  In this article, for the first time in the context of TOP trap, the necessary
and sufficient conditions for the adiabatic evolution of weak field seeking
states have been quantitatively examined. It has been well accepted since
decades that adiabaticity has to be obeyed by the atoms for successful magnetic
trapping. However, we show, on the contrary, that atoms can also be confined
beyond the adiabatic limit. Hence, our findings open new possibilities to relax
the restrictions of atom trapping in laboratories.
