Phases and phase transitions of quantum gases on optical lattices

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TECHNICAL SUMMARYThis award supports theoretical research in condensed matter and quantum many body theory, concentrating on phases and phase transitions which are difficult to realize in materials but may be possible to realize with cold atoms in optical lattice traps.Cold atomic systems can emulate the behavior of electrons and atoms in real materials. They can be used to create atomic counterparts of known condensed matter phenomena, or to study yet unexplored and undiscovered new states of matter. Feshbach resonances allow real-time tuning of interactions among the atoms, while optical lattices emulate crystalline lattices through which electrons typically move in real materials. These tools were used separately in the past to create atomic analogs of superfluids with variable interaction strength and atomic equivalents of phases of condensed matter systems possible on a lattice, such as Mott insulators. The PI will investigate the outcome of combining the two tools. It is expected that atomic systems placed in optical lattices whose interactions are controlled by Feshbach resonances will exhibit a variety of phases and phase transitions among them, including superfluids, band and Mott insulators, topological superfluids at high transition temperature, and new types of topological phase transitions, as well as unusual one dimensional phases. The PI will focus on the following issues. Fermionic atoms moving in three-dimensional optical lattices in the presence of Feshbach resonances can form states such as a paired superfluid, a band insulator and molecular Mott insulators. Precise phase diagrams encompassing these phases will be worked out. In two-dimensional optical lattices, topological superfluids can arise if one works with p-wave Feshbach resonances. When placed in optical lattices, transitions among various topological superfluids are possible, in a phase diagram which is expected to be rich and lead to more stable topological superfluids. The PI will investigate whether and how this happens. The PI will use a variety of methods to explore whether new phases occur in one dimensional lattices. These include the Fulde-Ferrell-Larkin-Ovchinnikov state as well as unusual states with decoupled quasicondensates. The PI will also study topological insulators which can be created with the ultracold atoms placed in lattices with topological band structure. The PI aims to find unconventional insulators which were not observed in materials. These can be obtained with the help of a variety of spin-orbit coupling techniques developed in the field. Different setups for these insulators will be investigated theoretically.The PI will educate students across institutions through the Boulder Summer School on Condensed Matter and Materials Physics and other summer school activities within the United states and abroad.NONTECHNICAL SUMMARY This award supports theoretical research and education with the aim to study matter and new phases of matter that arise in systems of many interacting atoms or electrons. Not all phases investigated theoretically have been or can be found in real materials because of difficulties in controlling the environment of the electrons or because they require special types of interactions that are difficult or impossible to realize through electrons in materials. Cold atoms trapped in lattices of laser light offer a way to simulate existing materials and create new states of matter. Atoms, whose interactions can be controlled in real time, can be trapped in an optical lattice created by lasers, cooled to very low temperatures, and made to behave like electrons do in solids or as hypothetical particles in theoretical models. The results of these 'simulations' can then be used to guide investigations seeking new states of matter in materials. This research will focus on studying the phases of cold atoms in optical lattices in the presence of strong interactions. The interplay of the interaction of atoms with the lattices formed by lasers and the interaction of atoms with each other, gives rise to a variety of states of matter. The PI will develop a kind of 'roadmap' showing which phases are possible for given interaction strengths. Some of the most exciting phases possible in lattices are topological insulators, some of which have been observed in materials made of, for example the elements bismuth and selenium. However many more types of topological insulator are predicted but have not yet been observed in materials. This research will explore ways to make them with cold atoms. The PI will educate students across institutions through the Boulder Summer School on Condensed Matter and Materials Physics and other summer school activities within the United states and abroad.