具有动量相关增益和损耗的宇称时间对称系统中的虚自旋轨道耦合
Imaginary spin-orbital coupling in parity-time symmetric systems with momentum-dependent gain and loss
摘要：
自旋-轨道耦合（SOC）和宇称-时间（$\mathcal{PT}$）对称性在凝聚态物理、冷原子物理、光学和声学等领域都引起了极大的研究兴趣，以发展自旋电子学、量子计算、精密传感器和新功能。自然SOC是一种内在的相对论效应。然而，现在对合成SOC的兴趣越来越大。在$\mathcal{PT}$对称自旋为1/2的系统中，动量相关的平衡增益和平衡损耗可以合成一种新的SOC，我们称之为虚SOC，虚SOC可以显著改变系统的能谱.首先，我们证明了它可以产生具有双谷结构的纯实能谱。因此，它具有产生超固体条纹态的能力。特别地，虚SOC条纹状态可以具有高对比度1。此外，虚SOC还可以产生具有可调谐复能带的谱，其中波是放大的或衰减的。因此，虚SOC也将在基于$\mathcal{PT}$的相干波放大器/吸收器的工程中找到应用。提出了在冷原子气体和非局域增益和损耗耦合波导系统中实现虚SOC的可能实验方案。
英文摘要：
Spin-orbital coupling (SOC) and parity-time ($\mathcal{PT}$) symmetry both have attracted paramount research interest in condensed matter physics, cold atom physics, optics and acoustics to develop spintronics, quantum computation, precise sensors and novel functionalities. Natural SOC is an intrinsic relativistic effect. However, there is an increasing interest in synthesized SOC nowadays. Here, we show that in a $\mathcal{PT}$-symmetric spin-1/2 system, the momentum-dependent balanced gain and loss can synthesize a new type of SOC, which we call imaginary SOC. The imaginary SOC can substantially change the energy spectrum of the system. Firstly, we show that it can generate a pure real energy spectrum with a double-valleys structure. Therefore, it has the ability to generate supersolid stripe states. Especially, the imaginary SOC stripe state can have a high contrast of one. Moreover, the imaginary SOC can also generate a spectrum with tunable complex energy band, in which the waves are either amplifying or decaying. Thus, the imaginary SOC would also find applications in the engineering of $\mathcal{PT}$-symmetry-based coherent wave amplifiers/absorbers. Potential experimental realizations of imaginary SOC are proposed in cold atomic gases and systems of coupled waveguides constituted of nonlocal gain and loss.
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