Jet backpack

What is the smallest jet engine that has been built and what is its
power?  Can the engines be mounted onto a backpack with fuel and
controls?  I have a rough sketch of how it is to be done but I would
like to know if it is practical and whether it will work.  I would be
glad if someone could suggest a few ideas on how to go about it.  I know
that NASA has built a few of these jetpacks for use on earth.  They
could propel a person upto 12 metres in the air.  In any case if not jets
what else can be used so that a person can strap it to his back and
have enough thrust to take off vertically and hover for a few seconds?