Non-relativistic limit in the 2+1 Dirac Oscillator: A Ramsey Interferometry Effect

Abstract

We study the non-relativistic limit of a paradigmatic model in Relativistic Quantum Mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a novel kind of Zitterbewegung which persists in this non-relativistic regime, and leads to an observable deformation of the particle orbit. This effect can be interpreted in terms of a Ramsey Interferometric phenomenon, allowing an insightful connection between Relativistic Quantum Mechanics and Quantum Optics. Furthermore, subsequent corrections to the non-relativistic limit, which account for the usual spin-orbit Zitterbewegung, can be neatly understood in terms of a Mach-Zehnder interferometer.

RevTex4 file, color figures, submitted for publication

References in corpus (4)

• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Exact solution of the two-dimensional Dirac oscillator
• The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model
• Spin-Orbit Pendulum: the Microscopic Stern-Gerlach Effect

Cited by in corpus (30)

• Zitterbewegung of electrons in graphene in a magnetic field
• On the Klein-Gordon oscillator subject to a Coulomb-type potential
• Theory of electron Zitterbewegung in graphene probed by femtosecond laser pulses
• On the interaction of the Dirac oscillator with the Aharonov-Casher system in topological defect backgrounds
• Rotating effects on the Dirac oscillator in the cosmic string spacetime
• Noninertial effects on the Dirac oscillator in a topological defect spacetime
• On a relativistic scalar particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential
• Dirac ocillator in the cosmic string spacetime in the context of gravity's rainbow
• Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background
• Atomic Zitterbewegung
• Photonic realization of the relativistic Dirac oscillator
• Quantum Magnetism of Spin-Ladder Compounds with Trapped-Ion Crystals
• Quantum phase transitions in the noncommutative Dirac Oscillator
• On an atom with a magnetic quadrupole moment subject to harmonic and linear confining potentials
• Remarks on the Dirac oscillator in $(2+1)$ dimensions
• The 2D $\kappa$-Dirac oscillator
• Quantum phase transitions of the Dirac oscillator in a minimal length scenario
• Thermodynamics of Quantum Phase Transitions of a Dirac oscillator in a homogenous magnetic field
• Gate-Tunable Graphene Quantum Dot and Dirac Oscillator
• Zitterbewegung of electrons in quantum wells and dots in presence of an in-plane magnetic field
• A Lorentz Invariant Pairing Mechanism: Relativistic Cooper Pairs
• Photonic realization of the deformed Dirac equation via the segmented graphene nanoribbons under inhomogeneous strain
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Zitterbewegung (trembling motion) of electrons in narrow gap semiconductors
• Mapping of the 2+1 q-deformed Dirac oscillator onto the q-deformed Jaynes-Cummings model: It's non-relativistic limit and Zitterbewegung effect
• Effect of internal magnetic flux on a relativistic spin-1 oscillator in the spinning point source-generated spacetime
• Photonic realization of the kappa-deformed Dirac equation
• Quantum phase transitions of the Dirac oscillator in the Anti-Snyder model
• Travelling to exotic places with cavity QED systems
• Canonical quantization of the Dirac oscillator field in (1+1) and (3+1) dimensions