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# The Energy Spectrum of Ultracold Atoms in a Synthetic Magnetic Field

One of the driving forces behind studying ultracold atoms is the exquisite control and flexibility available in experiments. This flexibility enables us to engineer new states of matter, e.g. cold atom emulators of other physical systems which are not presently accessible to experiment. The figure on the left shows the spectrum of energy levels of a cold atom in a laser configuration designed to make the atom mimic an electron confined in two dimensions, in a generalization of a magnetic field called a "non-Abelian gauge field." The atom's energy levels are functions of three parameters: a1 and a2 are related to the strengths of the artificial magnetic field, and ky represents the atom's momentum. Along the line (a1 = a2), the field reduces to the usual (Abelian) magnetic field.

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January 7, 2009

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