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We employ the perturbation series expansion for derivation of the reducedmaster equations for the three-site Bose-Hubbard model subject to strong atomlosses from the central site. The model describes a condensate trapped in atriple-well potential subject to externally controlled removal of atoms. Wefind that the $\pi$-phase state of the coherent superposition between the sidewells decays via two dissipation channels, the single-boson channel (similar tothe externally applied dissipation) and the boson-pair channel. The quantumderivation is compared to the classical adiabatic elimination within themean-field approximation. We find that the boson-pair dissipation channel isnot captured by the mean-field model, whereas the single-boson channel isdescribed by it. Moreover, there is a matching condition between the zero-pointenergy bias of the side wells and the nonlinear interaction parameter whichseparates the regions where either the single-boson or the boson-pairdissipation channel dominate. Our results indicate that the $M$-siteBose-Hubbard models, for $M>2$, subject to atom losses may require an analysiswhich goes beyond the usual mean-field approximation for correct description oftheir dissipative features. This is an important result in view of the recentexperimental works on the single site addressability of condensates trapped inoptical lattices.

The three-site Bose-Hubbard model subject to atom losses: the boson-pair dissipation channel and failure of the mean-field approach