Abstract
We propose how topologically non-trivial states can dynamically organize in a fermionic quantum gas which is confined to a two-dimensional optical lattice potential and coupled to the field of an optical cavity. The spontaneously emerging cavity field induces together with coherent pump laser fields a dynamical gauge field for the atoms. Upon adiabatic elimination of the cavity degree of freedom, the system is described by an effective Hofstadter model with a self-consistency condition which determines the tunneling amplitude along the cavity direction. The fermions are found to self-organize into topologically non-trivial states which carry an extended edge state for a finite system size. Due to the dissipative nature of the cavity field, the topological steady states are protected from external perturbations.
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