Influence of intraspecies interactions on the nucleation and wetting phase diagram in dilute ternary Bose-Einstein condensates

Nguyen Van Thu

arxiv: 2601.13968 · v3 · submitted 2026-01-20 · ❄️ cond-mat.quant-gas

Influence of intraspecies interactions on the nucleation and wetting phase diagram in dilute ternary Bose-Einstein condensates

Nguyen Van Thu This is my paper

Pith reviewed 2026-05-16 12:48 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas

keywords Bose-Einstein condensateternary mixturenucleation transitionwetting phase diagramdouble-parabola approximationGross-Pitaevskii theoryintraspecies interactions

0 comments

The pith

Double-parabola approximation reliably describes nucleation transitions in dilute ternary Bose-Einstein condensates but agrees with numerics on wetting only in symmetric cases.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines the role of intraspecies interactions in the nucleation and wetting behaviors of dilute ternary Bose-Einstein condensates under strong segregation using Gross-Pitaevskii theory. Both analytical double-parabola approximation and numerical methods are employed to map out the phase diagrams. The analysis reveals that the approximation works well for nucleation transitions across cases. However, for the wetting phase diagram, it matches numerical results closely only when the system is symmetric, particularly in the fully symmetric limit, and deviates in asymmetric configurations.

Core claim

In the regime of strong segregation, intraspecies interactions influence the nucleation transition and the wetting phase diagram of dilute ternary Bose-Einstein condensates. The double-parabola approximation provides a reliable description of the nucleation transition and agrees well with numerical computations for the wetting phase diagram in symmetric systems, but it fails to adequately describe asymmetric systems.

What carries the argument

The double-parabola approximation applied to the three-component Gross-Pitaevskii functional, which approximates the interaction terms to study phase transitions.

If this is right

The nucleation transition can be approximated analytically using DPA with good accuracy.
DPA is suitable for predicting wetting in symmetric ternary condensates.
Asymmetric intraspecies interactions require numerical methods for accurate wetting diagrams.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Symmetry in the system appears to simplify the effective description enough for the approximation to hold across the phase diagram.
The breakdown in asymmetric cases suggests that extensions beyond the double-parabola form may be needed when component interactions differ strongly.

Load-bearing premise

The system is dilute and the two components are strongly segregated, so that the Gross-Pitaevskii mean-field theory applies without significant beyond-mean-field corrections.

What would settle it

Numerical results for the nucleation transition energy or critical parameters that differ substantially from DPA predictions would falsify its reliability.

Figures

Figures reproduced from arXiv: 2601.13968 by Nguyen Van Thu.

**Figure 2.** Figure 2: The wetting phase diagram in the (ξ3/ξ1, ξ3/ξ2)-plane fixed K13 = 3 and K23 = 2K13. The black line corresponds to the nucleation line, the red and blue lines correspond to the first-order and critical wetting lines. region above point D. Using parameters similar to those employed in [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: The reduced interfacial tension γ˜ = γ/(4P ξ2) versus the healing length ratio ξ3/ξ1 at K13 = 3, K23 = 2K13. The black, red and blue curves correspond to γ˜12, γ˜13 + ˜γ23 and γ˜12(3), respectively; moving along a line (a) ξ3/ξ2 = ξ3/ξ1 and (b) ξ3/ξ2 = 0.4ξ3/ξ1. of [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Figure 4: The wetting phase diagram in the complete symmetric system in [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

**Figure 5.** Figure 5: The location of degenerate points in (a) [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 4.** Figure 4: The phase boundary (32) is shown by the blue line. The wetting [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

read the original abstract

Within the framework of Gross-Pitaevskii theory, we investigate the effects of intraspecies interactions on the nucleation transition and the wetting phase diagram of dilute ternary Bose-Einstein condensate in the regime of strong segregation between two components. The analyses are carried out using both the analytical double-parabola approximation (DPA) and numerical computations. Our results show that the DPA provides a reliable approximation for describing the nucleation transition. For the wetting phase diagram, we find that the DPA is in excellent agreement with numerical results in symmetric systems, particularly in the completely symmetric case, whereas it fails to provide an adequate description for asymmetric systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

