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Dynamics of Polar-Core Spin Vortices in Inhomogeneous Spin-1 Bose-Einstein Condensates
by Zachary L. Stevens-Hough, Matthew J. Davis, Lewis A. Williamson
Submission summary
| Authors (as registered SciPost users): | Matthew Davis · Lewis Williamson |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2404.13800v2 (pdf) |
| Date submitted: | 2024-10-23 08:35 |
| Submitted by: | Williamson, Lewis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In the easy-plane phase, a ferromagnetic spin-1 Bose-Einstein condensate is magnetized in a plane transverse to the applied Zeeman field. This phase supports polar-core spin vortices (PCVs), which consist of phase windings of transverse magnetization. Here we show that spin-changing collisions cause a PCV to accelerate down density gradients in an inhomogeneous condensate. The dynamics is well-described by a simplified model adapted from scalar systems, which predicts the dependence of the dynamics on trap tightness and quadratic Zeeman energy. In a harmonic trap, a PCV accelerates radially to the condensate boundary, in stark contrast to the azimuthal motion of vortices in a scalar condensate. In a trap that has a local potential maximum at the centre, the PCV exhibits oscillations around the trap centre, which persist for a remarkably long time. The oscillations coincide with the emission and reabsorption of axial spin waves, which reflect off the condensate boundary.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
List of changes
We have included plots of $F_\perp$ along the line of vortex motion in Fig. 1(a) and Fig. 3(a).
We have clarified that the total mass current remains zero with new text below Eq.~(12).
We have clarified that Eq.~(4) does not describe the stretched PCV (new text below Eq.~(10)) and have highlighted that exploring the non-trivial core structure that develops during the dynamics would be an interesting area for further research in the conclusion.
We have included text explaining the effect of trap softness at the end of Sec.~(5).
We have modified our results so that the initial state is obtained using purely imaginary time evolution. We have added new text to the conclusion discussing the effects of damping on the dynamics.
We have removed Refs [10] and [11] from the list [4-11] and also changed turbulence to quantum turbulence in the first sentence.
We have included additional references to experimental works realising spin defects and textures, see updated references in [18-23].
We have added text below Eq. (22) clarifying why we include the constant factor $\coth^{10}(1)$.
We have modified the text below Eq.~(3) to clarify that we expect our results to be representative of cases $|g_s|\ll g_n$. We have added new text to the conclusion discussing the possible changes that would occur for $|g_s|\sim g_n$, as occurs in $^7$Li.
We have included a $t=0$ frame in Fig 3.
We have added explicit expressions for the spin densities in terms of spin components, see new Eq (2).
We have clarified that the parameters are fits by relabelling them $v_\mathrm{fit}$ and $t_\mathrm{offset}$ and have clarified their physical interpretation below Eq. (23).
We have removed a mention of the trend of $\alpha$ on box size and included text below Eq.~(24) clarifying the dependence on initial vortex position.
We have mentioned the possibility of exploring finite-temperature dynamics in the conclusion, as part of new text discussing effects of damping.
We have add new text to the conclusion discussing the potential instability that arises for a fast-moving vortex.
We have clarified the origin of $F_z$ magnetization, see new text in the second paragraph of Sec 4.
We have added text describing this symmetry in a footnote at the bottom of page 4.
We have clarified that $\kappa$ is restricted to $\pm 1$ in the text above Eq (4) and at the start of Sec 3.
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The authors have sincerely responded to the questions I raised before.
However, I still do not understand the answer to question 3: the derivation of Eq. (10).
The authors say that it follows from symmetry under the transformation (Fx, Fy, Fz) -> (Fx, -Fy, -Fz). Why is the order parameter symmetric under this transformation? When we choose m=1, for example, Eq. (10) reads $|\psi_{-1}({\bf x}_1,t)|^2=|\psi_1({\bf x}_{-1},t)|^2$. This may hold in some symmetric configurations as the authors numerically simulated. However, I think it does not generally hold, in particular, in an inhomogeneous condensate. I guess Eq. (10) is also related to the approximation $\nabla\theta_1|_{{\bf x}_1}\approx -\nabla\theta_{-1}|_{{\bf x}_{-1}}$, which comes from choosing $\psi_0({\bf r})$ to be real.
I understand the result in this paper is correct: I expect $|\psi_{-1}({\bf x}_1,t)|^2=|\psi_1({\bf x}_{-1},t)|^2$ holds when ${\bf s}$ is always perpendicular to the density gradient, and indeed the authors show $\dot{\bf s}\perp \nabla \ln A$. I would like to ask the authors to derive Eq. (10) explicitly or to clarify the assumptions if the authors impose some assumptions.
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