From sequential to correlated tunneling of two bosons

The sequential to correlated-tunneling transition of two identical bosons confined in a symmetrical double well potential is studied using a time-dependent variational formalism. Increasing the strength of the short-range boson-boson interaction, the probability of finding both bosons in the same well allow to identify three regimes. For small values of the boson- boson coupling constante, this probability display beatings. Then, the probability of finding both bosons in the same well becomes quasi-periodical in time, for almost all values of the coupling constant; however, there is a zero-measure set, which contains an infinity of points, for which this probability is time-periodic. Finally, for larger values of the coupling constant, this probability changes periodically. Based on the dynamics of the probability of finding one boson on each well and increasing the boson-boson interaction, we find that tunnelling changes from a regime where one boson tunnels after the other to a regime in which they tunnel together.