P · Â vs x · Ê: Gauge invariance in quantum optics and quantum field theory

Funai, Nicholas; Louko, Jorma; Martin-Martinez, Eduardo

Abstract

We compare the predictions of the fundamentally motivated minimal coupling (^p⋅^A) and the ubiquitous dipole coupling (^x⋅^E) in the light-matter interaction. By studying the light-matter interaction for hydrogenlike atoms we find that the dipole approximation cannot be a priori justified to analyze the physics of vacuum excitations (a very important phenomenon in relativistic quantum information) since a dominant wavelength is absent in those problems, no matter how small (as compared to any frequency scale) the atom is. Remarkably, we show that the dipole approximation in those regimes can still be valid as long as the interaction time is longer than the light-crossing time of the atoms, which is a very reasonable assumption. We also highlight some of the subtleties that one has to be careful with when working with the explicitly gauge noninvariant nature of the minimal coupling, and we compare it with the explicitly gauge invariant dipole coupling.

Citation

Funai, N., Louko, J., & Martin-Martinez, E. (2019). P · Â vs x · Ê: Gauge invariance in quantum optics and quantum field theory. Physical Review D, 99(6), Article 065014. https://doi.org/10.1103/physrevd.99.065014

• Journal Article Type: Article
• Acceptance Date: Feb 28, 2019
• Online Publication Date: Mar 26, 2019
• Publication Date: Mar 15, 2019
• Deposit Date: Aug 22, 2019
• Publicly Available Date: Aug 28, 2019
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 99
• Issue: 6
• Article Number: 065014
• DOI: https://doi.org/10.1103/physrevd.99.065014
• Keywords: Quantum Physics; High Energy Physics - Theory
• Public URL: https://nottingham-repository.worktribe.com/output/2460630
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.99.065014