Monte Carlo Treatment of Bose and Fermi Gases

在过去的几年里，对冷原子气体的研究已经多样化。到目前为止，许多实验都是在强相互作用、高度相关的情况下进行的，在这种情况下，原子-原子相互作用的影响是不可忽视的。其中许多系统需要完整的、非微扰的量子力学多体处理。本文讨论了(I)准ID双分量费米气体和(Ii)掺杂玻色气体的多体理论描述.通过调谐一个外加磁场或在准一维双分量费米气体的S和p波道中的禁闭感应共振(CIR)附近的激光器，S和p波相互作用的相对和绝对强度基本上可以被调谐到任何值.在这一实验进展的推动下，我们将利用多体量子蒙特卡罗(MC)技术研究具有竞争S波和P波相互作用、变极化的囚禁准一维双组分费米气体。虽然已经预测了丰富的零温相图，但还没有同时处理S波和p波相互作用的定量研究。预计这项研究将揭示BEC-BCS交叉的一维模拟，在BEC-BCS交叉中，在S波通道中CIR的BEC侧的束缚玻色子分子经历到共振的BCS侧的成对费米子，即“库珀对”，以及p波配对。基准结果应该允许区分不同的平均场处理。对掺杂凝析油的研究有望获得丰富的物理学基础。例如，与液体4He相比，原子气体具有利用Feshbach共振对相互作用强度进行前所未有的控制的优势。对单个中性杂质在玻色气体中的初始自洽平均场研究表明，局域杂质态是存在的，局域化程度可以通过改变原子-杂质散射长度来控制。局域杂质态的存在可能导致新的量子计算方案和单原子器件的发展。使用MC技术的研究应该能揭示人们如何设计由非相互作用的中性杂质原子组成的分子，这些原子具有不同的“键长”。预测了杂质原子的结合是由原子背景和原子与杂质的相互作用引起的，即杂质分子的结合受原子-原子和原子杂质散射长度的影响。

Studies of cold atom gases have diversified over the past few years. To date, a number of experiments work in the strongly-interacting, highly-correlated regime, in which the effects of atom-atom interactions are non-negligible. Many of these systems require full, non-perturbative quantum mechanical many-body treatments. This proposal discusses the theoretical many-body description of (i) quasi-ID two-component Fermi gases and (ii) doped Bose gases.By tuning an external magnetic field or a laser in the vicinity of confinement-induced resonances (CIRs) in the s- and p-wave channels of a quasi-1D two-component Fermi gas, the relative and absolute strengths between the s- and p-wave interactions can be tuned to essentially any value. Motivated by this experimental progress, a study of trapped quasi-1D two-component Fermi gases with competing s- and p-wave interactions and varying polarization using many body quantum Monte Carlo (MC) techniques will be undertaken. Although a rich zero-temperature phase diagram has been predicted, no quantitative studies that treat both s- and p-wave interactions exist. It is anticipated that the study will shed light on the 1D analog of the BEC-BCS crossover, where bound bosonic molecules on the "BEC side" of the CIR in the s-wave channel undergo a transition to paired fermions, i.e., "Cooper pairs", on the "BCS side" of the resonance, and on p-wave pairing. Benchmark results should allow between different mean-field treatments to be discriminated.The study of doped condensates promises rich physics. Compared to liquid 4He, e.g., atomic gases have the advantage of unprecedented control of the interaction strength by utilizing Feshbach resonances. Initial self consistent mean-field studies of a single neutral impurity immersed in a trapped Bose gas indicate that localized impurity states exist and that the degree of localization can be controlled by varying the atom-impurity scattering length. The existence of localized impurity states may lead to the development of novel quantum computing schemes and single atom devices. Investigations, using MC techniques, should shed light on how one can design molecules consisting of non-interacting neutral impurity atoms with varying "bond lengths". The binding of the impurity atoms is predicted to be induced by the atom background and the atom-impurity interactions, i.e., the binding of the impurity molecule is mediated by the atom-atom and atom impurity scattering lengths