Non-Resonant Two-Photon Transitions in Length and Velocity Gauges

Abstract

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 Schroedinger propagator under a 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(-epsilon * | t |)]. We include a pertinent discussion.

8 pages; RevTeX; published in Physical Review A with Editor's suggestion; second version of preprint matches equation numbering in the published article

References in corpus (5)

• Lamb Shift of Laser-Dressed Atomic States
• Nonrelativistic Limit of the Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung and Gravitational Spin-Orbit Coupling
• Relativistic and Radiative Corrections to the Mollow Spectrum
• Functional Form of the Imaginary Part of the Atomic Polarizability
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Cited by in corpus (2)

• Relativistic and Radiative Corrections to the Dynamic Stark Shift: Gauge Invariance and Transition Currents in the Velocity Gauge
• Gauge dependence of spontaneous radiation spectrum in a time-dependent relativistic non-perturbative Coulomb field