Quantum electrodynamics with one degree of freedom for the photon field

S. A. Brown

Sergei V Prants

Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. We show that, even in the absence of any other interaction with environment, the interaction of the purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics. Atomic fractals with self-similar intermittency of smooth and unresolved structures are found in the exit-time scattering function. Tiny interplay between all the degrees of freedom is responsible for dynamical trapping of atoms even in a very short microcavity. Gedanken experiments are proposed to detect manifestations of atomic fractals in cavity quantum electrodynamics.

V.I. Ogievetskii, I.V. Polubarinov

L. R. Ram‐Mohan

Abstract Any discussion of electromagnetic field calculations requires the addressing of the gauge degree of freedom. The velocity-dependent potential and its inclusion in quantum calculations in the presence of electromagnetic fields has to account for the so-called gauge degree of freedom in electrodynamics. The origin of this degree of freedom and its application in the Aharonov-Bohm effect are elaborated on in detail. The gauge variational procedure leads to the determination of the conserved current in quantum mechanical applications.

Vladilen S Letokhov

C. Baxter

The minimal-coupling Hamiltonian for a nonrelativistic hydrogenic atom interacting with a photon field in the \ensuremath{\alpha}-Lorentz gauge is canonically gauge transformed to one with four arbitrary degrees of gauge freedom. The theory, nonrelativistic in the charge dynamics, is wholly covariant in its treatment of the scalar, transverse, and longitudinal electromagnetic fields. One degree of gauge freedom of the transformed Hamiltonian comes from the arbitrary scalar parameter contained within the \ensuremath{\alpha}-Lorentz gauge, while the others come from arbitrary parameters governing the gauge transformation. A Jaynes-Cummings-type model is constructed by suitable restrictions to the gauge freedom, and found to display an admixture of transverse and scalar interactions but no longitudinal component. The model gives the Lamb shift, correct to the second order of the electronic charge consistent with relativistic quantum electrodynamics.