  We present a feasible scheme to investigate the geometric phase for an atom
trapped in an optical cavity induced by the effective decay process due to
cavity photon loss. The cavity mode, together with the external driving fields,
acts as the engineered environment of the atom. When the parameters of the
reservoir is adiabatically and cyclically changed, the system initially in the
nontrivial dark state of the effective Lindblad operator undergoes a cyclic
evolution and acquires a geometric phase. The geometric phase can be observed
with the atomic Ramsey interference oscillation in the decoherence-free
subspace.
