Superfluid Atomic Bosons, Fermions and Their Mixtures

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The field of ultracold atomic physics has been progressing rapidly without signs of slowing down. Under this award, we will carry out a theoretical study of several important problems concerning the superfluid properties of cold atoms. These projects are of fundamental importance, and in the meantime are inspired by recent experimental progress in the field. We will consider the properties of cold atomic ensembles whose effective spatial dimensions in which they live are tuned. A tunable spatial dimension is not readily achievable in other materials. But for cold atoms, by adjusting the geometry of the trapping potential that is used to confine them, such a feat can be realized in the lab. We will also consider the novel properties of cold atoms under the manipulation of appropriately arranged laser fields. Under proper conditions, the laser beams can induce synthetic electromagnetic fields such that the neutral atoms behave like charged particles moving in electric and/or magnetic fields. These research projects are of great relevance to current experiments, some of which are being carried out by PI's colleagues at Rice University. These problems span a quite wide spectrum within the field of cold atoms with close ties to condensed matter physics and nonlinear physics. Students involved in these projects will receive a solid training in theoretical physics, including both analytical methods and numerical techniques. Such a training will be very valuable for their future career in science and engineering.