Fig. 1. (a) The ultracold fermions are trapped in a quasi-one-dimensional background optical lattice along the cavity axis . These fermions are pumped by two circular-polarized transverse (along ) lasers and the cavity mode is driven by a linear-polarized longitudinal (along ) laser. (b) the atomic energy levels and their transition. See main text for the corresponding transition processes and the definition of the labels. (a)超冷费米气沿着腔轴 方向被俘获在准一维背景光学晶格中, 费米气被两束圆偏振的横向(沿着 方向)抽运激光驱动, 腔模由一束线偏振的纵向(沿着 方向)驱动光驱动; (b)费米子的能级跃迁图, 图中相关的跃迁过程和符号的定义见正文

Fig. 2. (a) The cavity field for systems in different fillings with . The plotted parameters are chosen as , , , , and . (b) the cavity field for systems in different fillings with . The plotted parameters are chosen as , , , , and . We consider a lattice of sites 80 with different fillings. a)蓝失谐的情况 , 光场 在不同的晶格填充下随耦合强度 的变化. 图中其他参数的选择: , , , 和 ; (b)红失谐的情况 , 光场 在不同的晶格填充下随耦合强度 的变化. 图中其它参数的选择: , , , 和 . 我们考虑的具有80个格点的晶格对应不同的填充, 其中k_F/E_R不同的值对应不同的填充, k_F为费米动量

Fig. 3. The spin structure factors for systems in different fillings: (a) ; (b) ; (c) (The plotted parameters are the same as those in Fig. 2(a)). 静态自旋结构因子 　(a) ; (b) ; (c) . (图中对应的其它参数的选择与图2(a)中一致)

Fig. 4. The spin structure factors for systems in different fillings: (a) ; (b) ; (c) (The plotted parameters are the same as those in Fig. 2(b)). 静态自旋结构因子 　(a) ; (b) ; (c) (图中对应的其他参数的选择与图2(b)中一致)

Fig. 5. (a) The phase diagram in the plane for the system with blue-detuned atomic detuning (M, AF-SR, and FM-SR correspond to metallic phase, antiferromagnetic superradiant phase, and ferromagnetic superradiant phase, respectively. The plotted parameters are the same as those in Fig. 2(a)); (b) the phase diagram in the plane for the system with red-detuned atomic detuning (AF-SR corresponds to the antiferromagnetic superradiant phase. The plotted parameters are the same as those in Fig. 2(b)). (a)蓝失谐时 平面上的相图(M, AF-SR和FM-SR分别代表金属相、反铁磁关联的超辐射相和铁磁关联的超辐射相, 其它参数的选择与图2(a)相同); (b)红失谐时 平面上的相图(AF-SR代表反铁磁关联的超辐射相, 对应的其他参数的选择与图2(b)中一致)