Atomic interactions introduce an intrinsic non-linearity in Bosonic Josephson Junctions, making them richer than their condensed matter analogue. We experimentally study the effects of particle interactions on the tunneling dynamics of two coupled elongated Bose-Einstein condensate. The trapping geometry is a tunable double-well generated by an atom chip. 

Using radio-frequency dressing, we deform a single harmonic atom trap, in which the atoms are initially condensed, into a double-well potential and realize a splitting of the BEC wave function. A large spatial separation and a tilt of the double-well enable us to prepare a broad variety of initial states by precisely adjusting the initial population and relative phase of the two wave packets, while preserving the phase coherence. 

In particular, imprinting a global relative phase between the superfluids leads to Josephson oscillations that we can investigate for various coupling strengths. The observed dynamics exhibits a rapid relaxation toward a phase-locked equilibrium state, which goes beyond the predictions of the two site Bose-Hubbard model. As the relaxation escapes the existing description, both 1D and 3D, we account for it using an empirical friction and investigate the dependence of the damping magnitude with our experimental parameters. It results that the relaxation does not depend on the tunnel coupling and depends on the atom number as N-1/2. We currently search for a relaxation mechanism compatible with our experimental observations.