Delocalization to self-trapping transition of a Bose fluid confined in a double-well potential: An analysis via one- and two-body correlation properties

We revisit the delocalized to self-trapping transition in an interacting bosonic fluid confined in a double-well potential in the context of full quantum calculations. We first study one- and two-body properties in the energy eigenstates to determine the transition as a function of the energy of the fluid. This occurs provided the interparticle interaction is above a critical or threshold value. Next, we analyse the evolution in time of the same observables in a set of coherent states to show that the N-particle Bose fluid reaches stationary states, whose expectation values turn out to coincide with those in the eigenestates. This stationary or collapsed state alternates with recurrent revivals. Here we show that the time spent in the stationary state increases with the number of particles, relatively to the time during the revivals. This stationarity property is in severe contrast with that of mean-field states since these always appear as coherent oscillations either for delocalized or self-trapped states.