Self-similar scaling in the coherent dynamics of ultracold atoms

Well-resolved and long-lived atomic Bloch oscillations provide straightforward access to intriguing yet fascinating self-similar patterns. These could be observed in the quasienergy spectra of ultracold atomic wave packets subject to gravity in a driven optical lattice potential. As for the Hofstadter butterflylike energy spectra of crystal electrons in a uniform magnetic field, these atomic quasienergy spectra are shown to originate from commensurability between the Bloch oscillations period and the lattice driving period.