论文标题
Bose-Einstein冷凝物的几何量子动力学
Geometrizing quantum dynamics of a Bose-Einstein condensate
论文作者
论文摘要
我们表明，在弱相互作用方案中，玻色 - 因斯坦冷凝水的量子动力学可以通过庞加莱磁盘几何来制度。这样的磁盘上的每个点都代表热菲尔德双状态，这是该双曲线空间的度量的重叠。这种方法分别导致对稳定和不稳定模式的独特几何解释，分别是庞加莱磁盘上的封闭和开放轨迹。遵循测量学的共振模式自然等同于基本数量，包括时间，长度和温度。我们的工作提出了一个新的几何框架，可以连贯控制量子系统，并使用SU（1,1）回声逆转其动力学。在存在破坏SU（1,1）对称性的扰动的情况下，SU（1,1）的回声提供了一种新的手段来测量这些扰动，例如激发颗粒之间的相互作用。
We show that quantum dynamics of Bose-Einstein condensates in the weakly interacting regime can be geometrized by a Poincaré disk. Each point on such a disk represents a thermofield double state, the overlap between which equals the metric of this hyperbolic space. This approach leads to a unique geometric interpretation of stable and unstable modes as closed and open trajectories on the Poincaré disk, respectively. The resonant modes that follow geodesics naturally equate fundamental quantities including the time, the length, and the temperature. Our work suggests a new geometric framework to coherently control quantum systems and reverse their dynamics using SU(1,1) echoes. In the presence of perturbations breaking the SU(1,1) symmetry, SU(1,1) echoes deliver a new means to measure these perturbations such as the interactions between excited particles.
