Gouy Phase for Relativistic Quantum Particles

Abstract

Recently Gouy rotation was observed with focused non-relativistic electron vortex beams. If the electrons in vortex beams are very fast we have to take into account relativistic effects to completely describe the Gouy phase on them. Exact Hermite-Gaussian solutions to the Klein-Gordon equation for particle beams are obtained here that make explicit the 4-position of the focal point of the beam. These are Bateman-Hillion solutions with modified phase factors to take into account the rest mass of the particles. They enable a relativistic expression for the Gouy phase to be determined. It is in fact shown all the solutions are form invariant under Lorentz transformations. It is further shown for the exact solutions to correspond to those of the Schrödinger equation the relative time between the focal point and any point in the beam must be constrained to be a specific function of the relative spatial coordinates.

4 pages

References in corpus (6)

• Atomic scale electron vortices for nanoresearch
• Colliding particles carrying non-zero orbital angular momentum
• Imaging the dynamics of free-electron Landau states
• Reciprocal relativity of noninertial frames and the quaplectic group
• A Raman Waveplate for Spinor BECs
• Zitterbewegung of Klein-Gordon particles and its simulation by classical systems

Cited by in corpus (8)

• Observation of the quantum Gouy phase
• Gouy phase in non-classical paths in triple-slit interference experiment
• Fractional Angular Momenta, Gouy and Berry phases in Relativistic Bateman-Hillion-Gaussian Beams of Electrons
• Poisson's spot and Gouy phase
• Gouy phase of type-I SPDC-generated biphotons
• Biphoton phase-space correlations from Gouy-phase measurements using double slits
• Lorentz Covariant Quantum 4-Potential and Orbital Angular Momentum for the Transverse Confinement of Matter Waves
• Paraxial Dirac equation