# Topological matter in AMO systems

Topological phases, such as fractional quantum Hall states, are phases with no local order parameter and are instead characterized by more exotic quantities such as peculiar entanglement properties. The interest in topological phases stems to a large degree from the exotic nature of excitations in such systems, which not only carry fractional charge but also obey unusual statistics: when two such excitations, called anyons, are exchanged, they - in contrast to fermions that pick up a phase of π - can pick up a phase that can be a fraction of π. What is even more exotic is that certain topological phases have excitations that map the manybody wavefunction from one orthogonal state to another under exchange - such non-abelian anyons can be used to realize the dream of fault-tolerant topological quantum computation, which is intrinsically robust to errors. We are interested in finding ways to prepare topological states in AMO systems and study them in and out of equilibrium.

## Review:

- C. Nayak, S. Simon, A. Stern, M. Freedman, and S. Das Sarma,
**Non-Abelian anyons and topological quantum computation**,

Rev. Mod. Phys. 80, 1083 (2013); arXiv:0707.1889 [cond-mat.str-el].

## Some recent examples of our work:

- S. Ganeshan, A. V. Gorshkov, V. Gurarie, V. M. Galitski,
**Exactly soluble model of boundary degeneracy**,

arXiv:1604.02089 [cond-mat.str-el]. - Z.-X. Gong, M. F. Maghrebi, A. Hu, M. Foss-Feig, P. Richerme, C. Monroe, A. V. Gorshkov,
**Kaleidoscope of quantum phases in a long-range interacting spin-1 chain**,

Phys. Rev. B 93, 205115 (2016); arXiv:1510.02108 [cond-mat.str-el]. - Z.-X. Gong, M. F. Maghrebi, A. Hu, M. L. Wall, M. Foss-Feig, and A. V. Gorshkov,
**Topological phases with long-range interactions**,

Phys. Rev. B 93, 041102(R) (2016); arXiv:1505.03146 [cond-mat.quant-gas]. - N. Y. Yao, S. D. Bennett, C. R. Laumann, B. L. Lev, and A. V. Gorshkov,
**Bilayer fractional quantum Hall states with ultracold dysprosium**,

Phys. Rev. A 92, 033609 (2015); arXiv:1505.03099 [cond-mat.quant-gas]. - M. F. Maghrebi, S. Ganeshan, D. J. Clarke, A. V. Gorshkov, J. D. Sau,
**Parafermionic zero modes in ultracold bosonic systems**,

Phys. Rev. Lett. 115, 065301 (2015); arXiv:1504.04012 [cond-mat.quant-gas]. - M. F. Maghrebi, N. Y. Yao, M. Hafezi, T. Pohl, O. Firstenberg, and A. V. Gorshkov,
**Fractional Quantum Hall States of Rydberg Polaritons**,

Phys. Rev. A. 91, 033838 (2015); arXiv:1411.6624 [cond-mat.quant-gas]. - D. Vodola, L. Lepori, E. Ercolessi, A. V. Gorshkov, and G. Pupillo,
**Kitaev chains with long-range pairing**,

Phys. Rev. Lett. 113, 156402 (2014); arXiv:1405.5440 [cond-mat.str-el]. - A. V. Gorshkov, K. R. A. Hazzard, and A. M. Rey,
**Kitaev honeycomb and other exotic spin models with polar molecules**,

Mol. Phys. 111, 1908 (2013); arXiv:1301.5636 [cond-mat.quant-gas]. - N. Y. Yao, A. V. Gorshkov [co-first author], C. R. Laumann, A. Lauchli, J. Ye, and M. D. Lukin,
**Realizing Fractional Chern Insulators with Dipolar Spins**,

Phys. Rev. Lett. 110, 185302 (2013); arxiv:1212.4839 [cond-mat.str-el]. Physics Viewpoint. - S. R. Manmana, E. M. Stoudenmire, K. Hazzard, A. M. Rey, and A. V. Gorshkov,
**Topological phases ultracold in polar-molecule quantum magnets**,

Phys. Rev. B 87, 081106(R) (2013); arxiv:1210.5518 [cond-mat.quant-gas]. - N. Y. Yao, C. R. Laumann, A. V. Gorshkov, H. Weimer, L. Jiang, J. I. Cirac, P. Zoller, M. D. Lukin,
**Topologically protected quantum state transfer in a chiral spin liquid**,

Nature Commun. 4, 1585 (2013); arXiv:1110.3788 [quant-ph]. - N. Y. Yao, C. R. Laumann, A. V. Gorshkov [co-first author], S. D. Bennet, E. Demler, P. Zoller, and M. D. Lukin,
**Topological Flat Bands from Dipolar Spin Systems**,

Phys. Rev. Lett. 109, 266804 (2012); arxiv:1207.4479 [quant-ph]. - L. Jiang, G. K. Brennen, A. V. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M.D. Lukin, P. Zoller,
**Anyonic interferometry and protected memories in atomic spin lattices**,

Nature Phys. 4, 482 (2008); http://arxiv.org/abs/0711.1365 [quant-ph].