Gauge invariance of the natural lineshape and dissipative dynamics of a two-level atom

TL;DR

This paper demonstrates that using gauge-invariant Hamiltonians in the Coulomb gauge yields correct natural lineshapes and dissipative dynamics for two-level atoms, emphasizing the importance of gauge consistency in quantum optical calculations.

Contribution

It shows that properly truncated gauge-invariant Hamiltonians in the Coulomb gauge produce accurate spectra and master equations, resolving gauge-dependence issues in two-level atom models.

Findings

Correct spectrum obtained with Coulomb gauge Hamiltonian

Master equation remains gauge-invariant under certain conditions

Highlights importance of gauge-invariant truncation in quantum optics

Abstract

The calculation of the natural lineshape of an excited two-level atom (TLA) has long been known to be gauge-dependent, with certain experiments in better agreement with the lineshape calculated with the dipole gauge. We show that by using a Coulomb gauge Hamiltonian truncated in a manner consistent with the gauge principle, the correct output spectrum can be obtained. For TLAs undergoing dynamics arising from additional Hamiltonian couplings, we also show that the master equation is gauge-invariant under the same conditions of validity as the Born-Markov approximation, despite different gauges having different spectral densities. These results highlight the importance of using correctly truncated gauge-invariant Hamiltonians in input-output theory for accurate frequency-dependent spectra, even in weak coupling regimes.