We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.

In few-body physics, Efimov states are an infinite series of three-body bound states that obey universal discrete scaling symmetry when pairwise interactions are resonantly enhanced. Despite abundant reports of Efimov states in recent cold atom experiments, direct observation of the discrete scaling symmetry remains an elusive goal. Here we report the observation of three consecutive Efimov resonances in a heteronuclear Li-Cs mixture near a broad interspecies Feshbach resonance. The positions of the resonances closely follow a geometric series 1, λ, λ 2 . The observed scaling constant λexp = 4.9(4) is in good agreement with the predicted value of 4.88.The emergence of scaling symmetry in physical phenomena suggests a universal description that is insensitive to microscopic details. Well-known examples are critical phenomena, which are universal and invariant under continuous scaling transformations [1]. Equally intriguing are systems with discrete scaling symmetry, which are invariant under scaling transformations with a specific scaling constant [2]; a classic example is the selfsimilar growth of crystals, as in snowflakes. Surprisingly, such discrete scaling symmetry also manifests in the infinite series of three-body bound states that Vitaly Efimov predicted in 1970 [3].In the Efimov scenario, while pairs of particles with short-range resonant interactions cannot be bound, there exists an infinite series of three-particle bound states. These bound states have universal properties that are insensitive to the details of the molecular potential and display discrete scaling symmetry; the size R n and binding energy E n of the Efimov state with the nth lowest energy scale geometrically as R n = λR n−1 and E n = λ −2 E n−1 , where λ is the scaling constant. An alternative picture to understand discrete scaling symmetry is based on renormalization group limit cycles [4]. Away from the two-body scattering resonance, Efimov states couple to the scattering continuum and induce a series of threebody scattering resonances at scattering lengths a (n) − < 0, which also follow the scaling law a (Fig. 1)

Quantum criticality emerges when a many-body system is in the proximity of a continuous phase transition that is driven by quantum fluctuations. In the quantum critical regime, exotic, yet universal properties are anticipated; ultracold atoms provide a clean system to test these predictions. We report the observation of quantum criticality with two-dimensional Bose gases in optical lattices. On the basis of in situ density measurements, we observe scaling behavior of the equation of state at low temperatures, locate the quantum critical point, and constrain the critical exponents. We observe a finite critical entropy per particle that carries a weak dependence on the atomic interaction strength. Our experiment provides a prototypical method to study quantum criticality with ultracold atoms.