We put forward an approach to generate Wigner-negative states for field modes by engineering the field parity in driven-dissipative nonlinear systems. The parity of a radiation field is directly connected to its Wigner negativity, since the dominance of odd-parity Fock-state populations leads to a clear negative patch in the Wigner function, signaling the non-Gaussian nature of the state. Physically, the odd- or even-parity state associated with the corresponding population distribution can be modified by properly using the external coherent drive, along with incoherent excitation and dissipation. To elucidate this statement, we enumerate several typical systems in the presence of the drive or dissipation, targeted at transferring and trapping population in the odd-parity Fock-state subspace. Under reasonable experimental parameters, we confirm the steady-state Wigner negativity by simulations based on the Lindblad master equation, showing that the Wigner-negative effect is robust in the cases of odd-parity Fock-state population dominance. Our semianalytical estimates for the Wigner negativity agree quantitatively with the results of numerical simulations from the master equation. We also discuss the feasibility of implementing the proposed scheme on state-of-the-art superconducting-circuit architectures. This investigation opens a promising route to steady-state quantum non-Gaussian states and deepens insight into their nature.

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• Open quantum systems
• Quantum control
• Quantum state engineering
• Quantum states of light
• Cavity resonators