发表机构
Instituut-Lorentz, Universiteit Leiden（莱顿大学洛伦兹研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出玻色-爱因斯坦凝聚体中声子的Scharnhorst效应类比，预测声速因零点涨落增加，比光子效应大28个数量级，并探讨了低温观测前景。
AI 中文摘要
量子电动力学中的Scharnhorst效应预测，在两个镜子之间的真空涨落作用下，低频光子速度会出现超光速偏移$\delta c>0$。尽管该效应在理论上稳健（不违反因果性），但其幅度极其微小（对于间距为$1\\,\mu{\rm m}$的镜子，$\delta c/c\approx 10^{-32}$），超出了当前实验可达范围。在此，我们提出一种凝聚态类比方案，将电磁真空中的光子替换为玻色-爱因斯坦凝聚体中的声子激发。在理想化几何中，即零温下半径为$L$的二维圆柱表面，由于凝聚体的零点涨落，轴向声速会增加，其一阶修正为$\delta c/c\simeq 5\times 10^{-3}\\,\tilde{g}$（当$L\simeq 2\\,\xi$时），其中$\tilde{g}\simeq 10^{-1}$是玻色气体的无量纲相互作用常数，$\xi\simeq 1\\,\mu{\rm m}$为愈合长度。这比光子效应大28个数量级，主要原因是声子具有自相互作用，而光子仅通过大质量电子相互作用。我们讨论了观测声学Scharnhorst效应的前景，主要限制在于低温要求。
英文摘要
The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift $δc>0$ at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small ($δc/c\approx 10^{-32}$ for mirrors $1\,μ{\rm m}$ apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference $L$) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by $δc/c\simeq 5\times 10^{-3}\,\tilde{g}$ at $L\simeq 2\,ξ$, to first order in the dimensionless interaction constant $\tilde{g}\simeq 10^{-1}$ of the Bose gas of healing length $ξ\simeq 1\,μ{\rm m}$. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.
Comments7 pages, 2 figures
