Instructions
Use your throwing hand to sharply shoot the yo-yo out and down. You want to set it up in "sleep" position such that it will remain so for a while, to give you the chance to make the most of this trick.
Take the index finger of your non-throwing hand, and put it behind the string while the yo-yo is in its bottom position. At about the midpoint of the string, apply pressure in order to bring the yo-yo up from that point of the string, getting the yo-yo itself close to the index finger of your throwing hand.
Push on the string just above the yo-yo with the index finger of your throwing hand in such a way as to force the yo-yo to "jump" around and over that index finger from the back. Be sure to allow the yo-yo, as it comes around the top of your finger, to thread its groove with the yo-yo string.
Slide the index finger of your non-throwing hand down-while still maintaining pressure on the string-in front of and around the bottom of the yo-yo to come up the back side, to a point just under your other index finger. Once in this position, push the index finger of your non-throwing hand forward into the 2 strings that are now in front of it.
Bring the string up with slight pressure from the finger of your non-throwing hand and, at the same time, use the index finger of your throwing hand to come around the yo-yo from behind. Scoop down and around to the front so that the index finger can now come backward into those 2 strings.
Spin the yo-yo around in a vertical circle once or twice, using the setup of your fingers as a base to bring the yo-yo from behind, up and over the fingers and back around again. Once you've done 2 rotations like that, you can do a reverse rotation that will bring the yo-yo back into position to dismount. Then you've split the atom.