Two-level system in a bichromatic field

Abstract

The behavior of a two-level system interacting with a bichromatic classical field is studied. Analytic expressions are found for the Green's-function operator for the system if the field is weak and near resonance, and a systematic procedure is developed to obtain the Green's-function operator in a more general case. The results are used to calculate the probability of a transition from the lower to the upper state; resonance conditions occur when the level spacing of the system, ${\ensuremath{\omega}}_{ba}$, is near $n{\ensuremath{\omega}}_{\ensuremath{\lambda}}\ensuremath{-}(n\ensuremath{-}1){\ensuremath{\omega}}_{\ensuremath{\mu}}$, where $n$ is a positive or negative integer, and ${\ensuremath{\omega}}_{\ensuremath{\lambda}}$ and ${\ensuremath{\omega}}_{\ensuremath{\mu}}$ are the frequencies of the components of the field. The resonance frequency depends on the intensity of the field components. In addition, the cross section for scattering photons out of the field has been calculated. It is found that the spectrum of the scattered radiation consists of lines at frequency ${\ensuremath{\omega}}_{k}={\ensuremath{\omega}}_{\ensuremath{\mu}},{\ensuremath{\omega}}_{\ensuremath{\lambda}}$, and odd harmonics of these, combinations of the fundamental and the harmonics with $\ensuremath{\Delta}={\ensuremath{\omega}}_{\ensuremath{\lambda}}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\mu}}$, and satellites shifted from all of these features by an amount which depends on the intensity of the field and ${\ensuremath{\omega}}_{ba}$. The cross section is intensity dependent particularly insofar as the location of resonance peaks is concerned. It is suggested that this effect may be exploited in transferring intensity modulation of one component of the field to phase modulation in the other component.