An investigation into why macroscopic systems behave classically

We study why it is hard to make a macroscopic superposition of superfluid flows in a Bose-Einstein condensate. Initially we investigate N atoms trapped in a simple 1D ring with a barrier at one point and a phase applied around it. Perturbation theory is used to show that quasi-momentum (or flow) macroscopic superpositions can be made and we investigate factors which affect the cat state. The 1D ring is improved using the Bose-Hubbard model to study an array of Bose-Einstein condensates trapped in optical potentials and coupled to one another to form a ring. We derive an analytic expression to describe the quality of the cat, which agrees well with direct diagonalisation of the Hamiltonian for relatively small numbers of atoms. We show that for macroscopic superposition to be realised there are three factors that are required, other than an absence of decoherence, which become harder to satisfy when the system size increases. These are, (1) the energies of the two macroscopic states must be similar, (2) coupling between the two macroscopic states must be strong, and (3) other states must not be strongly coupled to the macroscopic states. The results help us to understand quantum mechanics on a macroscopic level