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arXiv:1502.06673 · Physical Review A

Coarsening dynamics driven by vortex-antivortex annihilation in ferromagnetic Bose-Einstein condensates

Kazue Kudo, Yuki Kawaguchi

Published May 12, 2015• 32 citations
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Abstract

In ferromagnetic Bose-Einstein condensates (BECs), the quadratic Zeeman effect controls magnetic anisotropy, which affects magnetic domain pattern formation. While the longitudinal magnetization is dominant (similar to the Ising model) for a negative quadratic Zeeman energy, the transverse magnetization is dominant (similar to the $XY$ model) for a positive one. When the quadratic Zeeman energy is positive, the coarsening dynamics is driven by vortex-antivortex annihilation in the same way as the $XY$ model. However, due to a superfluid flow of atoms, there exist several combinations of vortex-antivortex pairs in ferromagnetic BECs, which makes the coarsening dynamics more complicated than that of the $XY$ model. We propose a revised domain growth law, which is based on the growth law of the two-dimensional $XY$ model, for a two-dimensional ferromagnetic BEC with a positive quadratic Zeeman energy.

DOI
10.1103/physreva.91.053609

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In ferromagnetic Bose-Einstein condensates (BECs), the quadratic Zeeman effect controls magnetic anisotropy, which affects magnetic domain pattern formation. While the longitudinal magnetization is dominant (similar to the Ising model) for a negative quadratic Zeeman energy, the transverse magnetization is dominant (similar to the XYXYXY model) for a positive one. When the quadratic Zeeman energy is positive, the coarsening dynamics is driven by vortex-antivortex annihilation in the same way as the XYXYXY model. However, due to a superfluid flow of atoms, there exist several combinations of vortex-antivortex pairs in ferromagnetic BECs, which makes the coarsening dynamics more complicated than that of the XYXYXY model. We propose a revised domain growth law, which is based on the growth law of the two-dimensional XYXYXY model, for a two-dimensional ferromagnetic BEC with a positive quadratic Zeeman energy.
Magnetic domain patterns in a ferromagnetic Bose-Einstein condensate (BEC) show different properties depending on the quadratic Zeeman effect and dissipation. Another important factor that affects domain patterns and domain growth is superfluid flow of atoms. Domain growth in a ferromagnetic BEC with negative quadratic Zeeman energy is characterized by the same growth law as a (classical) binary fluid in the inertial hydrodynamic regime. In the absence of the superfluid flow, the domain growth law for negative quadratic Zeeman energy is the same as that of scalar conserved fields, such as binary alloys.
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.
The static properties, i.e., existence and stability, as well as the quench-induced dynamics of nonlinear excitations of the vortex-bright type appearing in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. The precessional motion of such coherent structures is subsequently monitored dynamically. Deformations of the above configurations across the relevant transitions are exposed and discussed in detail. It is further found that stationary states involving highly quantized vortices can be realized in both settings. Spatial elongations, precessional motion and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes being accessible in contemporary cold atom experiments.
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.
The static properties, i.e., existence and stability, as well as the quench-induced dynamics of vortex-bright type excitations in two-dimensional harmonically confined spin-1 Bose-Einstein condensates are investigated. Linearly stable vortex-bright-vortex and bright-vortex-bright solutions arise in both antiferromagnetic and ferromagnetic spinor gases upon quadratic Zeeman energy shift variations. Their deformations across the relevant transitions are exposed and discussed in detail, evincing also that emergent instabilities can lead to pattern formation. Spatial elongations, precessional motion, and spiraling of the nonlinear excitations when exposed to finite temperatures and upon crossing the distinct phase boundaries, via quenching of the quadratic Zeeman coefficient, are unveiled. Spin-mixing processes triggered by the quench lead, among others, to changes in the waveform of the ensuing configurations. Our findings reveal an interplay between pattern formation and spin-mixing processes accessible in contemporary cold atom experiments.
We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate (BEC) from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature (London) 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices depend also on the manner in which the magnetic field is changed. We point out an analogy between the formation of spin vortices from domain walls in a spinor BEC and that of vortex-antivortex pairs from dark solitons in a scalar BEC.