Figure 6: Simulation of the Chern number measurement for 
.
.From: Quantum simulation of 2D topological physics in a 1D array of optical cavities
(a) Calculated photon transmission 
. The magnetic flux φ0=1/6. The probing light frequency is at ω=−3.09κ, where lies the very narrow first energy band. (b) Calculated phase mismatch χ(kx,ky) of 
in the Brillouin zone resulting from two different phase conventions for 
in equation (10), defined by dividing the Brillouin zone into B1, whose boundary is marked by the red line and where 
is always nonzero, and B2, which contains all zero points of 
but where 
does not vanish. In one phase convention, 
is real in B1. In the other convention, 
is real in B2. The Chern number is determined by the integration of the gradient of χ(kx, ky) on the boundary of B1, ∂B1 (Supplementary Note 6). In a and b, the size of the simulator N=10. The OAM included in the calculation is l∈[−48, 48). Periodic boundary conditions are used in both the x and y directions. The photon loss rate γ=0.1κ.
