This project combines research and educational activities in several areas of theoretical ultracold atomic physics, focusing on the superfluid properties of cold atoms. Superfluidity is a novel quantum phase of matter, usually occurs at very low temperatures, in which particles flow without friction. The same physics also underlines the mechanism of superconductors. Ultracold atoms offer an ideal platform to study this quantum phenomenon. Particles in nature, being fundamental or composite, can be categorized into two classes --- bosons or fermions --- depending on whether their spin is integer or half integer. Both kinds can become superfluid under proper conditions. However, the properties and formation mechanisms of bosonic and fermionic superfluids differ greatly. The goal of this project is to investigate the novel properties of bosonic and fermionic superfluids, as well as their mixtures, in the context of ultracold atoms.
This research project is both of fundamental importance and of great relevance to current experiments in the field of cold atoms. They serve the purpose of providing theoretical guidance and support to cold atom experiments. The specific topics to be explored span a wide spectrum of fundamental problems in the field of cold atoms with close ties to solid state physics. These studies will shed new light on many outstanding problems in superconductors which are materials of technological significance. Students and postdoctoral fellows involved in this research will receive a solid training in theoretical cold atom physics which will be very valuable for their future career in science and engineering.
During this NSF grant period (7/1/2009 ~ 6/30/2012), my group have continued working in the field of theoretical ultracold atomic physics. This is an exciting field which explores various interesting behavior that atoms or molecules display when cooled to very low temperatures, a regime ruled by the laws of quantum mechanics. Our main focus is the properties of ensembles of ultracold atoms manipulated by external fields such as lasers, electromagnetic fields, etc. Atomic systems are particularly amenable to exquisite control. For example, one can easily control their effective spatial dimension by confine them in properly designed atom traps. This allows us to explore the physics of low-dimensional systems in which quantum effects are usually more pronounced. Our theoretical work is closely connected to the experimental efforts within our community. In addition, studies of ultracold atoms help us to gain crucial insights into other systems such as solid state superconductors, nuclear matters, etc., as a wonderful manifestation of the universality of the physics. These other systems are usually much more difficult to manipulate and study in the lab. The main outcomes of this research include the following: (1) We have investigated the properties of a polarized Fermi gas, i.e., a two-component Fermi gas with unequal population in its constituent components. The motivation of this problem goes all the way back to the 1960's when people were pondering the effects of a magnetic impurity on the superconductors. Such magnetic impurities tend to break the population balance of the spin-up and spin-down electrons that are paired to give rise to superconductivity. It was conjectured that a strong enough magnetic impurity will destroy the conventional superconductivity and may lead to more exotic superconductor states. The search for these novel states in solid materials turns out to be inconclusive. Cold atoms, due to their controllability, may be a much more suitable system to support such novel states. We have closely worked with our experimental colleagues (group led by Prof. Randy Hulet) and investigated the possibility of novel states in polarized Fermi gases. We have pointed out under what condition the novel states are favored and how they can be detected in the experiment. The experimental work on finding such states are still ongoing. (2) Unlike charged particles, neutral atoms do not respond directly to external electric or magnetic fields. However, by properly arranging the laser fields, artificial electric or magnetic fields can be created for neutral atoms. In other words, neutral atoms can be made to respond to laser fields just like charged particles respond to electric/magnetic fields. Furthermore, one can create more elaborate artificial fields which couple the internal dynamics of the atoms with their external center-of-mass motion (the so-called spin-orbit coupling). Ultracold atoms subject to spin-orbit coupling exhibits many novel properties. In particular, spin-orbit coupling in cold atoms may lead to new quantum states that do not appear anywhere else in nature. Our theoretical investigation of spin-orbit coupled atomic gases have provided new insights into this intriguing system. (3) We have studied properties of atomic Bose-Einstein condensate confined inside an optical cavity. The cavity supports very weak light fields that consists only a few photons. The atomic condensate behaves like a nonlinear dispersive medium to the photons, and the photons on the other hand, shift the internal levels of the atom. Through this mutual influence, the dynamics of the atoms and the photons are intimately coupled together which leads to interesting nonlinear behavior in both atomic and photonic fields.
