Creating topological matter by shaking atomic gases (Prof. N. Goldman)

In this context, optical lattices are ideally suited for generating a wide family of time-dependent potentials, which can be used to prepare interesting band structures for cold atoms. In this Colloquium, I will show how topological Bloch bands can be prepared using modulated optical superlattices. I will present an effective-Hamiltonian framework, which thoughtfully describes the dynamics of the periodically-driven atomic gas. I will then discuss methods to probe the topological features of the underlying band structure, such as the topologically invariant Chern number.

Finally, I will report on recent experimental measurements, which revealed the Chern number in an optical-lattice setup. These results constitute an important step towards the realization of novel topological states of matter, such as fractional Chern insulators.