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.

Figure 1

Simulations of the magnetization expectation value $\langle J_z\left(t\right)\rangle$ for a maximally mixed initial state of an ensemble of $N=10$ spins (left), and $N=100$ spins (right) for the master equation described by the first-order average dissipator in Eq. (23) (dotted black line), and of the cavity cooling with the local dephasing master equation in Eq. (10) for $\gamma =\lambda N\mathrm{\Gamma }$, and $\lambda =0,0.1,1,10$.

Figure 2

Simulations of the magnetization expectation value $\langle J_z\left(t\right)\rangle$ for the full spin-cavity master equation in Eq. (5) with the addition of a local dephasing dissipator for $N=10$ spins in a maximally mixed initial state, and a cavity truncated to four levels initialized in the ground state. Evolution under the first-order average dissipator is shown as the dotted black line in both figures.