We　propose　a　protocol　for　detecting　a　single　atom　in　a　cavity　with　the　help　of　the　chi((2))　nonlinear　medium.　When　the　chi((2))　nonlinear　medium　is　driven　by　an　external　laser　field,　the　cavity　mode　will　be　squeezed,　and　thus　one　can　obtain　an　exponentially　enhanced　light-matter　coupling.　Such　a　strong　coupling　between　the　atom　and　the　cavity　field　can　significantly　change　the　output　photon　flux,　the　quantum　fluctuations,　the　quantum　statistical　property,　and　the　photon　number　distributions　of　the　cavity　field.　This　provides　practical　strategies　to　determine　the　presence　or　absence　of　an　atom　in　a　cavity.　The　proposed　protocol　exhibits　some　advantages,　such　as　controllable　squeezing　strength　and　exponential　increase　of　atom-cavity　coupling　strength,　which　make　the　experimental　phenomenon　more　obvious.　We　hope　that　this　protocol　can　supplement　the　existing　intracavity　single-atom　detection　protocols　and　provide　a　promise　for　quantum　sensing　in　different　quantum　systems.