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The driven-dissipative Bose-Hubbard model can be experimentally realized witheither negative or positive onsite detunings, inter-site hopping energies, andonsite interaction energies. Here we use one-dimensional matrix product densityoperators to perform a fully quantum investigation of the dependence of thenon-equilibrium steady states of this model on the signs of these parameters.Due to a symmetry in the Lindblad master equation, we find that simultaneouslychanging the sign of the interaction energies, hopping energies, and chemicalpotentials leaves the local boson number distribution and inter-site numbercorrelations invariant, and the steady-state complex conjugated. This showsthat all driven-dissipative phenomena of interacting bosons described by theLindblad master equation, such as "fermionization" and "superbunching", canequivalently occur with attractive or repulsive interactions.

Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems