The binding and trapping of particles usually rely on conservative forces, described by unitary quantum dynamics. We show that both can also arise solely from spatially dependent dephasing, the simplest type of decoherence. This can be based on continuous weak position measurements in only selected regions of space, for which we propose a practical realization. For a single particle, we demonstrate a quantum particle in a box based on dephasing. For two particles, we demonstrate their binding despite repulsive interactions, if their molecular states are dephased at large separations only. Both mechanisms are experimentally accessible, as we show for an example with Rydberg atoms in a cold gas background.

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• Cooling & trapping
• Decoherence in quantum gases
• Potential energy surfaces
• Quantum Zeno dynamics
• Rydberg atoms & molecules
• Ultracold gases