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赝隙态提供了理想的设置。这些状态可能与人们知之甚少的高温超导体赝隙状态根本不同，同时由于显著的量子涨落而表现出相似的现象学。本项目主要研究光学晶格中超冷费米子的非常规超流体和绝缘态的理论研究。我们的想法是识别和表征共振配对费米子中的这些状态，并系统地探索现实晶格势中的对密度波和富尔德-费雷尔-拉金-奥夫钦尼科夫态的相图。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，以便它们可以在实验中实现。研究将主要依赖于两个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。科学展览和公开讲座等机会将被用来吸引来自北弗吉尼亚的高中生和本科生追求科学和工程方面的高等教育和职业，以及参与资助的研究项目。这笔拨款将进一步促进乔治梅森大学和乔治城大学在原子和凝聚态理论方面的高级研究项目的建设。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进行高度并行计算的经验。我们将鼓励未被充分代表的群体成员参与物理学，这项研究的结果将在全国黑人物理学家协会和全国西班牙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.