Collaborative Research: Correlated Superfluids and Insulators of Ultracold Fermionic Atomic Gases

光学晶格中的超冷原子为实现目前从理论研究中已知的一些最原始的伪能隙状态提供了理想的装置。这些状态可能从根本上不同于人们鲜为人知的高温超导体的伪隙状态，而由于显著的量子涨落，表现出类似的现象。本项目主要对光学晶格中超冷费米子的非传统超流和绝缘态进行理论研究。我们的想法是识别和刻画共振配对费米子中的这些态，并系统地研究现实晶格势中对密度波和Fulde-Ferrell-Larkin-Ovchinnikov态的相图。我们的主要目标之一是揭示这些状态存在所需的最小微观成分，以便在实验中实现它们。这项研究将主要依靠两个PI在最近的工作中提出的独特的数值方法组合：精确对角化和量子蒙特卡罗模拟(M.R.)，以及依赖于序参数的自由能最小化(P.N.)。该项目将利用乔治梅森大学和乔治敦大学的地理位置进行广泛的推广工作。科学博览会和公开讲座等机会将被用来吸引来自北弗吉尼亚州的高中生和本科生继续接受高等教育和从事科学和工程方面的职业，以及参与受资助的研究项目。这笔赠款将进一步促进乔治梅森大学和乔治敦大学在原子和凝聚态理论方面的高级研究计划的建立。这两所大学的研究生将接受高性能计算方面的培训，并将获得在美国高性能计算中心执行高度并行计算的经验。我们将鼓励代表不足的群体的成员参与物理学，这项研究的结果将在全国黑人物理学家协会和全国拉美裔物理学家协会的联合会议上报告。

Ultracold atoms in optical lattices provide an ideal set up for realizing some of the most pristine pseudogap states currently known from theoretical studies. Those states could be fundamentally different from the poorly understood pseudogap state of high-temperature superconductors, while exhibiting a similar phenomenology due to significant quantum fluctuations. This project focuses on the theoretical investigation of unconventional superfluid and insulating states of ultracold fermions in optical lattices. The idea is to identify and characterize those states in resonantly paired fermions and systematically explore the phase diagram of pair-density-wave and Fulde-Ferrell-Larkin-Ovchinnikov states in realistic lattice potentials. One of our main goals is to unveil the minimal microscopic ingredients required for the existence of those states so that they can be realized in experiments. The research will mostly rely on the unique combination of numerical methods that the two PIs have advanced in their recent work: exact diagonalization and quantum Monte Carlo simulations (M.R.), and order-parameter-dependent free energy minimization (P.N.).This project will incorporate a broad outreach effort taking advantage of the location of George Mason and Georgetown Universities. Opportunities such as science fairs and public lectures will be used to attract high school and undergraduate students from Northern Virginia to pursue higher education and careers in science and engineering, as well as participate in the funded research projects. This grant will further facilitate the building of advanced research programs in atomic and condensed matter theory at George Mason and Georgetown Universities. Graduate students at both universities will receive training in high performance computing, and will gain experience performing highly parallel calculations in high performance computing centers within the US. We will encourage the participation of members of underrepresented groups in Physics and the results of this research will be reported in the joint conferences of the National Society of Black Physicists and the National Society of Hispanic Physicists.