don't put carpet directly on concrete.. you're asking for moisture problems.
And as was stated, it is NOT efflorescence, that is leaching of minerals, "typically" only found in brick that wasn't sealed.
You have to put a vapor barrier down and some sort of padding. The cool floor coupled with the warm air is causing condensation on the carpet which is causing mold. Plus the concrete actually is a bit porous to moisture - so that doesn't help.