Simulation and measurement of topological phase transitions with alkaline-earth-metal atoms in optical lattices

We present a proposal to realize and detect topological phase transition in optical lattices with alkaline-earth-metal atoms. Using state-dependent lattices and laser-assisted tunneling, we realize a dimerized spin-$1/2$ antiferromagnetic chain with next-nearest-neighbor coupling. We show that the spin chain hosts two symmetric topological phases and undergoes the topological phase transition when we change the alternating strength of nearest-neighbor couplings. We propose to measure the topological phase transition by detecting the entanglement spectrum and nonlocal string order with a quantum gas microscope. Furthermore, from measurement results, we demonstrate the difference of statistical properties between two topological phases. Our proposal can be a promising platform for simulation of topological phase transition.