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Dipolar condensed atomic mixtures and miscibility under rotation
by Lauro Tomio, R. Kishor Kumar and Arnaldo Gammal
This Submission thread is now published as SciPost Phys. Proc. 3, 023 (2020)
Submission summary
As Contributors:  LAURO TOMIO 
Preprint link:  scipost_201911_00021v3 
Date accepted:  20191210 
Date submitted:  20191129 01:00 
Submitted by:  TOMIO, LAURO 
Submitted to:  SciPost Physics Proceedings 
Proceedings issue:  24th European Few Body Conference (University of Surrey, U.K.) 
Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
By considering symmetric and asymmetric dipolar coupled mixtures (with dysprosium and erbium isotopes), we report a study on relevant anisotropic effects, related to spatial separation and miscibility, due to dipoledipole interactions (DDIs) in rotating binary dipolar BoseEinstein condensates. The binary mixtures are kept in strong pancakelike traps, with repulsive twobody interactions modeled by an effective twodimensional (2D) coupled GrossPitaevskii equation. The DDI are tuned from repulsive to attractive by varying the dipole polarization angle. A clear spatial separation is verified in the densities for attractive DDIs, being angular for symmetric mixtures and radial for asymmetric ones. Also relevant is the massimbalance sensibility observed by the vortexpatterns in symmetric and asymmetricdipolar mixtures. In an extension of this study, here we show how the rotational properties and spatial separation of these dipolar mixture are affected by a quartic term added to the harmonic trap of one of the components.
Published as SciPost Phys. Proc. 3, 023 (2020)
Author comments upon resubmission
Response to the Referee's report
We thank the Referee for the positive evaluation of our study, as well as for recommendations which helped us to improve the manuscript. Below, we summarize the changes made in our revision, following the Referee's comments.
Referee:
Weaknesses: There is not much discussion about how the quartic potential could be created in practice, and why it would affect only (or mostly) the heavier species. While for the ErDy mixture it is clear that this may help invert the insideoutside densities, for the DyDy mixture the situation is less clear. If this additional trapping energy is considered to be due to the same trapping laser creating the harmonic confinement, it would appear that it should affect the lighter species more, as this is the one that will generally explore a larger spatial region.
Authors:
To address this suggestion, we have included [just after the Eq.(3)] a discussion about the experimental implementation of quartic potential, in which we cite a new reference (see [13]). Details are given in section 4 of this reference, as well as in other within cited references. We should further clarify here that both elements of the mixture can be trapped independently, with the quartic potential affecting only one of the components, chosen to be the heavier mass one. For this choice, by following details given in our Ref.[12], we need to remind that the mass ratio between the components affects the miscibility properties; and that the insideoutside positions of the densities (when going from zero to 90 degrees) in case of ErDy mixture is due to anisotropic effects of the dipolar interaction (even before adding the quartic potential).
Close to 90 degrees, Dy is providing more attractive interaction than Er.
Therefore, the radius of the Dy density shrinks, with the Er being pulled out at large $\varphi$. The quartic interaction with strength $\kappa$=0.05 is not enough to invert their radialspacial positions. For that, we need to increase the strength $\kappa$ of the quartic interactions, as verify by the Fig.4.
Referee:
1. The authors should introduce earlier on what they mean by symmetric" and
asymmetric" mixtures. This is done only on page 5
(lines 166167), when the concepts have been used much earlier in the text.
Authors: To address this comment, in our revision of the subsection ``Parametrization and numerical approach", we use the first sentences to clarify these terms, as being related to the dipolar symmetry of the mixtures. In the abstract and also along the text we try to emphasize that, by using "symmetric" and "asymmetric" as adjective for dipolar (as one could also think about the mass symmetry).
Referee: 2. The authors should provide some statement on the potential way to generate a controllable quartic potential in practice (e.g., an additional laser detuned from a particular transition of one species, so as to affect only that one?).
Authors: In the revised version, we have included a reference [13] related to the experimental possibilities for using quartic potentials in BECs. Within a mixture of two species, one should select one of them to apply the laser detuned for quadraticquartic interaction.
Referee: The authors could indicate the advantages, if any, of calculating the dipoleinteraction term by moving to momentum (Fourier) space. Does this provide any numerical advantage?
Authors: The nonlocal term with the magneticdipolar interactions in the integrand of Eq.(2) is quite singular at the origin, having nontrivial numerical solution in coordinate space. In view of that, one can circumvent this issue, by using Fourier convolution, which is of easy numerical implementation, as shown with more details in Ref.[10].
List of changes
[1] In the subsection 2.1, ``Model formalism", a discussion about the quartic trap and possible experimental realization is included within the seven lines after Eq.(3). There, we have also pointed out a reference [13] where more details can be found.
[2] In the subsection 2.2, ``Parametrization and numerical approach", the first four lines are new, by clarifying our ``symmetric" and ``asymmetric" definitions for the particular mixtures we are considering. Also, along the text we did some small modifications, accordingly (emphasizing the symmetry properties as adjective to dipolar).
[3] We remove the previous Ref.[13], because we notice that it was not being cited in the manuscript. In practice it was replaced by the new reference [13], which is being used to indicate possible experimental realizations.
Submission & Refereeing History
Published as SciPost Phys. Proc. 3, 023 (2020)
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Reports on this Submission
Anonymous Report 1 on 2019125 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_201911_00021v3, delivered 20191205, doi: 10.21468/SciPost.Report.1371
Report
The authors have addressed the main requests raised in the earlier referee report, with the only exception of a motivation for moving to Fourier space for their numerics. I do not find this a critical point questioning the validity of the paper, and thus I see it fit for publication in SciPost Physics Proceedings.