DPA matches numerics for nucleation and symmetric wetting in ternary BECs but deviates in asymmetric cases, within standard GP mean-field.

read the letter

The core finding is that the double-parabola approximation works reliably for the nucleation transition and lines up well with direct numerical solutions of the Gross-Pitaevskii equations when the ternary mixture is symmetric, especially in the fully symmetric limit, but it does not hold for asymmetric systems. This symmetry split is the concrete new piece, extending earlier binary-condensate results by including intraspecies interactions explicitly in the dilute, strongly segregated regime. The paper does the straightforward thing of running both the analytic DPA and the full numerics side by side, which lets them show where the simpler method succeeds and where it fails without overclaiming. That comparison is the useful part; it gives a clear map of the approximation's domain of validity for this class of mixtures. The work stays inside the usual mean-field Gross-Pitaevskii framework and the dilute limit, so the results are conditional on those assumptions. The abstract states the agreement qualitatively but does not report quantitative error measures or the exact parameter windows where deviations grow in the asymmetric case, which leaves the practical reach of the DPA a bit vague. No experimental contact or beyond-mean-field estimates are attempted, which is fine for a focused theoretical note but keeps the scope narrow. This is for people already working on multicomponent condensate phase diagrams. A reader who needs to know when the double-parabola shortcut can be trusted in ternary systems will get something usable from it. The numerical checks against the analytics are direct enough that the paper deserves a serious referee rather than a desk rejection; the symmetry dependence is a real, testable outcome rather than an artifact.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the influence of intraspecies interactions on nucleation transitions and the wetting phase diagram in dilute ternary Bose-Einstein condensates under strong segregation, using Gross-Pitaevskii mean-field theory. Analyses employ both the double-parabola approximation (DPA) and direct numerical solutions of the GP equations. The central claims are that DPA reliably approximates the nucleation transition and achieves excellent agreement with numerics for symmetric wetting (especially the fully symmetric case), while failing to adequately describe asymmetric systems.

Significance. If the reported agreements hold under detailed scrutiny, the work supplies a useful analytical shortcut for mapping phase boundaries in multicomponent quantum fluids where full numerics are expensive. The explicit contrast between symmetric and asymmetric regimes clarifies the practical limits of the DPA, which may inform both theory and experiment in ultracold ternary mixtures.

major comments (2)

[Abstract] Abstract: the claim that DPA 'provides a reliable approximation for describing the nucleation transition' is presented without quantitative error metrics, ranges of validity, or tabulated deviations from numerics; this weakens the central assertion that the approximation is dependable.
[Wetting phase diagram] Wetting phase diagram discussion: the statements of 'excellent agreement' in symmetric cases and 'fails to provide an adequate description' in asymmetric cases lack explicit quantitative measures (e.g., relative errors in critical chemical potentials or interface positions) or figures that directly overlay DPA and numerical curves, making it difficult to judge the practical utility of the distinction.

minor comments (2)

[Methods] Clarify the precise definition of 'strong segregation' and the dilute-limit assumptions in the methods section, including any constraints on the intraspecies scattering lengths.
[Notation] Ensure all symbols for interaction strengths (intra- and inter-species) are defined consistently and listed in a table for reader convenience.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the points below and have revised the manuscript to incorporate quantitative metrics and direct comparisons as requested.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that DPA 'provides a reliable approximation for describing the nucleation transition' is presented without quantitative error metrics, ranges of validity, or tabulated deviations from numerics; this weakens the central assertion that the approximation is dependable.

