaging the dynamics of free-electron Landau states

Abstract

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum-Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the first real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometer-size electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor, and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.

10 pages, 4 figures

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• Transmission of vortex electrons through a solenoid
• Experimental Realisation of a π/2 Vortex Mode Converter for Electrons Using a Spherical Aberration Corrector
• Energy loss spectroscopy of Buckminster C60 with twisted electrons: Influence of orbital angular momentum transfer on plasmon generation
• Theoretical and practical aspects of the design and production of synthetic holograms for transmission electron microscopy
• Revisiting the compatibility problem between the gauge principle and the observability of the canonical orbital angular momentum in the Landau problem
• Singularities and internal rotational dynamics of electron beams
• Gouy phase and quantum interference with cross-Wigner functions for matter-waves
• Nonstationary Laguerre-Gaussian states in magnetic field
• Poisson's spot and Gouy phase
• Gouy phase of type-I SPDC-generated biphotons
• A quantum logic gate for free electrons
• Universal Analytic Solution for the Quantum Transport of Structured Matter-Waves in Magnetic Optics
• Biphoton phase-space correlations from Gouy-phase measurements using double slits
• Measuring an electron beam's orbital angular momentum spectrum
• Geometry-Enabled Radiation from Structured Paraxial Electrons
• Radiation of breathing vortex electron packets in magnetic field
• Time-diffracting 2D wave vortices
• Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime