  We investigate the dynamics of fermionic atoms in a high-finesse optical
resonator after a sudden switch on of the coupling between the atoms and the
cavity. The atoms are additionally confined by optical lattices to a ladder
geometry. The tunneling mechanism on a rung of a ladder is induced by a cavity
assisted Raman process. At long times after the quantum quench the arising
steady state can carry a chiral current. In this work we employ exact
diagonalization techniques on small system sizes to study the dissipative
attractor dynamics after the quench towards the steady state and deviations of
the properties of the steady state from predictions obtained by adiabatically
eliminating the cavity mode.
