图 1  $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=30 $ (a)和$ \varOmega_{\text{R}}/\hbar\omega_{\bot}=70 $ (b)时能量最低的两条能级随m的变化, 插图分别为基态的密度和相位分布. 其他参数取值为$ l=1 $, $ \omega_{\bot}=2\pi\times 10 $ Hz, $ \omega_{z}=2\pi\times 200 $ Hz, $ W=25 \text{ μm} $

Fig. 1.  Variations of two single-particle lowest energy levels with m for $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=30 $ (a) and $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=70 $ (b), respectively. Other parameters are $ l=1 $, $ \omega_{\bot}=2\pi\times 10 $ Hz, $ \omega_{z}=2\pi\times 200 $ Hz, and $ W=25\text{ μm} $

图 2  (a), (b) 当$ \varOmega_{\text{R}}/\hbar\omega_{\bot}=30 $时, 最低能级在不同$\varpi $取值下随m的变化和基态角动量$ m_g $随$\varpi $的变化. (c), (d) 当$ \varOmega_{\text{R}}/\hbar\omega_{\bot}=70 $时, 最低能级在不同$\varpi $取值下随m的变化和基态角动量$ m_g $随$\varpi $的变化. (b)和(d)中的插图是$ \varpi=0.5 $和$ \varpi=0.7 $时基态密度和相位分布. (e)是以$\varpi $和$ \varOmega_\text{R}/\hbar\omega_{\bot} $为轴的二维参数空间中基态角动量的变化.其他参数取值分别为$ l=1 $, $ \omega_{\bot}=2\pi\times 10 $ Hz, $ \omega_z=2\pi\times 200 $ Hz, $ W=25{\text{ μm}} $

Fig. 2.  When $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=30 $, (a) is the variation of the single-particle lowest energy level with m for different $\varpi $, (b) shows the variation of the angular momentum $ m_g $ of the single-particle ground state with $\varpi $. When $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=70 $, (c) is the variation of the single-particle lowest energy level with m for different $\varpi $, (d) shows the variation of the angular momentum $ m_g $ of the single-particle ground state with $\varpi $. The insets in (b) and (d) are the density and phase of the single-particle ground state for $ \varpi=0.5 $ and $ \varpi=0.7 $, respectively. (e) is the variation of the angular momentum of the single-particle ground state with $\varpi $ and $ \varOmega_{\text{R}}/\hbar\omega_{\bot} $. Other parameters are $ l=1 $, $ \omega_{\bot}=2\pi\times 10 $ Hz, $ \omega_z=2\pi\times 200 $ Hz, and $ W=25{\text{ μm}} $.

图 3  (a) $ \varpi=0 $和$ l=2 $时, $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=100,\; 140,\; 160 $时的基态密度分布. (b), (c) $ l=1 $时, $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=30 $和70的基态角动量$ \left\langle \hat{L}_z\right\rangle $随旋转频率的变化, 插图为$ \varpi=0.5 $和$ \varpi=0.7 $时的基态密度和相位分布. 其他参数为$ a_{\uparrow\uparrow}= a_{\downarrow\downarrow}=100 a_{\text{B}} $, $ a_{\uparrow\downarrow}=50 a_{\text{B}} $, $ \omega_{\bot}=2\pi\times10 $ Hz, $ \omega_{z}=2\pi\times 200 $ Hz, $ N=1000 $和$ W=25{\text{ μm}} $, 其中$ a_{\text{B}} $为玻尔半径

Fig. 3.  (a) Densities of the mean-field ground states for $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=100,\; 140,\; 160 $ when $ \varpi=0 $ and $ l=2 $. (b), (c) For $ l=1 $, the variation of the angular momentum $ \left\langle \hat{L}_z\right\rangle $ of the mean-field ground state with the rotating frequency $\varpi $ for $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=30 $ and $ \varOmega_{\text{R}}/\hbar\omega_{\bot}=70 $, respectively. The insets in (b) and (c) are the density and phase of the mean-field ground state for $ \varpi=0.5 $ and $ \varpi=0.7 $, respectively. Other parameters are $ a_{\uparrow\uparrow}=a_{\downarrow\downarrow}=100 a_{\text{B}} $, $ a_{\uparrow\downarrow}=50 a_{\text{B}} $, $ \omega_{\bot}=2\pi\times10 $ Hz, $ \omega_{z}=2\pi\times 200 $ Hz, $ N=1000 $, and $ W=25{\text{ μm}} $, where $ a_{\text{B}} $ is the Bohr radius.