We experimentally study a driven-dissipative Josephson junction array, realized with a weakly interacting Bose Einstein condensate residing in a one-dimensional optical lattice. Engineered losses on one site act as a local dissipative process, while tunneling from the neighboring sites constitutes the driving force. We characterize the emerging steady-states of this atomtronic device. With increasing dissipation strength γ the system crosses from a superfluid state, characterized by a coherent Josephson current into the lossy site to a resistive state, characterized by an incoherent hopping transport. For intermediate values of γ, the system exhibits bistability, where a superfluid and a resistive branch coexist. We also study the relaxation dynamics towards the steady-state, where we find a critical slowing down, indicating the presence of a non-equilibrium phase transition.PACS numbers: 03.75. Lm, 74.40.Gh, 03.65.Yz, 42.50.Dv Non-equilibrium steady-states constitute fix points of the phase space dynamics of classical and quantum systems [1][2][3]. They emerge under the presence of a driving force and lie at the heart of transport phenomena such as heat conduction [4][5][6] or current flow [7][8][9]. They also naturally appear in open quantum systems [10,11] and are connected to the study of non-equilibrium thermodynamics and non-equilibrium quantum phase transitions [12]. It has been pointed out that engineering open quantum systems can induce a phase space dynamics which drives the quantum system in a pure state by solely dissipative means [13][14][15][16]. Controlling and understanding the non-equilibrium steady-states of an open many-body quantum system therefore offers new routes for quantum state engineering and out-of-equilibrium quantum dynamics. Here, we investigate the steady-states of a driven-dissipative Josephson junction array realized with a Bose-Einstein condensate in a one-dimensional optical lattice [17]. Varying the strength of the dissipation, the system can be tuned from superfluid to resistive transport. In between, it exhibits a region of bistability. The peculiar transport properties make such devices promising elements for complex atomtronic circuits. At the same time, they are an interesting candidate to study generic properties of an open quantum system. Our results manifest the high potential of open system control in ultracold quantum gases.Open quantum systems are characterized by the competition between the intrinsic unitary dynamics, governed by the Hamilton operator H, and the coupling to the environment, which induces non-unitary time evolution and quantum jumps, described by jump operators (â i ,â i † ) which act on the system with rates γ i [10]. The time evolution of the density matrix ρ in Markov approximation is then described by a master equation in Lindblad form [18]:FIG. 1. Schematics of the experiment. One site of an array of superfluids is subject to an incoherent local loss process with rate γ. The coherent tunneling coupling between the reservoir sites is given b...

We report on the observation of negative differential conductivity (NDC) in a quantum transport device for neutral atoms employing a multimode tunneling junction. The system is realized with a Bose-Einstein condensate loaded in a one-dimensional optical lattice with high site occupancy. We induce an initial difference in chemical potential at one site by local atom removal. The ensuing transport dynamics are governed by the interplay between the tunneling coupling, the interaction energy, and intrinsic collisions, which turn the coherent coupling into a hopping process. The resulting current-voltage characteristics exhibit NDC, for which we identify atom number-dependent tunneling as a new microscopic mechanism. Our study opens new ways for the future implementation and control of complex neutral atom quantum circuits.