Trapping and binding by dephasing

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 decoherence. This be based continuous weak position measurements in only selected regions space, for which we propose a practical realisation. For single particle, demonstrate particle-in-the-box dephasing. two particles, their despite repulsive interactions, if molecular states are dephased at large separations only. Both mechanisms experimentally accessible, as an example with Rydberg atoms cold gas background.