Cavity cooling to the ground state of an ensemble quantum system

We describe a method for initializing an ensemble of qubits in a pure ground state by applying collective cavity cooling techniques in the presence of local dephasing noise on each qubit. To solve the dynamics of the ensemble system we introduce a method for dissipative perturbation theory that applies average Hamiltonian theory in an imaginary-time dissipative interaction frame to find an average effective dissipator for the system dynamics. We use SU(4) algebra generators to analytically solve the first-order perturbation for an arbitrary number of qubits in the ensemble. We find that to first order the effective dissipator describes local ${T}_{1}$ thermal relaxation to the ground state of each qubit in the ensemble at a rate equal to the collective cavity cooling dissipation rate. The proposed technique should permit the parallel initialization of high purity states in large ensemble quantum systems based on solid-state spins.