is an emerging interdisciplinary field that seeks new functionality by creating devices and circuits where ultra-cold atoms, often superfluids, play a role analogous to the electrons in electronics. Hysteresis is widely used in electronic circuits, e.g., it is routinely observed in superconducting circuits 3 and is essential in rf-superconducting quantum interference devices [SQUIDs] 4 . Furthermore, hysteresis is as fundamental to superfluidity 5 (and superconductivity) as quantized persistent currents [6][7][8] , critical velocity [9][10][11][12][13][14] , and Josephson effects 15,16 . Nevertheless, in spite of multiple theoretical predictions 5,[17][18][19] , hysteresis has not been previously observed in any superfluid, atomic-gas Bose-Einstein condensate (BEC).Here we demonstrate hysteresis in a quantized atomtronic circuit: a ring of superfluid BEC obstructed by a rotating weak link. We directly detect hysteresis between quantized circulation states, in contrast to superfluid liquid helium experiments that observed hysteresis directly in systems where the quantization of flow could not be observed 20 and indirectly in systems that showed quantized flow 21,22 . Our techniques allow us to tune the size of the hysteresis loop and to consider the fundamental excitations that accompany hysteresis. The 1 arXiv:1402.2958v2 [cond-mat.quant-gas]

We report the direct observation of resistive flow through a weak link in a weakly interacting atomic Bose-Einstein condensate. Two weak links separate our ring-shaped superfluid atomtronic circuit into two distinct regions, a source and a drain. Motion of these weak links allows for creation of controlled flow between the source and the drain. At a critical value of the weak link velocity, we observe a transition from superfluid flow to superfluid plus resistive flow. Working in the hydrodynamic limit, we observe a conductivity that is 4 orders of magnitude larger than previously reported conductivities for a Bose-Einstein condensate with a tunnel junction. Good agreement with zero-temperature Gross-Pitaevskii simulations and a phenomenological model based on phase slips indicate that the creation of excitations plays an important role in the resulting conductivity. Our measurements of resistive flow elucidate the microscopic origin of the dissipation and pave the way for more complex atomtronic devices.

This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied theoretically the dynamics of a BEC after release from a toroidal trap potential by solving the 3D Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated theoretically by imprinting a linear azimuthal phase on the initial condensate wave function. The theoretical TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring-shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus, hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.

We investigate both experimentally and theoretically disorder induced damping of Bloch oscillations of Bose-Einstein condensates in optical lattices. The spatially inhomogeneous force responsible for the damping is realised by a combination of a disordered optical and a magnetic gradient potential. We show that the inhomogeneity of this force results in a broadening of the quasimomentum spectrum, which in turn causes damping of the centre-of-mass oscillation. We quantitatively compare the obtained damping rates to the simulations using the Gross-Pitaevskii equation. Our results are relevant for high precision experiments on very small forces, which require the observation of a large number of oscillation cycles.

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