There have been considerable research efforts devoted to quantum simulations of Fermi-Hubbard model with ultracold atoms loaded in optical lattices. In such experiments, the antiferromagnetically ordered quantum state has been achieved at half filling in recent years. The atomic lattice away from half filling is expected to host d-wave superconductivity, but its low temperature phases have not been reached. In a recent work, we proposed an approach of incommensurate quantum adiabatic doping, using quantum adiabatic evolution of an incommensurate lattice for preparation of the highly correlated many-body ground state of the doped Fermi-Hubbard model starting from a unit-filling band insulator. Its feasibility has been demonstrated with numerical simulations of the adiabatic preparation for certain incommensurate particle-doping fractions, where the major problem to circumvent is the atomic localization in the incommensurate lattice. Here we carry out a systematic study of the quantum adiabatic doping for a wide range of doping fractions from particle-doping to hole-doping, including both commensurate and incommensurate cases. We find that there is still a localization-like slowing-down problem at commensurate fillings, and that it becomes less harmful in the hole-doped regime. With interactions, the adiabatic preparation is found to be more efficient for that interaction effect destabilizes localization. For both free and interacting cases, we find the adiabatic doping has better performance in the hole-doped regime than the particle-doped regime. We also study adiabatic doping starting from the half-filling Mott insulator, which is found to be more efficient for certain filling fractions.
Universal magnetic energy scale in the doped Fermi-Hubbard model
Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；Fakultät für Physik, Ludwig-Maximilians-Universität（路德维希-马克西米利安大学物理学院）
Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics
最近在光晶格中的凝聚态模型的实验实现激发了对其非平衡行为的研究。基于有效BCS哈密顿量，已经对配对相互作用突然猝灭后超导体的动力学进行了预测;然而，它们的实验验证需要沿着双重约束制备哈伯德模型的合适激发态：（i）充分非绝热的斜坡方案对于激发非平衡动力学是必要的，以及（ii）必须避免超过超导性的临界温度的过热。对于通常讨论的相互作用斜坡，相应的能量尺度没有明确的分离。在这里，我们表明，这两个条件的匹配被简化的超冷费米子系统的内在弛豫行为：对于一个特殊的例子，我们检查的线性斜坡的预热化的瞬态制度[M。Moeckel和S. Kehrein，Phys. Rev. Lett. 100，175702（2008）]在使用Keldysh微扰理论从突然切换到绝热切换的交叉下。的动量分布的实时分析表现出早期的能量弛豫和后来的热化散射事件的时间分离。对于长但有限的斜升时间，该间隔可能很大。在预热化制度的动量分布类似于零温度费米液体的能量插入的斜坡仍然位于高能量模式。因此，超冷费米子被证明对加热具有鲁棒性，这简化了光晶格中非平衡BCS动力学的观察。
