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Bulletin of the American Physical Society

Topological Phase Transition with Cold Atoms Trapped in an Optical Lattice

Xiong-Jun Liu, Xin Liu, Congjun Wu, Jairo Sinova

Published Mar 17, 2010• 0 citations
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We present comparatively simple two-dimensional and three-dimensional checkerboardlike optical lattices possessing nontrivial topological properties accompanied by topological surface states. By simple tuning of the parameters, these lattices can have a topological insulating phase, a topological semimetallic phase, or a trivial insulating phase. This allows the study of different topological phase transitions within a single cold-atom system. In the topologically nontrivial phases, flat bands appear at the surfaces of the system. These surface states possess short localization lengths such that they are observable even in systems with small lattice dimensions.
With the rapid development of the laser cooling techniques, we can realize coherent quantum state manipulation of atoms. Invaluable results, such as topological phase transitions with artificial gauge fields, phase transitions induced by many body interaction, the atomic fountain frequency standard, the gravity constant using an interferometer, the magic wave optical lattice frequency standard, the cold ion frequency standard and the cold atom gravimeter and gyroscope results, have been obtained with respect to various applications, including quantum phase transitions, simulation of the novel quantum states, and precise measurement of the cold atoms. The laser cooling techniques frequently break the previous accuracy records; thus, they are gradually setting the new quantum measurement standards. In addition, some of these techniques play vital roles in geological prospecting and national defense. In this review, we will focus on the novel quantum states induced by laser cooling and the corresponding phase transitions as well as the optical detection and manipulation of the quantum phases. To be specific, the energy spectrum in a Bose-Einstein condensate (BEC) with spin-orbital angular momentum coupling is discrete, and a first-order phase transition can be observed between the states having different angular momentums. We investigated the topological phase transitions induced by the many-body interactions, in which we observed that when using different filling numbers and interactions, topological phase transitions can be observed in a hexagonal optical lattice with high orbitals and different topological states can be indexed using the Chern numbers. Further, based on our investigation, we observed the occurence of a quantum phase transition between the novel superfluid states, i.e., the Fulde-Ferrell-Larkin-Ovchinnikov superfluid states to the Sarma superfluid states, owing to the imbalanced Feshbach resonance. Finally, we developed methods to measure the optical spectrum of the nP Rydberg states of the 87Rb atoms and detect the quantum states in optical lattices; in addition, we constructed a multicomponent BEC interferometer.