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 have experimentally measured transport of superfluid, bosonic atoms in a mesoscopic system: a small channel connecting two large reservoirs. Starting far from equilibrium (superfluid in a single reservoir), we observe first resistive flow transitioning at a critical current into superflow, characterized by oscillations. We reproduce this full evolution with a simple electronic circuit model. We compare our fitted conductance to two different microscopic phenomenological models. We also show that the oscillations are consistent with LC oscillations as estimated by the kinetic inductance and effective capacitance in our system. Our experiment provides an attractive platform to begin to probe the mesoscopic transport properties of a dilute, superfluid, Bose gas.

Using a thermal sample of laser-cooled rubidium atoms, we have constructed a neutral-atom circuit analogous to an electronic capacitor discharged through a resistor. The atoms are confined using what we call a free-space atom chip, an optical dipole trap created using a generalized phase-contrast imaging technique. We have also calculated theoretical values for the capacitance and resistance, which agree with our experiments, as well as theoretical value for an atomic analog of electrical inductance. We show that atomic capacitance is analogous to the quantum capacitance, the atomic resistance is analogous to the ballistic, or Sharvin resistance, and the atomic inductance is analogous to kinetic inductance.