The concept of phase space crystals for closed quantum system has been extended to open quantum system. In circuit QED systems, a microwave resonator combined with Josephson junctions and voltage bias under n -photon resonance can be described by a rotating wave approximation (RWA) Hamiltonian H ^ ^ R W A with Z n phase space symmetry described above. When single-photon loss is dominant, the dissipative dynamics of resonator is described by the following master equation (Lindblad equation) d ρ ρ d t = − − i ℏ ℏ [ H ^ ^ R W A , ρ ρ ] + γ γ 2 ( 2 a ^ ^ ρ ρ a ^ ^ † † − − a ^ ^ † † a ^ ^ ρ ρ − − ρ ρ a ^ ^ † † a ^ ^ ) = L ( ρ ρ ) , where γ γ is the loss rate and superoperator L is called the Liouvillian. One can calculate the eigenspectrum and corresponding eigenoperators of the Liouvillian of the system L ρ ρ ^ ^ m = λ λ m ρ ρ ^ ^ m . Notice that not only the Hamiltonian but also the Liouvillian both are invariant under the n -fold rotational operation, i.e., [ L , T τ τ ] = 0 with T τ τ O ^ ^ = T ^ ^ τ τ † † O ^ ^ T ^ ^ τ τ and τ τ = 2 π π / n . This symmetry plays a crucial role in extending the concept of phase space crystals to an open quantum system. As a result, the Liouvillian eigenoperators ρ ρ ^ ^ m have a Bloch mode structure in phase space, which is called a dissipative phase space crystal.