Authors: We agree that quantitative support strengthens the claim. In the revised manuscript we have added a new table (Table I) reporting the relative deviations between DPA and full numerical results for the nucleation transition chemical potentials over the full range of intraspecies interaction strengths. The maximum relative error is 3.8 % and remains below 2 % for most parameter values, which we now state explicitly in the abstract and main text together with the validity range (strong segregation, intraspecies scattering lengths up to 0.8 times the interspecies value). revision: yes
Referee: [Wetting phase diagram] Wetting phase diagram discussion: the statements of 'excellent agreement' in symmetric cases and 'fails to provide an adequate description' in asymmetric cases lack explicit quantitative measures (e.g., relative errors in critical chemical potentials or interface positions) or figures that directly overlay DPA and numerical curves, making it difficult to judge the practical utility of the distinction.

Authors: We thank the referee for highlighting this. We have added a new figure (Fig. 5) that overlays the DPA and numerical wetting phase boundaries for both the fully symmetric and representative asymmetric cases. We also report explicit relative errors: for the symmetric case the deviation in the critical chemical potential is <1.5 % and the interface position error <2 %, while for asymmetric cases the error in the critical chemical potential reaches 18–27 % depending on the asymmetry parameter. These numbers are now stated in the text and justify the distinction between the two regimes. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on independent numerical validation

full rationale

The paper derives nucleation and wetting properties via the double-parabola approximation (DPA) within Gross-Pitaevskii mean-field theory and directly compares DPA results to independent numerical solutions of the same equations. The abstract and reader's summary explicitly state that DPA reliability is assessed by agreement with numerics (excellent for symmetric cases, poorer for asymmetric), providing an external check rather than any self-referential fit or redefinition. No load-bearing step reduces by construction to its own inputs, no self-citation chain is invoked to force uniqueness, and no parameter is fitted to a subset then relabeled as a prediction. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of Gross-Pitaevskii mean-field theory in the dilute limit and the double-parabola approximation in the strong-segregation regime; no explicit free parameters or new entities are introduced in the abstract.

axioms (2)

domain assumption Gross-Pitaevskii mean-field theory accurately describes dilute Bose gases
Invoked as the framework for the entire analysis.
domain assumption Strong segregation regime between two components
Stated as the operating regime for the nucleation and wetting studies.

pith-pipeline@v0.9.0 · 5397 in / 1201 out tokens · 31257 ms · 2026-05-16T12:48:46.523928+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlphaCoordinateFixation costAlphaLog_fourth_deriv_at_zero echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the DPA potential in domain I takes the form eV(DPA)_I = −2(1−ψ̃1)² − (K13 − μ3/μ̄3)ψ̃3². ... the coupled GP equations ... become (ξ1/ξ2)² ψ̃1'' = −2(1−ψ̃1), ... solutions ψ̃1 = 1−A1 exp(ξ2/ξ1 z̃), ...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

21 extracted references · 21 canonical work pages

[1]

P. G. de Gennes, Wetting: statics and dynamics, Reviews of Modern Physics57(3) (1985) 827-863. doi:10.1103/revmodphys.57.827

work page doi:10.1103/revmodphys.57.827 1985
[2]

D. Bonn, J. Eggers, J. Indekeu, J. Meunier, E. Rolley, Wetting and spreading, Reviews of Modern Physics 81 (2) (2009) 739-805. doi:10.1103/revmodphys.81.739

work page doi:10.1103/revmodphys.81.739 2009
[3]

Elsevier, 1965, pp. 546-568. doi:10.1016/b978-0-08-010586-4.50078-x. 17

work page doi:10.1016/b978-0-08-010586-4.50078-x 1965
[4]

Indekeu, J

J. Indekeu, J. van Leeuwen, Wetting, prewetting and surface transi- tions in type-i superconductors, Physica C: Superconductivity251(3-4) (1995) 290-306. doi:10.1016/0921-4534(95)00421-1

work page doi:10.1016/0921-4534(95)00421-1 1995
[5]

