## (a) Energy eigenvalues of the Hamiltonian in equation (2) for *N* = 50, α = 0.4 (circles connected with a line) and α = 2.5 (squares)

**Figure 3.** (a) Energy eigenvalues of the Hamiltonian in equation (2) for *N* = 50, α = 0.4 (circles connected with a line) and α = 2.5 (squares). (b) Energy gap Δ*E*/*S* as a function of the coupling strength α for *N* = 500 (solid line) and *N* = 800 (dotted line).

**Abstract**

We study the quantum dynamics of a Bose–Josephson junction made up of two coupled Bose–Einstein condensates. We analyse different dynamical branches of Josephson oscillations within an 'effective potential' approach. At a critical coupling strength, a transition takes place between the dynamical branches of Josephson oscillations, which is also manifested in the energy spectrum, and pairs of (quasi)-degenerate excited states appear above the critical coupling strength. This phenomenon can be understood in terms of change in shape of the 'effective potential'. Possible novel quantum phenomena like decay of metastable 'π-oscillation' by 'macroscopic quantum tunnelling' (MQT) and MQT between the 'self-trapped' states with equal and opposite number imbalance become evident from the simple picture of 'effective potential'.