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。

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.