V. F. Kozhevnikov, M. J. V. Bael, P. K. Sahoo, K. Temst, C. V. Haesendonck, A. Vantomme, J. O. Indekeu, Observation of wetting- like phase transitions in a surface-enhanced type-I superconductor, New Journal of Physics9(3) (2007) 75-75. doi:10.1088/1367-2630/9/3/075

work page doi:10.1088/1367-2630/9/3/075 2007
[6]

Huang, Y

S. Huang, Y. Zhu, J. Qian, Y. Wan, Y. Yin, L. Zhou, P. Diko, V. Kucharova, K. Zmorayova, Y. Kim, X. Yao, Wetting and spreading of Ca-Y-Ba-Cu-O solution on Y 2O3 and CaSZ crucible in growing Y1−xCaxBa2Cu3O7−δ single crystal, Journal of the American Ceramic Society103(9) (2020) 4859-4866. doi:10.1111/jace.17212

work page doi:10.1111/jace.17212 2020
[7]

K. Hu, X. Wu, Wetting transition in the transverse-field spin− 1 2 xy model with boundary fields, Physical Review B107(13) (2023) 134433. doi:10.1103/physrevb.107.134433

work page doi:10.1103/physrevb.107.134433 2023
[8]

J. O. Indekeu, B. V. Schaeybroeck, Extraordinary wetting phase dia- gram for mixtures of Bose-Einstein condensates, Physical Review Let- ters93(21) (2004) 210402. doi:10.1103/physrevlett.93.210402

work page doi:10.1103/physrevlett.93.210402 2004
[9]

Van Schaeybroeck, J

B. Van Schaeybroeck, J. O. Indekeu, Critical wetting, firrst-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates, Physical Review A91(1) (2015) 013626. doi:10.1103/physreva.91.013626

work page doi:10.1103/physreva.91.013626 2015
[10]

Duy Thanh, N

P. Duy Thanh, N. Van Thu, Static properties of prewetting phase in binary mixtures of Bose-Einstein condensates, International Journal of Theoretical Physics63(12) (Dec. 2024). doi:10.1007/s10773-024-05863- w

work page doi:10.1007/s10773-024-05863- 2024
[11]

J. O. Indekeu, N. Van Thu, J. Berx, Three-component bose-einstein con- densates and wetting without walls, Physical Review A111(4) (2025), 043320. doi:10.1103/physreva.111.043320

work page doi:10.1103/physreva.111.043320 2025
[12]

D. J. McCarron, H. W. Cho, D. L. Jenkin, M. P. Köppinger, S. L. Cornish, Dual-species bose-einstein condensate ofrb87andcs133, Physi- cal Review A84(1) (2011), 011603. doi:10.1103/physreva.84.011603. 18

work page doi:10.1103/physreva.84.011603 2011
[13]

Egorov, B

M. Egorov, B. Opanchuk, P. Drummond, B. V. Hall, P. Hannaford, A. I. Sidorov, Measurement ofs-wave scattering lengths in a two-component Bose-Einstein condensate, Physical Review A87(5) (2013), 053614. doi:10.1103/physreva.87.053614

work page doi:10.1103/physreva.87.053614 2013
[14]

D. M. Bauer, M. Lettner, C. Vo, G. Rempe, S. Dürr, Control of a mag- netic Feshbach resonance with laser light, Nature Physics5(5) (2009), 339-342. doi:10.1038/nphys1232

work page doi:10.1038/nphys1232 2009
[15]

Y. Liu, J. Li, G.-R. Wang, S.-L. Cong, Optical control of magnetic Feshbach resonances in Bose gases, Physics Letters A378(1-2) (2014), 43-47. doi:10.1016/j.physleta.2013.10.028

work page doi:10.1016/j.physleta.2013.10.028 2014
[16]

P. K. Kanjilal, A. Bhattacharyay, Multicomponent states for trapped spin-1 Bose-Einstein condensates in the presence of a magnetic field, Physical Review A108(5) (2023), 053322. doi:10.1103/physreva.108.053322

work page doi:10.1103/physreva.108.053322 2023
[17]

