Exploring ground states and excited states of spin-1 Bose–Einstein condensates by continuation methods

Chen, Jen-Hao; Chern, I‐Liang; Wang, Weichung

doi:10.1016/j.jcp.2010.11.048

Cited by 18 publications

(11 citation statements)

References 24 publications

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“…This particular continuation scheme is proposed on top of the pseudo-arclength continuation method [14,29,30,31]. In the first stage, we employ the continuation algorithm proposed in [14] to trace the ground state solution curve by setting q = 0 and treating both g n and g s as continuation parameters. The target point is the ground state of the spin-1 BEC in the absence of an external magnetic field.…”

Section: The Parameter Switching Continuation Methodsmentioning

confidence: 99%

“…Second, we summarize some features of the ground states of the spin-1 without magnetic field as follows (see [14,25] for more details).…”

Section: Remarks On Ground Statesmentioning

confidence: 99%

“…By trapping all Zeeman states of an atomic species in an optical trap, these spinor BEC possess a wealth of phenomena not found in single-component condensates, including spin vortex [6], spin textures [7,8], domain wall structure [9,10], and spontaneous demagnetization dynamics [11,12]. It is well known that the sign of atomic spin-exchange interaction determines the ground state property of spin-1 condensate, and leads to different quantum phases [3,13,14]. Moreover, under an applied external magnetic field, the spontaneous symmetry breaking in a 87 Rb spinor BEC has recently been observed [7].…”

Section: Introductionmentioning

confidence: 99%

“…The ground state structure of the spin-1 condensate in the absence of an external magnetic field has been well examined both theoretically [23,24,25] and numerically [26,14,27]. The essential feature of these works is that, in ferromagnetic systems the ground state contains all three components which are constant multiples of a scalar wave function, while the ground state contains no zero-component in antiferromagnetic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the pseudo-arclength continuation method (PACM) [29,30,31], we develop a numerical scheme to study these problems. First, together with the characteristics of the ground state of the spin-1 condensate without magnetic field [14], we trace the ground state solution curve varied by the spin-independent and spin-exchange coupling constants. We next treat the QZ effect as a continuation parameter, and take the target solution under zero magnetic field as the starting state to trace the ground state solution curve subject to nonzero magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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A Complete Study of the Ground State Phase Diagrams of Spin-1 Bose–Einstein Condensates in a Magnetic Field Via Continuation Methods

2014

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We present a complete investigation of the ground state patterns and phase diagrams of the spin-1 Bose-Einstein condensates (BEC) confined in a harmonic or box potential under the influence of a homogeneous magnetic field. A pseudoarclength continuation method with parameter switching technique is developed to study the BEC systems numerically. The continuation process is performed on the parameter space consisting of the spin-independent interaction, spinexchange interaction and the quadratic Zeeman (QZ) energy parameters. In the first stage of the parameter switching process, we fix the QZ energy term to be zero and vary the interaction parameters from zero to the desired physical values. Next, we fix the interaction parameters and vary the QZ energy parameter in both positive and negative regions. Two types of phase transitions are found, as we vary the QZ parameter. The first type is a transition from a two-component (2C) state to a three-component (3C) state. The second type is a symmetry breaking in the 3C state. Then, a phase separation of the spin components follows. In the semi-classical regime, we find that these two phase transition curves are gradually merged.

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