Recently, the statistical effect of fermionic superradiance is approved by series of experiments both in free space and in a cavity. The Pauli blocking effect can be visualized by a 1/2 scaling of Dicke transition critical pumping strength against particle number Nat for fermions in a trap. However, the Fermi surface nesting effect, which manifests the enhancement of superradiance by Fermi statistics is still very hard to be identified. Here we studied the influence of localized fermions on the trap edge when both pumping optical lattice and the trap are presented. We find due to localization, the statistical effect in superradiant transition is enhanced. Two new scalings of critical pumping strength are observed as 4/3, and 2/3 for mediate particle number, and the Pauli blocking scaling 1/3 (2d case) in large particle number limit is unaffected. Further, we find the 4/3 scaling is subject to a power law increasing with rising ratio between recoil energy and trap frequency in pumping laser direction. The divergence of this scaling of critical pumping strength against $N_{\rm at}$ in $E_R/\omega_x\rightarrow+\infty$ limit can be identified as the Fermi surface nesting effect. Thus we find a practical experimental scheme for visualizing the long-desired Fermi surface nesting effect with the help of trap induced localization in a two-dimensional Fermi gas in a cavity.

中文翻译：

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通过陷阱诱导局域化检测费米子 Dicke 跃迁的费米面嵌套效应

最近，费米子超辐射的统计效应被自由空间和空腔中的一系列实验所证实。泡利阻塞效应可以通过 Dicke 跃迁临界泵浦强度对陷阱中费米子的粒子数 Nat 的 1/2 缩放来可视化。然而，费米统计表明超辐射增强的费米面嵌套效应仍然很难被识别。在这里，我们研究了当同时存在泵浦光学晶格和陷阱时局部费米子对陷阱边缘的影响。我们发现由于局域化，超辐射跃迁的统计效果得到了增强。观察到临界泵送强度的两个新标度为 4/3，中间粒子数为 2/3，大粒子数限制中的 Pauli 阻塞标度 1/3（2d 情况）不受影响。此外，我们发现 4/3 缩放比例服从幂律，随着泵浦激光方向上反冲能量与陷阱频率之间比率的增加而增加。在 $E_R/\omega_x\rightarrow+\infty$ 极限中，临界泵浦强度与 $N_{\rm at}$ 的差异可以被识别为费米面嵌套效应。因此，我们找到了一种实用的实验方案，可以借助空腔中的二维费米气体中的陷阱诱导局域化来可视化长期需要的费米表面嵌套效应。在 $E_R/\omega_x\rightarrow+\infty$ 极限中，临界泵浦强度与 $N_{\rm at}$ 的差异可以被识别为费米面嵌套效应。因此，我们找到了一种实用的实验方案，可以借助空腔中的二维费米气体中的陷阱诱导局域化来可视化长期需要的费米表面嵌套效应。在 $E_R/\omega_x\rightarrow+\infty$ 极限中，临界泵浦强度与 $N_{\rm at}$ 的差异可以被识别为费米面嵌套效应。因此，我们找到了一种实用的实验方案，可以借助空腔中的二维费米气体中的陷阱诱导局域化来可视化长期需要的费米表面嵌套效应。