Abstract
We study the ground state phases of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential. Based on variational analysis, the conditions of phase transition between magnetized and unmagnetized phases are obtained analytically for the first time, and the physical mechanism of inducing phase transition is revealed. The competition relationship among spin-independent interaction, spin-dependent interaction, spin-orbit (SO) coupling and harmonic potential for generating phase transition is discussed systematically. We predict that the spin-dependent interaction plays key role in ground state phase transition. Interestingly, the phase transition of the ground state degenerate to the single particle case in free space when spin-dependent interaction is absent. In addition, the harmonic potential strengthens the influence of atomic interactions on the phase boundary. Our results provide theoretical evidence for deep understanding the ground sate phase transition of the system.
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