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 a study of three-dimensional (3D) localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part.Our observations are compatible with the self-consistent theory of Anderson localization, taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold. 1Anderson localization (AL) was proposed more than 50 years ago [1] to understand how disorder can lead to the total cancellation of conduction in certain materials. It is a purely quantum, one-particle effect, which can be interpreted as due to interference between the various amplitudes associated with the scattering paths of a matter wave propagating among impurities [2]. Anderson localization is predicted to strongly depend on the dimension [3]. In the three-dimensional (3D) case, a mobility edge is predicted, which corresponds to an energy threshold separating localized from extended states. Determining the precise behavior of the mobility edge remains a challenge for numerical simulations, microscopic theory and experiments [2]. The quest for AL has been pursued not only in condensed matter physics [4], but also in wave physics [5]: for instance with light waves [6][7][8][9], microwaves [10,11] and acoustic waves [12]. Following theoretical proposals [13][14][15][16][17][18], recent experiments [19,20] have shown that ultracold atoms in optical disorder constitute a remarkable system to study 1D localization [21][22][23]. Here, we report a study of 3D localization of ultracold atoms suspended against gravity, and released in a 3D optical disordered potential with short correlation lengths in all directions. We observe density profiles composed of a steady localized part and a diffusive part. Our observations are compatible with the self-consistent theory of AL [24], taking into account the specific features of the experiment, and in particular the broad energy distribution of the atoms placed in the disordered potential. The localization we observe cannot be interpreted as trapping of particles with energy below the classical percolation threshold.Our scheme (Fig. 1a) is a generalization of the one that allowed us to demonstrate AL in 1D [15,19]. It involves a dilute Bose-Einstein condensate (BEC) with several 10 4 atoms of 87 Rb, initially in a shallow quasi-isotropic Gaussian optical trap, released and suddenly submitted to an optical disordered potential generated by a laser speckle [25]. The atoms, in the |F = 2, m F = −2 hyperfine state of the ground electronic state, are suspended by a magnetic gradient that compensates gravity (the residual component of the magnetic potential is isotropic and repulsive, of the form −mω 2 r 2 /2, with ω = ...

In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.