Emergence of superfluidity in a dynamical system of ul- tracold atoms

– The dynamics of a Bose-Einstein condensate is studied theoretically in a combined periodic plus harmonic external potential. Different dynamical regimes of stable and unstable collective dipole and Bloch oscillations are analysed in terms of a quantum mechanical pendulum model. Nonlinear interactions are shown to counteract quantum-mechanical dephasing and lead to superfluid behaviour. The study of transport properties of ultracold atoms in corrugated potentials has become an intensely discussed topic since the first experiments with Bose-Einstein condensates (BECs) in optical lattices almost a decade ago [1–13]. The observed or predicted phenomena are often discussed by concepts borrowed from the phenomenology of extended systems. This approach led to the characterisation of superfluid and insulating phases and phase transitions [4, 12], modulational instability [14, 15], and dissipative behaviour [3, 13]. In this Letter we approach the problem from a different, somewhat holistic point of view and treat the BEC in the external potential as a finite dynamical system. Specifically, we consider the generic model of a BEC in a one-dimensional (1D) optical lattice in a classical tight-binding approximation with additional harmonic trapping in the lattice axis. By exploiting a mapping of this system to a quantum mechanical pendulum model under the influence of interactions, we immediately find a rich description of different dynamical regimes. The problem of ultracold atoms in a combined potential from a 1D optical lattice and a harmonic trap has been discussed before in many experimental and theoretical works. A dynamical superfluid-insulator transition has been predicted in Ref. [4] for a BEC on the basis of a modulational instability caused by nonlinear interactions. A similar effect of insulating behaviour, however, was observed in noninteracting fermions [8]. The latter was interpreted as a very different mechanism in terms of a semiclassical pendulum model. Experiments with BECs [5,6] and further numerical analysis [16,17] gave ambiguous results in showing reduced mobility of Bosons without revealing the mechanism. In this Letter we study the BEC in a combined harmonic and lattice trap as a dynamical system. An exact mapping of the lattice dynamics of the noninteracting system to a simple