  The longitudinal coupling of a system to the bath usually induces the pure
dephasing of the system. In this paper, we study the collective dephasing
induced dissipation and decoherence in a coupled-qubit system with a common
bath. It is shown that, compared with the case of the same system with
independent baths, the interference between the dephasing processes of
different qubits induced by the common bath significantly changes the
dissipation of the system. For the system of two coupled qubits, the
interference leads to a faster decoherence in the non-single-excitation
subspaces and a slower dissipation (and decoherence) in the single-excitation
subspace. For the system of multiple coupled qubits, we also find the slower
dissipation in the single-excitation subspace and obtain the decay rates of the
first excited states for different system sizes numerically. All our results on
collective dephasing induced dissipation can be explained based on a simple
model with Fermi's golden rule.
