Topology

Spielman's review.

Berry phase

Direct measurement of the Zak phase in topological Bloch bands

They work with 1D dimerized optical lattice (or as they call it a superlattice), which leads to the Rice-Mele Hamiltonian: $\bar H = -\sum_n(Ja^\dagger_n b_n+J'a^\dagger b_{n-1}+\text{h.c.})+\Delta\sum_n(a^\dagger_n a_n-b^\dagger_n b_n)$. If Δ is tuned to be equal then the system corresponds to the Su-Schrieffer-Heeger (SSH) model, which has two topologically distinct phases. The Zak phase difference between them is equal to π.

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  Two phases