The elusive Hofstadter's butterfly could soon be spotted in lattices of ultracold atoms, now that two groups of researchers have independently created the conditions required for a spectacular fractal pattern to emerge from ultracold rubidium atoms held in optical lattices. Although neither team has directly observed the fractal pattern, they have created physical systems with the right conditions for Hofstadter's butterfly to emerge. The research could also lead to the development of new ways to simulate quantum systems with exotic electric properties.
In 1976 the American physicist Douglas Hofstadter – famous for the 1979 book Gödel, Escher, Bach – first outlined the concept of the butterfly that bears his name. He predicted that stunning self-similar patterns now known as "fractals" would arise in the energy spectrum of electrons in crystalline solids exposed to extremely large magnetic fields. Due to the periodic nature of the electric fields in a crystal, the electrons are restricted to series of energy bands. When a magnetic field is applied to electrons inside a crystal, their motion is modified by the Lorentz force and they move around in circles. Hofstadter calculated that as the magnetic field becomes stronger, the energy bands split again and again, producing a butterfly-like energy spectrum.
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