$\hat{p}\cdot \hat{A}$ vs $\hat{x}\cdot \hat{E}$: Gauge invariance in quantum optics

Nicholas Funai, Jorma Louko, Eduardo Martin-Martinez

We compare the predictions of the fundamentally motivated minimal coupling ($\hat{\mathbf{p}}\cdot \hat{\mathbf{A}}$) and the ubiquitous dipole coupling ($\hat{\boldsymbol{x…