Fig. 1. The energies of degenerate quantum states
and the superposition state of odd parity
of left(right)-displaced number states varies as the spin-orbit coupling strength
. It is seen that for
, the superposition state has the lowest energy which is the best approximation for the ground state in our interest. And for the cases of
, the energies of the two quantum states have pitchforks.The relevant parameters is Ω=1.4 and the results are in agreement with those in Ref.[19].
简并量子态
能量
与左右平移奇宇称叠加态
能量
随SO耦合强度
的变化 可见
叠加态
能量最低, 更接近基态; 而对于激发态
, 二者能量随参数变化出现交叉; 相关参数取值为
, 与文献[19]精确解的结果基本一致
Fig. 2. The coarse dynamics evulution of momentum distribution of single particle (left for 3D; right for 2D) with
and
. The initial state is set as
. Momentum
is defined by
.
原子动量分布概率的粗粒动力学演化 (3D, 左侧; 2D, 右侧) 相关参数取值为
,
, 初态为
, 动量
Fig. 3. The coarse dynamics evolution of position distribution of single particle (left for 3D; right for 2D) with the same parameters and the initial state in Fig. 2 and
.
原子空间位置分布概率的粗粒动力学演化(3D, 左侧; 2D, 右侧) 相关参数取值及初态同图2, 位置
Fig. 4. Time evolution of
with the initial state being
and the parameters
and
. The time is scaled by the tunneling period
.
原子极化
随时间演化初态为
, 参数取值为
和
, 时间以因子
标度