Efficient continuation methods for spin-1 Bose–Einstein condensates in a magnetic field

ABSTRACT

We study linear stability analysis for spin-1 Bose–Einstein condensates (BEC). We show that all bounded solutions of this physical system are neutrally stable. In particular, all steady-state solutions of the physical system, and the associated discrete steady-state solutions are neutrally stable. Next, we consider the physical system without the affect of magnetic field. By exploiting the physical properties of both ferromagnetic and antiferromagnetic cases, we develop efficient multi-level pseudo-arclength continuation algorithms combined with a spectral collocation method for these two cases, respectively. When the magnetic field is imposed on the physical system, an additional multi-level continuation algorithm is described for the ferromagnetic case. Extensive numerical results for spin-1 BEC in a magnetic field, and in optical lattices are reported.

KEYWORDS:

• Gross–Pitaevskii equations
• stability analysis
• ground state
• spectral collocation method
• Zeeman energy

AMS SUBJECT CLASSIFICATIONS:

• 65N35
• 35P30
• 35Q55

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the Ministry of Science and Technology, Taiwan through Project MOST 103-2115-M-231-001-MY2.