Judging by the color/finish of your door jamb, I would use a wood transition that spans the gap. Stain it to match. You can trim the door stop to fit the transition completely under the door. Use the same technique you would use for trimming jambs when you install tile. You can cut a strip of cork ... but it would have been better to have notched the cork when you laid it so the piece would be continuous. Oh well.
Here is a pic which gives you the idea, even though it is not the exact match to your situation.