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.

The statistical mechanics description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. For quantum many-body systems statistical mechanics predicts the equilibration of highly excited non-equilibrium state towards a featureless thermal state. Hence, it is highly desirable to explore possible ways to avoid ergodicity in quantum systems. Many-body localization presents one generic mechanism for a strong violation of ergodicity relying on the presence of quenched disorder. In my talk I will discuss a different mechanism of the weak ergodicity breaking relevant for the experimentally realized Rydberg-atom quantum simulator [1]. This mechanism arises from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems [2]. I will construct the weak deformation of the Rydberg chain Hamiltonian that makes revivals virtually perfect [3]. In the second part of the talk I will provide a dynamical perspective on quantum scars. I will show the occurrence of mixed phase space within time-dependent variational principle (TDVP) description of dynamics. I will use TDVP to find new scars and explore their response to perturbations of the Hamiltonian. Finally, I will argue that the mixed phase space generally leads to non-universal dependence of thermalization on the initial state and discuss a new opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable [1].