  We analyze Josephson's oscillation of Bose particles in the open
(dissipative) Bose-Hubbard dimer. First, we excite the dimer from the vacuum
state into a state suitable for observing the oscillation by using a special
protocol for external driving. Next, we switch off the driving and observe the
oscillation. It is shown that the main mechanism for the decay of Josephson's
oscillation is the dephasing due to fluctuating number of particles in open
systems. An analytical estimate for the decay time is obtained.
