We investigate the stability of a hard-axis polar state in a spin-1 antiferromagnetic Bose-Einstein condensate under a magnetic field gradient, where the easy-plane spin anisotropy is controlled by a negative quadratic Zeeman energy
q<0. In a uniform magnetic field, the axial polar state is dynamically unstable and relaxes into the planar polar ground state. However, under a field gradient ${B}^{\ensuremath{'}}$, the excited spin state becomes metastable down to a certain threshold
qth, and as
q decreases below
qth its intrinsic dynamical instability is rapidly recalled. The incipient spin excitations in the relaxation dynamics appear with stripe structures, indicating the rotational symmetry breaking by the field gradient. We measure the dependences of
qth on ${B}^{\ensuremath{'}}$ and the sample size, and we find that
qth is highly sensitive to the field gradient in the vicinity of ${B}^{\ensuremath{'}}=0$, exhibiting power-law behavior of $|{q}_{\text{th}}|\ensuremath{\propto}{B}^{\ensuremath{'}\ensuremath{\alpha}}$ with $\ensuremath{\alpha}\ensuremath{\sim}0.5$. Our results demonstrate the significance of the field gradient effect in the quantum critical dynamics of spinor condensates.
The ground-state properties of a spin-orbit-coupled rotating Bose-Einstein condensate with a gradient magnetic field in a toroidal trap are studied. When gradient magnetic fields are taken into account, the results are quite novel in that, in the spin-orbit-coupled nonrotating Bose-Einstein condensate with small gradient magnetic field intensity, the ferromagnetic system presents a plane-wave phase and satisfies the translational symmetry, and the antiferromagnetic system presents a stripe phase. With the increase of the magnetic field intensity, the translational symmetry of the ground state of the ferromagnetic system is broken, and the phase change tends to be similar in both ferromagnetic and antiferromagnetic systems. Considering the spin-orbit-coupled rotating Bose-Einstein condensate, the system gradually transforms from the nonsingle half-skyrmion chain to the single half-skyrmion chain with the increase of the gradient magnetic field, while the single half-skyrmion chain transforms to the nonsingle half-skyrmion chain with the increase of spin-orbit coupling. In addition, we obtain the phase diagram as a function of the gradient magnetic field and the spin-orbit-coupling intensity.
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.