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arXiv:1810.02493 · Physical Review A

Dynamics of a quenched spin-1 antiferromagnetic condensate in a harmonic trap

L. M. Symes, D. Baillie, P. B. Blakie

Published Dec 14, 2018• 14 citations
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Abstract

In this paper we consider a recent experiment [Phys. Rev. A 95, 053638 (2017)] in which an antiferromagnetic spin-1 condensate of $^{23}\mathrm{Na}$ atoms was quenched from the easy-axis polar phase into the easy-plane polar phase. We simulate the phase-transition dynamics by using a classical field method with noisy initial conditions and find good agreement with the experimental observations. We analyze the late-time dynamics in terms of phase ordering by using the nematic order parameter that we have developed in earlier work [Phys. Rev. A 96, 013602 (2017)]. We show that these experiments are able to explore the early stages of universal phase ordering where the domains grow diffusively.

DOI
10.1103/physreva.98.063618

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We consider the formation of order in a quasi-two-dimensional antiferromagnetic spin-1 condensate quenched from an easy-axis to an easy-plane nematic phase. We define the relevant order parameter to quantify the spin-nematic degrees of freedom and study the evolution of the spin-nematic and superfluid order during the coarsening dynamics using numerical simulations. We observe dynamical scaling in the late-time dynamics, with both types of order extending across the system with a diffusive growth law. We identify half-quantum vortices as the relevant topological defects of the ordering dynamics and demonstrate that the growth of both types of order is determined by the mutual annihilation of these vortices.
We demonstrate that a quasi-two-dimensional spin-1 condensate quenched to a ferromagnetic phase undergoes universal coarsening in its late time dynamics. The quench can be implemented by a sudden change in the applied magnetic field and, depending on the final value, the ferromagnetic phase has easy-axis (Ising) or easy-plane (XY) symmetry, with different dynamical critical exponents. Our results for the easy-plane phase reveal a fractal domain structure and the crucial role of polar-core spin vortices in the coarsening dynamics.
Spinor Bose-Einstein condensates exhibit both superfluid and magnetic order, and accommodate phases with rich symmetry properties and topological defects. Transitions between these phases can be induced by tuning external fields. In this thesis we explore the dynamics of order formation in a quasi-2D spin-1 ferromagnetic condensate following a quench from an unmagnetised phase to one of three ferromagnetic phases. The ferromagnetic phases exhibit distinct symmetry properties (easy-plane, easy-axis or isotropic) and support distinct topological defects. In each phase we observe scale invariant ordering and identify the relevant topological defect affecting the order parameter growth. We find that each phase is characterised by a distinct dynamic critical exponent. In the easy-plane phase we identify a persistent turbulent cascade that affects spin ordering long after all topological defects have annihilated. In addition to our exploration of phase ordering dynamics, we study a microscopic model of spin vortex dynamics in the easy-plane phase. Our work provides a comprehensive theoretical study of phase ordering in a conservative system, provides a thorough foundation for studies of phase ordering in antiferromagnetic and higher spin condensates, and offers prospects for further research into fundamental questions regarding the ordering properties of spin systems. Our work is pertinent to current experiments, which have explored the initial stages of phase ordering in both ferromagnetic and antiferromagnetic spin-1 condensates.
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.
We show that the early time dynamics of easy-axis magnetic domain formation in a spinor condensate is described by percolation theory. These dynamics could be initialized using a quench of the spin-dependent interaction parameter. We propose a scheme to observe the same dynamics by quenching the quadratic Zeeman energy and applying a generalized spin rotation to a ferromagnetic spin-1 condensate. Using simulations we investigate the finite-size scaling behavior to extract the correlation length critical exponent and the transition point. We analyze the sensitivity of our results to the early-time dynamics of the system, the quadratic Zeeman energy, and the threshold condition used to define the positive (percolating) domains.
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.