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arXiv:1811.08544 · Physical Review A

Metastable hard-axis polar state of a spinor Bose-Einstein condensate under a magnetic field gradient

Joon Hyun Kim, Deokhwa Hong, Seji Kang, Yong-il Shin

Published Feb 4, 2019• 10 citations
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Abstract

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 ${q}_{\text{th}}$, and as $q$ decreases below ${q}_{\text{th}}$ 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 ${q}_{\text{th}}$ on ${B}^{\ensuremath{'}}$ and the sample size, and we find that ${q}_{\text{th}}$ 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.

DOI
10.1103/physreva.99.023606

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We investigate the critical dynamics of spin superflow in an easy-plane antiferromagnetic spinor Bose-Einstein condensate. Spin-dipole oscillations are induced in a trapped condensate by applying a linear magnetic field gradient and we observe that the damping rate increases rapidly as the field gradient increases above a certain critical value. The onset of dissipation is found to be associated with the generation of dark-bright solitons due to the modulation instability of the counterflow of two spin components. Spin turbulence emerges as the solitons decay because of their snake instability. We identify another critical point for spin superflow, in which transverse magnon excitations are dynamically generated via spin-exchanging collisions, which leads to the transient formation of axial polar spin domains.
We investigate the phase-transition dynamics of a quasi-two-dimensional antiferromagnetic spin-1 Bose-Einstein condensate from the easy-axis polar phase to the easy-plane polar phase, which is initiated by suddenly changing the sign of the quadratic Zeeman energy qqq. We observe the emergence and decay of spin turbulence and the formation of half-quantum vortices (HQVs) in the quenched condensate. The characteristic time and length scales of the turbulence generation dynamics are proportional to ${|q|}^{\ensuremath{-}1/2}$ as inherited from the dynamic instability of the initial state. In the evolution of the spin turbulence, spin-wave excitations develop from large to small length scales, suggesting a direct energy cascade, and the spin population for the axial polar domains exhibit a nonexponential decay. The final equilibrated condensate contains HQVs, and the number is found to increase and saturate with increasing ∣q∣|q|∣q∣. Our results demonstrate the time-space scaling properties of the phase-transition dynamics near the critical point and the peculiarities of the spin-turbulence state of the antiferromagnetic spinor condensate.
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We investigate the early-time dynamics of a quasi-two-dimensional spin-1 antiferromagnetic Bose-Einstein condensate after a sudden quench from the easy-plane to the easy-axis polar phase. The postquench dynamics shows a crossover behavior as the quench strength $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}$ is increased, where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}$ is defined as the ratio of the initial excitation energy per particle to the characteristic spin interaction energy. For a weak quench of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}<1$, long-wavelength spin excitations are dominantly generated, leading to the formation of irregular spin domains. With increasing $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}$, the length scale of the initial spin excitations decreases, and we demonstrate that the long-wavelength instability is strongly suppressed for high $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{q}>2$. The observed crossover behavior is found to be consistent with the Bogoliubov description of the dynamic instability of the initial spinor condensate.
We have experimentally observed the dynamics of an antiferromagnetic sodium Bose-Einstein condensate quenched through a quantum phase transition. Using an off-resonant microwave field coupling the F = 1 and F = 2 atomic hyperfine levels, we rapidly switched the quadratic energy shift q from positive to negative values. At q = 0, the system undergoes a transition from a polar to antiferromagnetic phase. We measured the dynamical evolution of the population in the F = 1, mF = 0 state in the vicinity of this transition point and observed a mixed state of all 3 hyperfine components for q < 0. We also observed the coarsening dynamics of the instability for q < 0, as it nucleated small domains that grew to the axial size of the cloud.