We　revisit　the　protocols　to　create　maximally　entangled　states　between　two　Josephson　junction　(JJ)　charge　phase　qubits　coupled　to　a　microwave　field　in　a　cavity　as　a　quantum　data　bus.　We　analyze　a　novel　mechanism　of　quantum　decoherence　due　to　the　adiabatic　entanglement　between　qubits　and　the　data　bus,　the　off-resonance　microwave　field.　We　show　that　even　if　the　variable　of　the　data　bus　can　be　adiabatically　eliminated,　the　entanglement　between　the　qubits　and　data　bus　remains　and　can　decohere　the　superposition　of　two-particle　state.　Fortunately　we　can　construct　a　decoherence-free　subspace　of　two-dimension　to　against　this　adiabatic　decoherence.　To　carry　out　the　analytic　study　for　this　decollerence　problem,　we　develop　Frohlich　transformation　to　re-derive　the　effective　Hamiltonian　of　these　systems,　which　is　equivalent　to　that　obtained　from　the　adiabatic　elimination　approach.