  Temperature effect on quantum tunneling in a Cooper-pair-box coupled to a
quantum oscillator is studied by both numerical and analytical calculations. It
is found that, in strong coupling regions, coherent tunneling of a
Cooper-pair-box can be destroyed by its coupling to a quantum oscillator and
the tunneling becomes thermally activated as the temperature rises, leading to
failure of the Cooper-pair-box. The transition temperature between the coherent
tunneling and thermo-activated hopping is determined and physics analysis based
on small polaron theory is also provided.
