超冷费米气体中与$s$波相互作用的球自旋轨道耦合的Rashbon束缚态
Rashbon bound states associated with a spherical spin-orbit coupling in an ultracold Fermi gas with an $s$-wave interaction
摘要：
研究了具有球形自旋轨道相互作用的超冷费米气体$H_{\rm so}=λ{\bf p}\cdot{\bf σ}$（其中${\bf σ}=(σ_x,σ_y,σ_z)$为泡利矩阵）中拉希邦束缚态的形成和强耦合效应.将Nozières和Schmitt-Rink（NSR）的强耦合理论扩展到包括这种自旋-轨道耦合，我们确定了超流相变温度$T_{\rm c}$，作为配对相互作用强度$U_s$以及自旋-轨道耦合强度$λ$的函数。通过计算描述Cooper通道波动的NSR粒子-粒子散射矩阵的极点，我们澄清了$U_{s}$ - $λ$相图中Rashbon束缚态主导超流相变的区域。由于反对称自旋轨道相互作用$H_{\rm so}$破坏了系统的反转对称性，因此，Rashbon束缚态自然不仅具有自旋单重态和偶宇称对称性，而且具有自旋三重态和奇宇称对称性。因此，我们的结果也将是有用的研究这种宇称混合效应在BCS-BEC交叉区的自旋-轨道耦合费米气体。
英文摘要：
We investigate the formation of rashbon bound states and strong-coupling effects in an ultracold Fermi gas with a spherical spin-orbit interaction, $H_{\rm so}=λ{\bf p}\cdot{\bf σ}$ (where ${\bf σ}=(σ_x,σ_y,σ_z)$ are Pauli matrices). Extending the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR) to include this spin-orbit coupling, we determine the superfluid phase transition temperature $T_{\rm c}$, as functions of the strength of a pairing interaction $U_s$, as well as the spin-orbit coupling strength $λ$. Evaluating poles of the NSR particle-particle scattering matrix describing fluctuations in the Cooper channel, we clarify the region where rashbon bound states dominate the superfluid phase transition in the $U_{s}$-$λ$ phase diagram. Since the antisymmetric spin-orbit interaction $H_{\rm so}$ breaks the inversion symmetry of the system, rashbon bound states naturally have, not only a spin-singlet and even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus, our results would be also useful for the study of this parity mixing effect in the BCS-BEC crossover regime of a spin-orbit coupled Fermi gas.
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