In open quantum systems, we study the geometric phases acquired for a two-level atom coupled to a bath of fluctuating vacuum massless scalar fields due to linear acceleration and circular motion without and with a boundary. In free space, as we amplify acceleration, the geometric phase acquired purely due to linear acceleration case firstly is smaller than the circular acceleration case in the ultrarelativistic limit for the initial atomic state $\theta \in (0,\frac{\pi }{2})\cup (\frac{\pi }{2},\pi )$, then equals to the circular acceleration case in a certain acceleration, and finally, is larger than the circular acceleration case. The spontaneous transition rates show a similar feature. This result is different from the case of a bath of fluctuating vacuum electromagnetic fields that has been studied. Considering the initial atomic state $\theta \in (0,\pi )$, we find that the geometric phase acquired purely due to linear acceleration always equals to the circular acceleration case for the certain acceleration. The feature implies that, in a certain condition, one can simulate the case of the uniformly accelerated two-level atom by studying the properties of the two-level atom in circular motion. Adding a reflecting boundary, we observe that a larger value of a geometric phase can be obtained compared to the absence of a boundary. Besides, the geometric phase fluctuates along $z$, and the maximum of geometric phase is closer to the boundary for a larger acceleration. We also find that geometric phases can be acquired purely due to the linear acceleration case and circular acceleration case with $\theta \in (0,\pi )$ for a smaller $z$.

中文翻译：

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由于线性加速度和圆周运动，耦合到波动真空标量场的两能级原子获得的几何相位

在开放量子系统中，我们研究了由于线性加速度和无边界和有边界的圆周运动，耦合到波动真空无质量标量场浴的两能级原子所获得的几何相位。在自由空间中，当我们放大加速度时，在初始原子态的超相对论极限下，纯粹由线性加速度首先获得的几何相位小于圆形加速度$\theta \in (0,\frac{\pi }{2})\cup (\frac{\pi }{2},\pi )$，则在一定加速度下等于圆周加速度情况，最后，大于圆周加速度情况。自发转换率显示出类似的特征。这个结果与已经研究过的波动真空电磁场浴的情况不同。考虑初始原子状态$\theta \in (0,\pi )$，我们发现纯粹由于线性加速度获得的几何相位总是等于一定加速度的圆周加速度情况。该特征意味着，在一定条件下，通过研究二级原子做圆周运动的性质，可以模拟匀加速二级原子的情况。添加反射边界，我们观察到与没有边界相比，可以获得更大的几何相位值。此外，几何相位随$z$, 几何相位的最大值更接近边界以获得更大的加速度。我们还发现，几何相位可以纯粹由于线性加速度情况和圆周加速度情况而获得$\theta \in (0,\pi )$对于较小的$z$.