Four-wave mixing in potassium vapor with an off-resonant double- Λ system

Abstract

We investigate both theoretically and experimentally four-wave mixing (FWM) in hot potassium vapor, generated by a copropagating pump and probe in an off-resonant double-$\mathrm{\ensuremath{\Lambda}}$ system, and present conditions when this atomic system is (1) a strong phase-insensitive parametric amplifier and (2) a source of large-amplitude squeezing. Theoretically, nonperturbative numerical calculations of optical Bloch-Maxwell equations have been solved for a four-level atomic system of K in order to derive the atomic polarization and then amplitudes of propagating optical waves, pump, probe, and conjugate. For potassium, to our knowledge, there are no such comparisons of theoretical and experimental results of gains of twin beams under the large range of FWM parameters as presented here. Results have shown that one-photon detuning has to be slightly larger than the Doppler broadened transition for large gains and strong squeezing. The gain is particularly large for small red two-photon detuning ($\ensuremath{-}2--6\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$) and high K density ($5.5--10\ifmmode\times\else\texttimes\fi{}{10}^{12}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$). Following experimentally and theoretically determined relation between gains, probe transmissions, and squeezing in Rb and Cs, we have found parameters of FWM when maximum squeezing in hot K vapor is expected.