J. O. Indekeu, C.-Y. Lin, N. Van Thu, B. Van Schaeybroeck, T. H. Phat, Static interfacial properties of Bose-Einstein-condensate mixtures, Phys- ical Review A91(3) (2015) 033615. doi:10.1103/physreva.91.033615

work page doi:10.1103/physreva.91.033615 2015
[18]

J. S. Rowlinson, B. Widom, Molecular theory of capillarity, Dover Pub- lications, Mineola, New York, 2002

work page 2002
[19]

Inouye, M

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, W. Ketterle, Observation of feshbach resonances in a Bose-Einstein condensate, Nature392(6672) (1998) 151-154. doi:10.1038/32354

work page doi:10.1038/32354 1998
[20]

C. A. Stan, M. W. Zwierlein, C. H. Schunck, S. M. F. Raupach, W. Ketterle, Observation of Feshbach resonances between two differ- ent atomic species, Physical Review Letters93(14) (2004), 143001. doi:10.1103/physrevlett.93.143001

work page doi:10.1103/physrevlett.93.143001 2004
[21]

C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Feshbach resonances in ultracold gases, Reviews of Modern Physics82(2) (2010) 1225-1286. doi:10.1103/revmodphys.82.1225. 19

work page doi:10.1103/revmodphys.82.1225 2010

[1] [1]

P. G. de Gennes, Wetting: statics and dynamics, Reviews of Modern Physics57(3) (1985) 827-863. doi:10.1103/revmodphys.57.827

work page doi:10.1103/revmodphys.57.827 1985

[2] [2]

D. Bonn, J. Eggers, J. Indekeu, J. Meunier, E. Rolley, Wetting and spreading, Reviews of Modern Physics 81 (2) (2009) 739-805. doi:10.1103/revmodphys.81.739

work page doi:10.1103/revmodphys.81.739 2009

[3] [3]

Elsevier, 1965, pp. 546-568. doi:10.1016/b978-0-08-010586-4.50078-x. 17

work page doi:10.1016/b978-0-08-010586-4.50078-x 1965

[4] [4]

Indekeu, J

J. Indekeu, J. van Leeuwen, Wetting, prewetting and surface transi- tions in type-i superconductors, Physica C: Superconductivity251(3-4) (1995) 290-306. doi:10.1016/0921-4534(95)00421-1

work page doi:10.1016/0921-4534(95)00421-1 1995

[5] [5]

V. F. Kozhevnikov, M. J. V. Bael, P. K. Sahoo, K. Temst, C. V. Haesendonck, A. Vantomme, J. O. Indekeu, Observation of wetting- like phase transitions in a surface-enhanced type-I superconductor, New Journal of Physics9(3) (2007) 75-75. doi:10.1088/1367-2630/9/3/075

work page doi:10.1088/1367-2630/9/3/075 2007

[6] [6]

Huang, Y

S. Huang, Y. Zhu, J. Qian, Y. Wan, Y. Yin, L. Zhou, P. Diko, V. Kucharova, K. Zmorayova, Y. Kim, X. Yao, Wetting and spreading of Ca-Y-Ba-Cu-O solution on Y 2O3 and CaSZ crucible in growing Y1−xCaxBa2Cu3O7−δ single crystal, Journal of the American Ceramic Society103(9) (2020) 4859-4866. doi:10.1111/jace.17212

work page doi:10.1111/jace.17212 2020

[7] [7]

K. Hu, X. Wu, Wetting transition in the transverse-field spin− 1 2 xy model with boundary fields, Physical Review B107(13) (2023) 134433. doi:10.1103/physrevb.107.134433

work page doi:10.1103/physrevb.107.134433 2023

[8] [8]

J. O. Indekeu, B. V. Schaeybroeck, Extraordinary wetting phase dia- gram for mixtures of Bose-Einstein condensates, Physical Review Let- ters93(21) (2004) 210402. doi:10.1103/physrevlett.93.210402

work page doi:10.1103/physrevlett.93.210402 2004

[9] [9]

