17 February 2014 ICFO PRL highlighted in Science

Dynamics of edge states as revealed by spin-selective imaging.

Revealing Fractals and Edge States in Synthetic Dimensions. In a collaboration with world-leading experts in synthetic gauge fields for ultracold atoms, researchers Alessio Celi (ICFO), Pietro Massignan (ICFO) , Julius Ruseckas (Vilnius, Lithuania), Nathan Goldman (ENS, Paris), Ian Spielman, Gediminas Juzeliūnas (Vilnius, Lithuania) and ICREA Professor at ICFO, Maciej Lewenstein, have recently published a paper in Physics Review Letters which has earned the distinction of “Editor’s Choice” in Science. Quantum matter can exhibit striking properties when confined to a low-dimensional space. This is the case for particles moving in two-dimensional crystals subjected to high magnetic fields. In this configuration, the energy spectrum ruling the dynamics takes the shape of a celebrated fractal figure: the Hofstadter butterfly.

Unfortunately, visualizing these fractal properties remains a challenging task, as it generally requires magnetic fields of tremendous strength. In this work, researchers introduce a novel way to build two-dimensional lattices for cold atoms, which simultaneously generates a magnetic field whose strength is sufficient to access the Hofstadter butterfly.

Specifically, they exploit the internal states of an atom to represent the coordinates of a \"synthetic\" dimension; hopping along this direction is obtained exploiting transitions between the internal states. Coupling the internal states of atoms moving in a 1D optical lattice offers a direct and simple scheme to generate an artificial 2D lattice penetrated by arbitrarily large magnetic flux.

The cold-atom realization of topologically-protected edge states and Hofstadter-butterfly spectrum becomes remarkably simple in this scheme, which should be implemented soon in experiments based on available technologies.

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