标题： 几何相位辅助探测高能修改色散引起的洛伦兹不变性破缺 显示英文标题

标题： Geometric phase assisted detection of Lorentz-invariance violation from modified dispersion at high energies

摘要： 许多量子引力理论提出了形式为$\omega_{|\mathbf{k}|}=|\mathbf{k}|f(|\mathbf{k}|/M_\star)$的洛伦兹破缺色散关系，其在远低于$M_\star$的能量尺度下近似恢复洛伦兹不变性$\omega_{|\mathbf{k}|}\approx|\mathbf{k}|$。然而，通常认为这一尺度接近普朗克尺度，因此洛伦兹破缺理论的特征较弱，其实验检验变得极其具有挑战性。由于几何相位（GP）对弱效应具有累积性和敏感性的特性，我们在此研究了与具有此类洛伦兹破缺色散关系的量子场耦合的惯性原子探测器所获得的几何相位。我们表明，在洛伦兹破缺场论情况下，几何相位依赖于探测器的速度，这与洛伦兹对称性情况下的几何相位无关速度的情况完全不同。特别是，我们证明了几何相位可能在任何低于 1 的某个地方下降的$f$情况下表现出剧烈的低能洛伦兹破缺。我们将我们的分析应用于检测由圈量子引力启发的聚合物量子化，并表明在低于当前离子对撞机快速度的探测器速度辅助下，探测器可以获得可实验检测到的几何相位。此外，几何相位的累积性质可能会极大地促进相关检测。 显示英文摘要

摘要： Many theories of quantum gravity propose Lorentz-violating dispersion relations of the form $\omega_{|\mathbf{k}|}=|\mathbf{k}|f(|\mathbf{k}|/M_\star)$, which approximately recover to the Lorentz invariance, $\omega_{|\mathbf{k}|}\approx|\mathbf{k}|$, at the energy scales much below $M_\star$. However, usually such a scale is assumed to be near the Planck scale, thus the feature of the Lorentz-violating theory is weak and its experimental test becomes extremely challenging. Since the geometric phase (GP) is of accumulative and sensitive nature to weak effects, here we explore the GP acquired by an inertial atomic detector that is coupled to a quantum field with this kind of Lorentz-violating dispersion. We show that for the Lorentz-violating field theory case the GP depends on the velocity of the detector, which is quite different from the Lorentz symmetry case where the GP is independent of the detector's velocity. In particular, we show that the GP may present a drastic low-energy Lorentz violation for any $f$ that dips below unity somewhere. We apply our analysis to detecting the polymer quantization motivated by loop quantum gravity, and show the detector acquires an experimentally detectable GP with the assist of detector's velocity that below current ion collider rapidities. Furthermore, the accumulative nature of GP might facilitate the relevant detection significantly.