Quantum effects in four-wave mixing in a cavity

Abstract

The four-wave-mixing signal at $2{\ensuremath{\omega}}_{1}\ensuremath{-}{\ensuremath{\omega}}_{2}$ from a collective system of $N$ two-level atoms dissipating through spontaneous emission and dephasing and driven by weak external fields of frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}$ in a cavity of arbitrary $Q$ is found by evaluating exactly the susceptibility ${\ensuremath{\chi}}^{(3)}({\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{1},\ensuremath{-}{\ensuremath{\omega}}_{2})$. The exact results show that the customarily employed secular approximation for treating the problem of a strongly coupled atom-cavity system is hopelessly inadequate for describing the process of four-wave mixing.