Quantum information approach to a Bose-Einstein condensate in a tilted double-well system

We study the ground-state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground-state transitions under different tilt values. For a very small tilt (for example 10(-10)), two transitions are found. For a moderate tilt (for example 10(-3)), only one transition is found. For a large tilt (for example 10(-1)), no transition is found. We explain this by analysing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with the particle number N. This means that for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-N limit it can be.