Fig. 1. Level diagram of an OFR. An impurity atom in the state is immersed in a Fermi gas of alkaline-earth-like atoms in the state. and are the Zeeman shifts of the and manifolds, respectively. 类碱土金属原子中的OFR能级图. 杂质原子处于 态, 费米海处于 态. 通过相互作用, 杂质原子和费米海中原子会被散射到闭通道的两个态上. 和 是两个能级的塞曼移动

Fig. 2. (a), (b) The eigenenergy in the molecular state varies with and ; (c) the wave functions' distribution in the open and closed channels; (d) the effective mass for the molecular state whose energy is closed to the threshold energy when . Reproduced from Ref. [23]. (a), (b) 分子态的能量随 和 的变化; (c) 分子态的波函数分布情况; (d) 接近阈值能量 的分子态, 在 时的有效质量. 引自参考文献[23]

Fig. 3. (a), (b) The eigenenergy in the attractive polaron state varies with and ; (c) the wave functions' distribution in the open and closed channels; (d) the effective mass for the attractive polaron state when . Parameters here are the same as those in Fig. 2. Reproduced from Ref. [23]. (a), (b) 吸引极化子态的能量随 和 的变化; (c) 吸引极化子态的波函数分布情况; (d) 吸引极化子态在 时的有效质量, 图中发散点为 , 对应于 . 图中参数与图2中一致. 引自参考文献[23]

Fig. 4. (a), (b) The eigenenergy of the molecule (black solid) and polaron (blue dashed) states vary with and . The transition point is around and ; (c) the transition point (black solid) and the corresponding energy (red solid) vary with particle density. Reproduced from Ref. [23]. (a), (b) 分子态(黑色实线)和吸引极化子态(蓝色虚线)的本征能量随 和 的变化, 吸引极化子态到分子态的转变发生在 和 处; (c) 转变点 (黑色实线)和对应的转变能量 (红色实线)随粒子数密度的变化. 引自参考文献[23]

Fig. 5. The spectral function of the polaron state as a function of and energy for . The red solid line represents the energy of molecule state, which is given by Eq. (8), and the black dashed-dotted line is the energy of attractive polaron state given by Eq. (11). The value of the crossing point for these two lines is . The blue dashed line denotes the repulsive polaron energy given by Eq. (15). At large negative , the branch of repulsive polaron merges into the molecule-hole continuum, which is represented by the broad light yellow area. When is a positive value, because of the closed channel scattering continuum, the repulsive polaron branch will be blurred. Reproduced from Ref. [30]. 极化子态的谱函数 随 和能量变化的彩色图. 图中红色实线表示分子态能量, 由(8)式计算得到. 黑色点划线为吸引极化子态能量, 由(11)式计算得到. 两条线相交于 处. 图中蓝色虚线代表排斥极化子能量, 由(15)式得到. 当 为较大负值时, 排斥极化子与图中由浅黄色区域代表的粒子-空穴连续区域重合. 当 大于零时, 由于存在闭通道散射, 排斥极化子分支会变得模糊. 引自参考文献[30]

Fig. 6. (a), (b) Quasiparticle residues and effective masses for the attractive (blue dashed) and repulsive (red solid) polarons as functions of ; (c) the decay rate varies with . Reproduced from Ref. [65]. (a), (b) 极化子态的准粒子残余和有效质量随 的变化, 其中红色实线对应排斥极化子态, 蓝色虚线对应吸引极化子态; (c) 排斥极化子态的衰变率随 的变化. 引自参考文献[65]

Fig. 7. Level diagram of an OFR, which has two fermi seas. An impurity atom in the state is immersed in a Fermi gas of alkaline-earth-like atoms in the and states. and are the Zeeman shifts of the and manifolds, respectively. 双费米面情况下, 类碱土金属原子的OFR能级图. 杂质原子处于 态, 费米海处于 态和 态. 通过相互作用, 杂质原子和费米海中原子会被散射到闭通道的两个态上. 和 是两个能级的塞曼移动

Fig. 8. The eigen energies of molecule and attractive polaron states vary with when and (a) , (b) , (c) ; (d) the transition point varies with , where the black solid line represents and the red dashed-dotted line is the Fermi level . Reproduced from Ref. [30]. 质心动量为零, ((a)), ((b)), ((c))时, 分子态和吸引极化子态的本征能量随 的变化; (d) 吸引极化子态到分子态的转变点随 的变化, 其中, 黑色实线为计算得到的转变点, 红色点划线为费米能级 . 引自参考文献[30]

Fig. 9. The fractions of wave functions for molecule ((a), (c)) and attractive polaron states ((b), (d)) with zero center-of-mass momentum. The parameter in this figure is for (a) and (b), for (c) and (d). Reproduced from Ref. [30]. (a), (c) 分子态的波函数分布情况; (b), (d) 吸引极化子态的波函数分布, 此时质心动量为零. (a)和(b)中, , (c)和(d)中, . 引自参考文献[30]

Fig. 10. (a), (b) The quasiparticle residue and the effective mass vary with for different values of . The obvious kink structure when appears near . The inset of (a) is the residues for attractive polarons; (c) the decay rates vary with for different values of . Reproduced from Ref. [30]. (a), (b) 在 等于不同值时, 排斥极化子态的准粒子残余和有效质量随 的变化情况. 图(a)中的插图描绘了吸引极化子态的准粒子残余随 的变化情况. 图中, 当 时出现的非解析行为发生在 处; (c) 排斥极化子态的衰变率 在 等于不同值时随 的变化情况. 引自参考文献[30]

Fig. 11. The eigen energies of molecule and attractive polaron states vary with when in a two-dimensional system and (a) , (b) , (c) ; (d) the transition point varies with , where the black solid line represents and the red dashed line is the Fermi level . (a)-(c) 二维系统中, 质心动量为零, ((a)), ((b)), ((c))时, 分子态和吸引极化子态的本征能量随 的变化; (d) 吸引极化子态到分子态的转变点随 的变化, 其中黑色实线为计算得到的转变点, 红色虚线为费米能级

Fig. 12. The decay rates of the repulsive polaron state in a a two-dimentional system vary with for different values of . 二维系统中 等于不同值时排斥极化子态的衰变率 随 的变化情况