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Chinese Physics B

SU(3) spin–orbit-coupled Bose–Einstein condensate confined in a harmonic plus quartic trap

Hao Li, Fanglin Chen

Published Jul 1, 2019• 8 citations
Publisher

Abstract

We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap. The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail. For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture. For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.

DOI
10.1088/1674-1056/28/7/070302

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We consider a SU(3) spin–orbit coupled Bose–Einstein condensate confined in a harmonic plus quartic trap. The ground-state wave functions of such a system are obtained by minimizing the Gross–Pitaevskii energy functional, and the effects of the spin-dependent interaction and spin–orbit coupling are investigated in detail. For the case of ferromagnetic spin interaction, the SU(3) spin–orbit coupling induces a threefold-degenerate plane wave ground state with nontrivial spin texture. For the case of antiferromagnetic spin interaction, the system shows phase separation for weak SU(3) spin–orbit coupling, where three discrete minima with unequal weights in momentum space are selected, while hexagonal honeycomb lattice structure for strong SU(3) SOC, where three discrete minima with equal weights are selected.
We consider a SU(3) spin-orbit-coupled Bose gas with nonlocal soft-core interactions confined in a harmonic trapping potential. The presence of SU(3) spin-orbit coupling induces three minima of the single-particle spectrum. In the absence of spin-exchange interaction, our results show that regardless of the sign of the soft-core interaction, the ground state occupies one single minimum in the momentum space and corresponds to a threefold-degenerate magnetized phase. For the ferromagnetic condensate, the ground state shows an amplitude-modulated plane-wave state, where its modulated amplitude and frequency are related to the strength of the soft-core interaction and SU(3) spin-orbit coupling, respectively. In particular, due to the subtle balance of the soft-core interaction and SU(3) spin-orbit coupling, a stable higher-order spin vortex lattice can be formed in the lattice phase of an antiferromagnetic condensate, where the density distributions of each component and the total system show spatial configurations with threefold and sixfold symmetries, respectively. We also give an experimental protocol to observe such states within current experimental capacity.
We consider the SU(3) spin–orbit coupled spin-1 Bose–Einstein condensates in a two-dimensional harmonic trap. The competition between the SU(3) spin–orbit coupling and the spin-exchange interaction results in a rich variety of lattice configurations. The ground-state phase diagram spanned by the isotropic SU(3) spin–orbit coupling and the spin–spin interaction is presented. Five ground-state phases can be identified on the phase diagram, including the plane wave phase, the stripe phase, the kagome lattice phase, the stripe-honeycomb lattice phase, and the honeycomb hexagonal lattice phase. The system undergoes a sequence of phase transitions from the rectangular lattice phase to the honeycomb hexagonal lattice phase, and to the triangular lattice phase in spin-1 Bose–Einstein condensates with anisotrpic SU(3) spin–orbit coupling.
Abstract In the mean-field framework, using variational analysis and numerical simulation, we investigate the effect of anharmonic trap and atomic interaction on the ground-state phases of spin-orbit (SO) coupled Bose–Einstein condensates (BECs) in the harmonic plus quartic potential. Then, the Gaussian wave function is selected to predict the analytical conditions of the phase transition boundary of the SO coupled BECs by using the variational method. We found that the anharmonicity of the external potential induces the SO coupled BECs to undergo a phase transition between the zero-momentum phase and plane-wave phase, which is more pronounced in the cases of weak harmonic potential or strong interspecies interaction. Since the potential energy of the system modified by anharmonicity competes with other energies of the system, the anharmonicity changes the critical SO coupling strength and Raman coupling strength when the phase transition occurs. At the same time, the critical anharmonic coefficients are also affected by interspecies interaction and harmonic potential. Finally, the correctness of the theoretical results is verified by numerical simulation of the Gross-Pitaevskii equation.
Abstract We consider the ground state properties of SU(3) spin–orbit-coupled (SOC) Bose–Einstein condensates (BECs) with soft-core interaction trapped in radially periodic potential. By minimizing the energy of the condensate, the effects of spin–orbit coupling and soft-core long-range interaction on the ground-state structure of such a system have been investigated for ferromagnetic and antiferromagnetic spin interaction cases. In the absence of soft-core interaction, our results show that the system has a rich variety of ground state phases, such as typical vortices, antivortices, domain wall and hexagonal vortex lattice. It is found that the spontaneous symmetry breaking and isolated density peaks appear in the system with the addition of soft-core interaction. We illustrate the physical mechanisms of different interactions in SU(3) SOC BECs.
Starting from the Hamiltonian of the second quantization form, the weakly interacting Bose–Einstein condensate with spin–orbit coupling of Weyl type is investigated. It is found that the SU (2) nonsymmetric term, i.e., the spin-dependent interaction, can lift the degeneracy of the ground states with respect to the z component of the total angular momentum J z , casting the ground condensate state into a configuration of zero J z . This ground state density profile can also be affirmed by minimizing the full Gross–Pitaevskii energy functional. The spin texture of the zero J z state indicates that it is a knot structure, whose fundamental group is π 3 ( M ) ≅ π 3 ( S 2 ) = Z .
We investigate the ground states of spin-1 Bose–Einstein condensates (BECs) with spin–orbit coupling in a radially periodic potential by numerically solving the coupled Gross–Pitaevskii equations. In the radially periodic potential, we first demonstrate that spin–orbit-coupled antiferromagnetic BECs support a multiring petal phase. Polar–core vortex can be observed from phase profiles, which is manifested as circularly symmetric distribution. We further show that spin–orbit coupling can induce multiring soliton structure in ferromagnetic BECs. It is confirmed especially that the wave-function phase of the ring corresponding to uniform distribution satisfies the rotational symmetry, and the wave-function phase of the ring corresponding to partial splitting breaks the rotational symmetry. Adjusting the spin–orbit coupling strength can control the number of petal in antiferromagnetic BECs and the winding numbers of wave-function in ferromagnetic BECs. Finally, we discuss effects of spin-independent and spin-dependent interactions on the ground states.