Solid state systems derive their richness from the interplay between interparticle interactions and novel band structures that deviate from those of free particles. Strongly interacting systems, where both of these phenomena are of equal importance,
exhibit a variety of theoretically interesting and practically useful phases. Systems of ultracold atoms are rapidly emerging as precise and controllable simulators, and it is precisely in this strongly interacting regime where simulation is the most useful. Here we demonstrate how to hybridize Bloch bands in optical lattices to introduce long-range ferromagnetic order in an itinerant atomic system. We find spontaneously broken symmetry for bosons with a double-well dispersion condensing into one of two distinct minima, which we identify with spin-up and spin-down. The density dynamics following a rapid quench to the ferromagnetic state confirm quantum interference between the two states as the mechanism for symmetry breaking. Unlike spinor condensates, where interaction is driven by small spin-dependent differences in scattering length, our interactions scale with the scattering length itself, leading to domains which equilibrate rapidly and develop sharp boundaries characteristic of a strongly interacting ferromagnet.
Doped Mott insulators have been shown to have a strong propensity to form patterns of holes and spins often referred to as stripes. In copper-oxides, doping also gives rise to the pseudogap state, which transforms into a high temperature superconduct
or with sufficient doping or by reducing the temperature. A long standing question has been the interplay between pseudogap, which is generic to all hole-doped cuprates, and stripes, whose static form occurs in only one family of cuprates over a narrow range of the phase diagram. Here we examine the spatial reorganization of electronic states with the onset of the pseudogap state at T* in the high-temperature superconductor Bi2Sr2CaCu2O8+x using spectroscopic mapping with the scanning tunneling microscope (STM). We find that the onset of the pseudogap phase coincides with the appearance of electronic patterns that have the predicted characteristics of fluctuating stripes. As expected, the stripe patterns are strongest when the hole concentration in the CuO2 planes is close to 1/8 (per Cu). While demonstrating that the fluctuating stripes emerge with the onset of the pseudogap state and occur over a large part of the cuprate phase diagram, our experiments indicate that they are a consequence of pseudogap behavior rather than its cause.
