I guess you mean 1 quadrillion.
Then, the next number is one quadrillion and one.
But I think you mean the next one as in thousand, million, billion, etc, in which case the answer is:
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There is no such thing as a "quatrillion" (or a "qua trillion" for that matter). Perhaps you are thinking of a "quadrillion"?. What comes after quadrillions would be quintillions.
Quadrillion comes after trillion. If you add one to a trillion, the number becomes a trillion and one, a trillion and two, etc.
A trillion and one.
A trillion and two duh
One hundred trillion and one (100,000,000,000,001)