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arXiv:1611.08922 · Physical Review A

Different growth rates for spin and superfluid order in a quenched spinor condensate

Andréane Bourges, P. B. Blakie

Published Feb 17, 2017• 33 citations
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Abstract

In this paper we study the coarsening dynamics of a spinor condensate quenched into an easy-axis ferromagnetic phase by a sudden change in the quadratic Zeeman energy. We show that applying a spin rotation prior to changing the Zeeman energy accelerates the development of local order and reduces heating. We examine the longitudinal spin ordering and the superfluid ordering of the system and show that the respective order parameter correlation functions exhibit dynamic scaling in the late-time dynamics. Our results also demonstrate that these two types of order grow at different rates, i.e., with different dynamic critical exponents. The spin domain area distribution is calculated and is shown to have power-law scaling behavior expected from percolation theory.

DOI
10.1103/physreva.95.023616

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In this paper we study the coarsening dynamics of a spinor condensate quenched into an easy-axis ferromagnetic phase by a sudden change in the quadratic Zeeman energy. We show that applying a spin rotation prior to changing the Zeeman energy accelerates the development of local order and reduces heating. We examine the longitudinal spin ordering and the superfluid ordering of the system and show that the respective order parameter correlation functions exhibit dynamic scaling in the late-time dynamics. Our results also demonstrate that these two types of order grow at different rates, i.e., with different dynamic critical exponents. The spin domain area distribution is calculated and is shown to have power-law scaling behavior expected from percolation theory.
We examine the dynamics of a quasi-two-dimensional spin-1 condensate in which the quadratic Zeeman energy qqq is suddenly quenched to a value where the system has a ferromagnetic ground state. There are two distinct types of ferromagnetic phases, i.e., a range of qqq values where the magnetization prefers to be in the direction of the external field (easy axis) and a range of qqq values where it prefers to be transverse to the field (easy plane). We study the quench dynamics for a variety of qqq values and show that there is a single dynamic critical exponent to characterize the scale-invariant domain growth for each ferromagnetic phase. For both quenches we give simple analytic models that capture the essential scale-invariant dynamics and correctly predict the exponents. Because the order parameter for each phase is different, the natures of the domains and the relevant topological defects in each type of coarsening are also different. To explore these differences we characterize the fractal dimension of the domain walls and the relationship of polar-core spin vortices to the domains in the easy-plane phase. Finally, we consider how the energy liberated from the quench thermalizes in the easy-axis quench. We show that local equilibrium is established in the spin waves on moderate time scales, but continues to evolve as the domains anneal.
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 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.
In zero magnetic field the ground-state manifold of a ferromagnetic spin-1 condensate is SO(3) and exhibits Z_{2} vortices as topological defects. We investigate the phase-ordering dynamics of this system after being quenched into this ferromagnetic phase from a zero-temperature unmagnetized phase. Following the quench, we observe the ordering of both magnetic and gauge domains. We find that these domains grow diffusively, i.e., with domain size L(t)∼t^{1/2}, and exhibit dynamic scale invariance. The coarsening dynamics progresses as Z_{2} vortices annihilate; however, we find that at finite energy a number of these vortices persist in small clumps without influencing magnetic or gauge order. We consider the influence of a small nonzero magnetic field, which reduces the ground-state symmetry, and show that this sets a critical length scale such that when the domains reach this size the system dynamically transitions in order parameter and scaling behavior from an isotropic to an anisotropic ferromagnetic superfluid.
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.