We study the dynamics of a Bose-Hubbard model coupled to an engineered environment which in the noninteracting limit induces an effective nonreciprocal hopping as described by the Hatano-Nelson model. At strong interactions, two bosons occupying the same site form a so-called repulsively bound pair, or doublon. Using tensor-network simulations, we clearly identify a distinct doublon light cone and show that the doublon inherits nonreciprocity from that of single particles. Applying the idea of reservoir engineering at the level of doublons, we introduce a new set of dissipators and we analytically show that then the doublon dynamics are governed by the Hatano-Nelson model. This brings about a two-particle non-Hermitian skin effect and nonreciprocal doublon motion. Combining features of the two models we study, we show that single particles and doublons can be made to spread with opposite directionality, opening intriguing possibilities for the study of dynamics in interacting nonreciprocal models.

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• Bose gases
• Doublon
• Non-reciprocal propagation
• 1-dimensional systems
• Non-Hermitian systems
• Quantum many-body systems
• Bose-Hubbard model
• Lindblad equation
• Perturbation theory
• Tensor network methods