Monte Carlo Treatment of Bose and Fermi Gases

在过去的几年中，对冷原子气体的研究已经多样化了。迄今为止，许多实验都是在强相互作用、高度相关的状态下进行的，在这种状态下，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。本文讨论了(i)准id双组分费米气体和（ii）掺杂玻色气体的理论多体描述。在准一维双组分费米气体的s波和p波通道中，通过调节一个外部磁场或激光在约束诱导共振（CIRs）附近，s波和p波相互作用之间的相对强度和绝对强度可以调谐到任何值。在这一实验进展的激励下，将利用多体量子蒙特卡罗（MC）技术研究具有s波和p波相互作用和变化极化的被困准一维双组分费米气体。虽然预测了丰富的零温度相图，但没有同时处理s波和p波相互作用的定量研究。预计该研究将揭示BEC-BCS交叉的一维模拟，其中s波通道中CIR“BEC侧”的束缚玻色子分子在共振的“BCS侧”和p波配对上经历成对费米子的转变，即“库珀对”。基准测试结果应该允许在不同的平均场处理之间进行区分。掺杂凝聚体的研究预示着丰富的物理学。与液态he相比，原子气体具有利用费什巴赫共振控制相互作用强度的前所未有的优势。在捕获玻色气体中对单个中性杂质的初始自一致平均场研究表明，存在局域化的杂质态，局域化的程度可以通过改变原子-杂质的散射长度来控制。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。研究，使用MC技术，应该阐明如何设计由具有不同“键长”的不相互作用的中性杂质原子组成的分子。预测杂质原子的结合是由原子背景和原子-杂质相互作用诱导的，即杂质分子的结合是由原子-原子和原子杂质散射长度介导的

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