Phase diagram of rotating Bose-Einstein condensates trapped in power-law and hard-wall potentials

Abstract

We investigate the rotational phase diagram of a quasi-two-dimensional, weakly-interacting Bose-Einstein condensate confined in power-law and in hard-wall trapping potentials. For weak interactions, the system undergoes discontinuous transitions between multiply-quantized vortex states as the rotation frequency of the trap increases. In contrast, stronger interactions induce continuous phase transitions toward mixed states involving both singly and multiply-quantized vortex states. A central result is the qualitative (and experimentally observable) difference between power-law and hard-wall confinement: In hard-wall traps, the leading instability always involves states with nonzero density at the trap center, whereas in power-law traps the density vanishes as the rotation frequency increases. The two different types of confinement give rise to scaling properties in the derived phase diagrams.

Figures (8)

• Figure 1: The phase diagram, where on the $x$ axis is the rotational frequency of the trap $\Omega$ (in units of $\omega$) and on the $y$ axis is the (dimensionless) coupling $g$. Here we have a power-law trapping potential, with $p = 2$, $\lambda = 0.05$ (higher) and $\lambda = 0.08$ (lower). The straight lines give the discontinuous transitions, while the curves give the continuous ones.
• Figure 2: (Colour online). The density (left) and the phase (right) of the order parameter -- with $p=2$ and $\lambda = 0.08$ -- for the case of a multiply-quantized vortex state in a power-law trap, with $m_0 = 16$ (higher), towards the instability involving the states with $(m_0-q, m_0, m_0+q) = (7, 16, 25)$ (lower). Here the axes are measured in units of $a_0$, and the density in units of $a_0^{-2}$.
• Figure 3: The phase diagram, where on the $x$ axis is the rotational frequency of the trap $\Omega$ (in units of $\omega$) and on the $y$ axis is the (dimensionless) coupling $g$. Here we have a power-law trapping potential, with $\lambda = 0.001$, $p = 3$ (higher) and $p = 4$ (lower). The straight lines give the discontinuous transitions, while the curves give the continuous ones.
• Figure 4: (Colour online). The density (left) and the phase (right) of the order parameter -- with $p=3$ and $\lambda = 0.001$ -- for the case of a multiply-quantized vortex state in a power-law trap, with $m_0 = 16$ (higher), towards the instability involving the states with $(m_0-q, m_0, m_0+q) = (6, 16, 26)$ (lower). Here the axes are measured in units of $a_0$, and the density in units of $a_0^{-2}$.
• Figure 5: (Colour online). The density (left) and the phase (right) of the order parameter, for the case of multiply-quantized vortex state in a power-law trap, with $p=4$ and $\lambda = 0.001$, $m_0 = 16$ (higher), towards the instability involving the states with $(m_0-q, m_0, m_0+q) =(12, 16, 20)$ (lower). Here the axes are measured in units of $a_0$, and the density in units of $a_0^{-2}$.