关联超流体中的赝能隙相变研究

This project will investigate unconventional superfluid and insulating states of fermionic ultracold atoms in optical lattices. The two related objectives are to 1) identify and characterize the pseudogap states of resonantly paired fermions at zero and finite temperatures, and 2) systematically explore the phase diagram of pair density wave (PDW) states in realistic lattice potentials. This research will mostly rely on the unique combination of numerical methods that the PI have advanced in his recent work: exact diagonalization and quantum Monte Carlo simulations..The most pristine pseudogap states are bosonic Mott insulators of Cooper pairs found in the BEC regime of attractively interacting lattice fermions. These s-wave paired insulators are fundamentally different from the poorly understood pseudogap state of high-temperature superconductors, but exhibit a similar phenomenology due to significant quantum fluctuations. A lattice potential required to stabilize such states often leads to spontaneous translational symmetry breaking or magnetization as well. The resulting PDW, visible so far only in theoretical studies, is a remarkable example of how intricate correlations common to complicated solid state systems can emerge from a few simple microscopic ingredients that can be routinely created in ultracold atom laboratories. This project will, therefore, pinpoint the needed experimental conditions for the observation of such correlated states. The unconventional correlated states of matter explored in here are experimentally feasible in trapped ultracold gases due to their dependence on tunable lattice potentials and nearly resonant interactions. At the same time, the theoretical models that host such states, as well as their detailed experimental realizations, are ideal enough to allow accurate analysis using the state-of-art numerical methods of many-body quantum mechanics that the PI specialize in. The detailed analysis of the experimental implications and signatures of the phenomena discussed here, will significantly advance the role of atomic physics in the exploration of novel many-body physics. The insights gained in this research will have inter-disciplinary character and indirectly benefit the understanding of high temperature superconductivity.

本项目将研究光晶格中超冷费米性原子系统的非常规超流态和绝缘态，包括1）确认和表征零温下共振配对费米子的赝能隙态；2）真实晶格势下配对密度波态的相图。研究主要采用严格对角化和量子蒙特卡罗方法的有机结合。最初的赝能隙态主要是玻色化的库珀对莫特绝缘体，出现于吸引相互作用晶格费米子系统的玻色-爱因斯坦凝聚区域。这些s波配对的绝缘体不同于高温超导体中的赝能隙态，但由于显著的量子涨落二者却表现出一些相似的现象。用于稳定这些态的晶格势通常会导致自发的平移对称性破缺，因而导致的配对密度波非常值得关注，即凝聚态中常见的复杂关联如何被超冷原子实验制造的一些简单微观成分实现。该项目将精确观察到这些关联态所需的实验条件。因其与可调的晶格势的依赖关系，非常规的关联态可在被囚禁的超冷原子气体实验中实现。同时，承载这些态的理论模型以及实验实现条件足够理想，能通过多体量子系统的数值方法对其进行精确的分析和描述。

该项目的关注点在如何利用配对对称性来研究赝能隙物理。这种配对对称性与在凝聚态体系中的配对对称性并不一定相关，背后的机制是，是由于d波配对的实验利用目前的冷原子技术难以实现，但新的配对形式可能揭示会揭示超导中的前驱相的重要性。我们使用了精确的数值方法来理解新的配对形式，这样可以避开传统方法中的一些缺点。这些方法包括精确对角化、密度矩阵重正化群和投影量子蒙特卡罗。需要强调的是，我们发现在莫特绝缘体中，如果对分裂的库伯对之间进行调节，有可能可以实现有效的远程配对。最近在这个方向上已经发表了4篇文章，同时在一些非平衡量子多体系统的相关方向上还有另外的12篇文章也已经发表。进一步对学生和博士后进行训练，以及为国际和国家合作提供资金，是该提案成功的根本。