Engineering non-equilibrium material states with cold atoms in optical cavities

A triumph of 20th century condensed matter physics is the understanding of the phases of matter, arising from interacting many body problems in thermal equilibrium. However, not all matter is in equilibrium, and the understanding of matter out of equilibrium is far less developed. To develop our understanding of this, it is necessary both to develop new theoretical techniques, and to identify clean experimental systems where these approaches can be tested against known problems. Ultracold atoms have provided an excellent testbed for simulating canonical models in equilibrium, and can be adapted to probe non-equilibrium physics. In particular, ultracold atoms placed in optical cavities can be used to prepare and control non-equilibrium states of matter. Specifically, these experiments involve driving by scattering a pump laser into the optical cavity, leading to cavity mediated interactions between atoms, accompanied with collective dissipation processes. While experiments on atoms single mode cavities have been studied extensively, experiments on multimode cavities are only just beginning. These have the potential to transform the kinds of behaviour one can study. Our theoretical group collaborates closely with the experimental group of Benjamin Lev (Stanford) who have built a multimode optical cavity[1,2], and are now in the position to use this to explore novel states of matter. Several ideas in this direction have been proposed[3,4,5], including liquid crystaline phases of matter[3], spin glass states [4] and Hopfiled associative memories[5]. However, understanding of the non-equilibrium nature of these phases is yet unclear. This PhD will explore a number of these topics; we will work in close collaboration with the Lev group in Stanford, so the precise projects will be determined in order to match ongoing and future experiments. We will make use of a variety of analytical and numerical techniques, potentially including matrix product state calculations. [1] "Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED", V. D. Vaidya, Y. Guo, R. M. Kroeze, K. E. Ballantine, A. J. Kollár, J. Keeling, and B. L. Lev, Phys. Rev. X 8 011002 (2018) [2] "Sinor self-ordering of a quantum gas in a cavity." R. M. Kroeze, Y. Guo, V. D. Vaidya, J. Keeling, B. L. Lev, Phys. Rev. Lett. 121 163601 (2018) [3] "Emergent Crystallinity and Frustration with Bose-Einstein Condensates in Multimode Cavities", S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Nat. Phys. 5, 845 (2009). [4] "Frustration and Glassiness in Spin Models with Cavity-Mediated Interactions." S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Phys. Rev. Lett. 107, 277201 (2011). [5] "Exploring Models of Associative Memory via Cavity Quantum Electrodynamics", S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Philos. Mag. 92, 353 (2012).