We reexamine the invariance of two-photon transition matrix elements and corresponding two-photon Rabi frequencies under the "gauge" transformation from the length to the velocity gauge. It is shown that gauge invariance, in the most general sense, only holds at exact resonance, for both one-color as well as two-color absorption. The arguments leading to this conclusion are supported by analytic calculations which express the matrix elements in terms of hypergeometric functions, and ramified by a "master identity" which is fulfilled by off-diagonal matrix elements of the Schrödinger propagator under the transformation from the velocity to the length gauge. The study of the gauge dependence of atomic processes highlights subtle connections between the concept of asymptotic states, the gauge transformation of the wave function, and infinitesimal damping parameters for perturbations and interaction Hamiltonians that switch off the terms in the infinite past and future [of the form exp(-ε|t|)]. We include a pertinent discussion.




This research has been supported by the National Science Foundation (Grant PHY-1403973).

Keywords and Phrases

Hamiltonians; Photons; Wave functions, Analytic calculations; Asymptotic state; Damping parameters; Gauge invariance; Gauge transformation; Hypergeometric functions; Off-diagonal matrix elements; Two-photon transitions, Linear transformations

International Standard Serial Number (ISSN)

2469-9926; 2469-9934

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2016 American Physical Society (APS), All rights reserved.

Publication Date

01 Aug 2016

Included in

Physics Commons