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Progress in Natural Science Materials International

Bose—Einstein凝聚相干输出的量子多体理论：I.因子化与原子相干

孙昌璞, 苗元秀

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

基于热力学极限下的Ｂｏｇｏｌｉｕｂｏｖ近似，提出了描述磁阱陷中Ｂｏｓｅ型原子输出到自由传播了模式的线性量子多体理论。证明如果阱陷中的原子开始处于Ｂｏｓｅ－Ｅｉｎｓｔｅｉｎ凝聚状态，由于演化波函数的因子化结构，输出的原子将处于一个由多体相干态描述的宏观量子态上，即输出的原子束是相干的。该理论给出了计算输出原子谱分布及至空间分布的一般公式。

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基于热力学极限下的Ｂｏｇｏｌｉｕｂｏｖ近似，提出了描述磁阱陷中Ｂｏｓｅ型原子输出到自由传播了模式的线性量子多体理论。证明如果阱陷中的原子开始处于Ｂｏｓｅ－Ｅｉｎｓｔｅｉｎ凝聚状态，由于演化波函数的因子化结构，输出的原子将处于一个由多体相干态描述的宏观量子态上，即输出的原子束是相干的。该理论给出了计算输出原子谱分布及至空间分布的一般公式。
We examine the density profiles of the quantum degenerate Bose-Fermi mixture of 174Yb^{174}\mathrm{Yb}174Yb-173Yb^{173}\mathrm{Yb}173Yb, experimentally observed recently, in the mean-field regime. In this mixture there is a possibility of tuning the Bose-Bose and Bose-Fermi interactions simultaneously using two well-separated optical Feshbach resonances, and it is a good candidate to explore phase separation in Bose-Fermi mixtures. Depending on the Bose-Bose scattering length aBB{a}_{\mathrm{BB}}aBB​, as the Bose-Fermi interaction is tuned the density of the fermions is pinched or swapping with bosons occurs.
We calculate the shift in the critical temperature of Bose-Einstein condensation for a dilute Bose-Fermi mixture confined by a harmonic potential, to lowest order in both the Bose-Bose and Bose-Fermi coupling constans. The relativ importance of the effect on the critical temperature of the boson-fermion interactions is investigated as a function of the parameters of mixture. The possible relevance of the shift of the transition temperature in current experiments on trapped Bose-Fermi mixtures is discussed.
We provide a detailed presentation of the functional renormalisation group (FRG) approach for weakly-interacting Bose–Bose mixtures, including a complete discussion on the RG equations. To test this approach, we examine thermodynamic properties of balanced three-dimensional Bose–Bose gases at zero and finite temperatures and find a good agreement with related works. We also study ground-state energies of repulsive Bose polarons by examining mixtures in the limit of infinite population imbalance. Finally, we discuss future applications of the FRG to novel problems in Bose–Bose mixtures and related systems.