Abstract

Classical soft-matter systems exhibit a wealth of spatially ordered states (e.g., liquid crystals and quasicrystals), while solid-state quantum systems offer a similar variety of internal ordering (e.g., magnetism and superfluidity). I shall describe how ultracold atomic systems can be induced, via dispersion-engineering [1], to develop both forms of order at once—giving rise to quantum crystalline, liquid-crystalline, and quasicrystalline states [2]—and how these “intertwined-order” states support hybrid spatial and internal defects (in particular, vortices bound to disclinations), the unbinding of which gives rise to novel two-dimensional melting transitions [3]. If time permits, I will discuss realizations of states with “vestigial” order [4] in cold-atom systems coupled to optical cavities [5].

[1] S. Gopalakrishnan, C.V. Parker, and E. Demler, Phys. Rev. Lett. 114, 045301 (2015)

[2] S. Gopalakrishnan, I. Martin, and E. Demler, Phys. Rev. Lett. 111, 185304 (2013)

[3] S. Gopalakrishnan, J.C.Y. Teo, and T.L. Hughes, Phys. Rev. Lett. 111, 025304 (2013)

[4] L. Nie, G. Tarjus, and S.A. Kivelson. PNAS 111 , 7980 (2014)

[5] S. Gopalakrishnan and E. Demler (in preparation)