We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential, we engineer spatially dependent complex tunneling amplitudes. Thereby, atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal-symmetric Hamiltonian underlying the quantum spin Hall effect; i.e., two different spin components experience opposite directions of the magnetic field.

No abstract

We report on the observation of the Meissner effect in bosonic flux ladders of ultracold atoms. Using artificial gauge fields induced by laser-assisted tunneling, we realize arrays of decoupled ladder systems that are exposed to a uniform magnetic field. By suddenly decoupling the ladders and projecting into isolated double wells, we are able to measure the currents on each side of the ladder. For large coupling strengths along the rungs of the ladder, we find a saturated maximum chiral current corresponding to a full screening of the artificial magnetic field. For lower coupling strengths, the chiral current decreases in good agreement with expectations of a vortex lattice phase. Our work marks the first realization of a low-dimensional Meissner effect and, furthermore, it opens the path to exploring interacting particles in low dimensions exposed to a uniform magnetic field.The Meissner effect is the hallmark signature of a superconductor exposed to a magnetic field [1,2]. For a type-II superconductor, full screening of the applied external field occurs up to a critical field H c1 . Such a screening is the result of circular surface currents on the superconductor that generate an opposite field, canceling the applied field. The superconductor thus acts as a perfect diamagnet in the Meissner phase. For larger field strengths H > H c1 , however, the superconductor is not able to fully screen the applied field and an Abrikosov vortex lattice phase is formed in the system. In lowdimensional quantum systems it has been a longstanding challenge to probe analogue ideas and to investigate the interplay of orbital magnetic field effects and interactions. While a single one-dimensional system does not allow for any orbital magnetic field effects, a ladder system is the simplest extension where these are permitted [3][4][5][6][7][8].Here we report on the realization of such bosonic ladders for ultracold atoms exposed to a uniform artificial magnetic field created by laser-assisted tunneling [9][10][11][12][13][14][15][16][17]. Previously, such ladders have been discussed in the context of Josephson-junction arrays [3,[18][19][20][21] and more recently also for ultracold atoms exposed to an artificial gauge field [6][7][8]. In our experiment we can measure the probability current on either leg of the ladders and, in addition, observe the momentum distribution of the system after time-of-flight expansion. Rather than varying the external field strength, we determine the response of the system as a function of the ratio of transverse rung coupling K to coupling along the legs of the ladder J (see Fig. 1). In full analogy to the type-II superconductor, we find evidence for a Meissner phase with maximum chiral currents that screen the applied field. Below a critical coupling strength (K/J) c we find a decreasing chiral current, in good agreement with theoretical expectations for a vortex phase with only partial screening. b a y x J Ke ilφ d y d x l l+1 1 E (J) 0 4 -4 q (π/d y ) 0 -1 K/J 0 1 2 3 (K/J) C L R FIG. 1. Experimental...