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arXiv 2210.06237cond-mat.quant-gascond-mat.stat-mech
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原子和分子玻色-爱因斯坦凝聚体的激发寿命

Lifetime of Excitations in Atomic and Molecular Bose-Einstein Condensates

Matteo Bellitti, Garry Goldstein, Chris R. Laumann

摘要:

最近的实验进展产生了分子超流体(MSF)在热平衡,这打开了大门,一类新的实验研究相关的热力学和动力学响应。本文综述了原子超流(ASF)和MSF相的相图和准粒子谱的理论图象。我们进一步计算了单圈阶准粒子寿命的参数依赖性。在MSF阶段,$U(1)$粒子数对称性破缺为$\mathbb{Z}_2$,并且除了有间隙的$\mathbb{Z}_2$保护的类原子模式之外,光谱还表现出无间隙的Goldstone模式。在ASF阶段,$U(1)$对称性完全破坏,留下Goldstone模式和未保护的带隙模式。在这两个阶段中,戈德斯通模的衰变速率由著名的别利亚耶夫结果给出,就像在单组分凝聚体中一样。在MSF阶段,带隙模式急剧上升到临界切伦科夫动量,超过该动量它发射声子。在ASF阶段,即使在小动量下,带隙模也以恒定速率衰减。这些衰减率支配着微阱隧穿实验中的光谱响应,并导致原子穿过分子云发射的透射光谱中的尖锐特征。

英文摘要:

Recent experimental progress has produced Molecular Superfluids (MSF) in thermal equilibrium; this opens the door to a new class of experiments investigating the associated thermodynamic and dynamical responses. We review the theoretical picture of the phase diagram and quasiparticle spectrum in the Atomic Superfluid (ASF) and MSF phases. We further compute the parametric dependence of the quasiparticle lifetimes at one-loop order. In the MSF phase, the $U(1)$ particle number symmetry breaks to $\mathbb{Z}_2$ and the spectrum exhibits a gapless Goldstone mode in addition to a gapped $\mathbb{Z}_2$-protected atom-like mode. In the ASF phase, the $U(1)$ symmetry breaks completely, leaving behind a Goldstone mode and an unprotected gapped mode. In both phases, the Goldstone mode decays with a rate given by the celebrated Belyaev result, as in a single component condensate. In the MSF phase, the gapped mode is sharp up to a critical Cherenkov momentum beyond which it emits phonons. In the ASF phase, the gapped mode decays with a constant rate even at small momenta. These decay rates govern the spectral response in microtrap tunneling experiments and lead to sharp features in the transmission spectrum of atoms fired through molecular clouds.

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