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Bulletin of the American Physical Society

Emergence of dynamical edge-state instabilities in 2D interacting bosonic systems

Bogdan Galilo, Ryan Barnett, Derek K. K. Lee

Published Mar 5, 2015• 0 citations
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In this work, we consider the dynamics of bosons in bands with nontrivial topological structure. In particular, we focus on the case where bosons are prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory about the initial state can have a dynamical instability, and we show that it is possible to achieve the interesting situation where the topological edge modes are unstable while all bulk modes are stable. Thus, after the initial preparation, the edge modes will become rapidly populated. We illustrate this with the Su-Schrieffer-Heeger model which can be realized with a double-well optical lattice and is perhaps the simplest model with topological edge states. This work provides a direct physical consequence of topological bands whose properties are often not of immediate relevance for the near-equilibrium properties of bosonic systems.

arXiv:1308.1972•Physical Review A•Dec 19, 2013•66 citations
In this Letter, it is shown that interactions can facilitate the emergence of topological edge states of quantum-degenerate bosonic systems in the presence of a harmonic potential. This effect is demonstrated with the concrete model of a hexagonal lattice populated by spin-one bosons under a synthetic gauge field. In fermionic or noninteracting systems, the presence of a harmonic trap can obscure the observation of edge states. For our system with weakly interacting bosons in the Thomas-Fermi regime, we can clearly see a topological band structure with a band gap traversed by edge states. We also find that the number of edge states crossing the gap is increased in the presence of a harmonic trap, and the edge modes experience an energy shift while traversing the first Brillouin zone which is related to the topological properties of the system. We find an analytical expression for the edge-state energies and our comparison with numerical computation shows excellent agreement.
We consider a system of interacting spin-one atoms in a hexagonal lattice under the presence of a synthetic gauge field. Quenching the quadratic Zeeman field is shown to lead to a dynamical instability of the edge modes. This, in turn, leads to a spin current along the boundary of the system which grows exponentially fast in time following the quench. Tuning the magnitude of the quench can be used to selectively populate edge modes of different momenta. Implications of the intrinsic symmetries of the Hamiltonian on the dynamics are discussed. The results hold for atoms with both antiferromagnetic and ferromagnetic interactions.
In this work, we consider the dynamics of bosons in bands with nontrivial topological structure. In particular, we focus on the case where bosons are prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory about the initial state can have a dynamical instability, and we show that it is possible to achieve the interesting situation where the topological edge modes are unstable while all bulk modes are stable. Thus, after the initial preparation, the edge modes will become rapidly populated. We illustrate this with the Su-Schrieffer-Heeger model which can be realized with a double-well optical lattice and is perhaps the simplest model with topological edge states. This work provides a direct physical consequence of topological bands whose properties are often not of immediate relevance for the near-equilibrium properties of bosonic systems.