Dissipative creation of three-dimensional entangled state in optical cavity via spontaneous emission

We present a dissipative protocol to engineer two $^{87}Rb$ atoms into a form of three-dimensional entangled state via spontaneous emission. The combination of coupling between ground states via microwave fields and dissipation induced by spontaneous emission make the current scheme deterministic and a stationary entangled state can always be achieved without state initialization. Moreover, this scheme can be straightforwardly generalized to preparation of an $N$-dimensional entangled state in principle.