现有的低温原子气体的研究大多局限于原子间短程相互作用的框架内。将低温原子气体载人谐振腔中，有望通过谐振腔中腔光子作为媒介实现原子间的长程相互作用。这种原子与谐振腔中光场的强耦合已在实验上发现的谐振腔中BEC的超辐射现象中展现出奇妙的效应。我们随即对谐振腔中单分量费米气体的理论研究揭示费米子和玻色子的不同的量子统计决定了不同的超辐射转变条件。本项目将研究谐振腔中两分量费米气体的超辐射转变。我们将重点研究分量间的相互作用在BEC-BCS crossover中对超辐射转变条件的影响。我们还将确定在什么样的实验参数空间里，费米子的自旋自由度能和腔光场强耦合在一起，从而研究由自旋关联驱使的超辐射转变。

Current research in cold atomic gases is mostly restricted within the frame that atoms are interacting through short range potentials. Loading atomic gases into cavities has the potential of realizing long range atomic interactions mediated by cavity light fields. The strong coupling between atoms and cavity light fields has manifested interesting effects in the experiments of the superradiance of BEC loaded in cavities. Our subsequent theoretical study of a Fermi gas of a single species in cavities has revealed that quantum statistics between fermions and bosons gives rise to difference in the condition for superradiance transition. Present proposal plans to study the superradiance transition in a two-component Fermi gas. We will focus on the atomic interaction effects between the two components through the BEC-BCS crossover on the transition. We will also determine the experimentally relevant parameter regime where strong coupling between the cavity light fields and the atomic spin degree of freedom can be realized. Sequentially we will study the superradiance transition driven by the spin correlation of the Fermi gas.