Wang Ce, Liu Chang, Shi Zhe-Yu
Institute for Advanced Study, Tsinghua University, Beijing 100084, China.
School of Physics Science and Engineering, Tongji University, Shanghai 200092, China.
Phys Rev Lett. 2022 Nov 11;129(20):203401. doi: 10.1103/PhysRevLett.129.203401.
The concept of contact interaction is fundamental in various areas of physics. It simplifies physical models by replacing the detailed short-range interaction with a zero-range contact potential that reproduces the same low-energy scattering parameter, i.e., the s-wave scattering length. In this Letter, we generalize this concept to open quantum systems with short-range two-body losses. We show that the short-range two-body losses can be effectively described by a complex scattering length. However, in contrast to closed systems, the dynamics of an open quantum system is governed by the Lindblad master equation the includes a non-Hermitian Hamiltonian as well as an extra recycling term. We thus develop proper methods to regularize both terms in the master equation in the contact (zero-range) limit. We then apply our regularized complex contact interaction to study the dynamic problem of a weakly interacting and dissipating Bose-Einstein condensate. It is found that the physics is greatly enriched because the scattering length is continued from the real axis to the complex plane. For example, we show that a strong dissipation may prevent an attractive Bose-Einstein condensate from collapsing. We further calculate the particle decay in this system to the order of (density)^{3/2} which resembles the celebrated Lee-Huang-Yang correction to the ground state energy of interacting Bose gases [Lee and Yang, Phys. Rev. 105, 1119 (1957)PHRVAO0031-899X10.1103/PhysRev.105.1119; Lee, Huang, and Yang, Phys. Rev. 106, 1135 (1957)PHRVAO0031-899X10.1103/PhysRev.106.1135]. Possible methods for tuning the complex scattering length in cold atomic gas experiments are also discussed.
接触相互作用的概念在物理学的各个领域都至关重要。它通过用零程接触势取代详细的短程相互作用来简化物理模型，该接触势能再现相同的低能散射参数，即s波散射长度。在本信函中，我们将这一概念推广到具有短程两体损耗的开放量子系统。我们表明，短程两体损耗可以用复散射长度有效描述。然而，与封闭系统不同，开放量子系统的动力学由林德布拉德主方程支配，该方程包含一个非厄米哈密顿量以及一个额外的再循环项。因此，我们开发了适当的方法来在接触（零程）极限下对主方程中的这两项进行正则化。然后，我们应用正则化的复接触相互作用来研究弱相互作用且耗散的玻色 - 爱因斯坦凝聚体的动力学问题。结果发现，由于散射长度从实轴延续到复平面，物理现象大大丰富了。例如，我们表明强耗散可能会阻止吸引性玻色 - 爱因斯坦凝聚体坍缩。我们进一步计算了该系统中粒子衰变到（密度）^{3/2}阶，这类似于著名的李 - 黄 - 杨对相互作用玻色气体基态能量的修正[李和杨，《物理评论》105，1119（1957年）PHRVAO0031 - 899X10.1103/PhysRev.105.1119；李、黄和杨，《物理评论》106，1135（1957年）PHRVAO0031 - 899X10.1103/PhysRev.106.1135]。还讨论了在冷原子气体实验中调节复散射长度的可能方法。
