Unifying the p⋅A and d⋅E interactions in photodetector theory

A new technique is introduced in which a canonical transformation is used to transform the atom-radiation Hamiltonian to one without counter-rotating terms. As well as allowing an exact treatment of a one-mode dipole-coupled photodetection model, the theory predicts the existence of squeezing induced by the detector coupling. A feature of the canonical transformation used here is that the resulting interaction Hamiltonian has a symmetric combination of the p⋅A and d⋅E interactions. This allows the resolution of long-standing questions about the correct interaction Hamiltonian to use in photodetector theory. The new theory is able to handle dipole-coupled radiative transitions over ultrafast time scales of the order of a single oscillation period, where the rotating-wave approximation is invalid. The coupling of the detector to the radiation field is predicted to vary as $f^{\mathrm{-}1/2}$ at high frequencies, and as $f^{+1/2\mathrm{}}$ at low frequencies.