Monte Carlo Treatment of Bose and Fermi Gases

在过去的几年里，冷原子气体的研究已经多样化。迄今为止，许多实验都是在强相互作用、高关联的情况下进行的，其中原子-原子相互作用的影响是不可忽略的。许多这样的系统需要完整的、非微扰的量子力学多体处理。该方案讨论了准一维双组分费米气体和掺杂玻色气体的理论多体描述，通过在准一维双组分费米气体的s波和p波通道中的约束诱导共振（CIR）附近调谐外磁场或激光，可以将s波和p波相互作用之间的相对强度和绝对强度调谐到基本上任意的值。受这一实验进展的启发，将采用多体量子蒙特卡罗（MC）技术研究具有竞争性s波和p波相互作用和不同偏振的准一维双组分费米气体。虽然一个丰富的零温相图已被预测，没有定量的研究，治疗s-和p-波相互作用存在。预计该研究将揭示BEC-BCS交叉的1D类似物，其中s波通道中CIR的“BEC侧”上的结合玻色子分子经历到配对费米子的转变，即，“库珀对”，在谐振的“BCS侧”，以及p波配对。基准测试的结果应该允许不同的平均场处理之间的区别。掺杂凝聚的研究承诺丰富的物理。与液体4 He相比，例如，原子气体具有通过利用Feshbach共振对相互作用强度进行前所未有的控制的优点。 初始的自洽平均场的研究表明，一个单一的中性杂质沉浸在一个被困玻色气体中的局域杂质状态的存在和本地化的程度可以通过改变原子杂质散射长度控制。局域杂质态的存在可能会导致新的量子计算方案和单原子器件的发展。调查，使用MC技术，应该阐明如何可以设计分子组成的非相互作用的中性杂质原子与不同的“键长”。杂质原子的结合被预测为由原子背景和原子-杂质相互作用引起，即，杂质分子的结合由原子-原子和原子杂质散射长度介导

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