We explore the self-sustained Josephson-junction dynamics in dipolar supersolids, predicting the possibility of self-trapping alongside the experimentally observed Josephson oscillations [G. Biagioni et al., Nature (London) 629, 773 (2024)]. Using an asymmetric two-mode (ATM) model to describe a triangular dipolar supersolid, validated through Gross-Pitaevskii simulations, we demonstrate that the system's symmetry enables a consistent two-mode mapping despite the presence of seven droplets. Hence the associated Hamiltonian allows us to straightforwardly determine the self-trapping regime. Additionally, we show that bringing the system into rotation preserves its ability to sustain the Josephson-junction dynamics across its full range and we assess the robustness of the ATM model under these conditions. We further find that the off-axis droplets move in the radial direction during the evolution in accordance with the size of the central droplet. Such movements do not interfere with the model predictions.

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• Bose-Einstein condensates
• Dipolar gases
• Josephson junctions
• Supersolids