Topological growing of Laughlin states in synthetic gauge fields

We suggest a scheme for the preparation of highly correlated Laughlin (LN) states in the presence of synthetic gauge fields, realizing an analogue of the fractional quantum Hall effect in photonic or atomic systems of interacting bosons. It is based on the idea of growing such states by adding weakly interacting composite fermions (CF) along with magnetic flux quanta one-by-one. The topologically protected Thouless pump ("Laughlin's argument") is used to create two localized flux quanta and the resulting hole excitation is subsequently filled by a single boson, which, together with one of the flux quanta forms a CF. Using our protocol, filling 1/2 LN states can be grown with particle number N increasing linearly in time and strongly suppressed number fluctuations. To demonstrate the feasibility of our scheme, we consider two-dimensional (2D) lattices subject to effective magnetic fields and strong on-site interactions. We present numerical simulations of small lattice systems and discuss also the influence of losses.