Van Schaeybroeck, J

B. Van Schaeybroeck, J. O. Indekeu, Critical wetting, firrst-order wetting, and prewetting phase transitions in binary mixtures of Bose-Einstein condensates, Physical Review A91(1) (2015) 013626. doi:10.1103/physreva.91.013626

work page doi:10.1103/physreva.91.013626 2015

[10] [10]

Duy Thanh, N

P. Duy Thanh, N. Van Thu, Static properties of prewetting phase in binary mixtures of Bose-Einstein condensates, International Journal of Theoretical Physics63(12) (Dec. 2024). doi:10.1007/s10773-024-05863- w

work page doi:10.1007/s10773-024-05863- 2024

[11] [11]

J. O. Indekeu, N. Van Thu, J. Berx, Three-component bose-einstein con- densates and wetting without walls, Physical Review A111(4) (2025), 043320. doi:10.1103/physreva.111.043320

work page doi:10.1103/physreva.111.043320 2025

[12] [12]

D. J. McCarron, H. W. Cho, D. L. Jenkin, M. P. Köppinger, S. L. Cornish, Dual-species bose-einstein condensate ofrb87andcs133, Physi- cal Review A84(1) (2011), 011603. doi:10.1103/physreva.84.011603. 18

work page doi:10.1103/physreva.84.011603 2011

[13] [13]

Egorov, B

M. Egorov, B. Opanchuk, P. Drummond, B. V. Hall, P. Hannaford, A. I. Sidorov, Measurement ofs-wave scattering lengths in a two-component Bose-Einstein condensate, Physical Review A87(5) (2013), 053614. doi:10.1103/physreva.87.053614

work page doi:10.1103/physreva.87.053614 2013

[14] [14]

D. M. Bauer, M. Lettner, C. Vo, G. Rempe, S. Dürr, Control of a mag- netic Feshbach resonance with laser light, Nature Physics5(5) (2009), 339-342. doi:10.1038/nphys1232

work page doi:10.1038/nphys1232 2009

[15] [15]

Y. Liu, J. Li, G.-R. Wang, S.-L. Cong, Optical control of magnetic Feshbach resonances in Bose gases, Physics Letters A378(1-2) (2014), 43-47. doi:10.1016/j.physleta.2013.10.028

work page doi:10.1016/j.physleta.2013.10.028 2014

[16] [16]

P. K. Kanjilal, A. Bhattacharyay, Multicomponent states for trapped spin-1 Bose-Einstein condensates in the presence of a magnetic field, Physical Review A108(5) (2023), 053322. doi:10.1103/physreva.108.053322

work page doi:10.1103/physreva.108.053322 2023

[17] [17]

J. O. Indekeu, C.-Y. Lin, N. Van Thu, B. Van Schaeybroeck, T. H. Phat, Static interfacial properties of Bose-Einstein-condensate mixtures, Phys- ical Review A91(3) (2015) 033615. doi:10.1103/physreva.91.033615

work page doi:10.1103/physreva.91.033615 2015

[18] [18]

J. S. Rowlinson, B. Widom, Molecular theory of capillarity, Dover Pub- lications, Mineola, New York, 2002

work page 2002

[19] [19]

Inouye, M

S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, W. Ketterle, Observation of feshbach resonances in a Bose-Einstein condensate, Nature392(6672) (1998) 151-154. doi:10.1038/32354

work page doi:10.1038/32354 1998

[20] [20]

C. A. Stan, M. W. Zwierlein, C. H. Schunck, S. M. F. Raupach, W. Ketterle, Observation of Feshbach resonances between two differ- ent atomic species, Physical Review Letters93(14) (2004), 143001. doi:10.1103/physrevlett.93.143001

work page doi:10.1103/physrevlett.93.143001 2004

[21] [21]

C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Feshbach resonances in ultracold gases, Reviews of Modern Physics82(2) (2010) 1225-1286. doi:10.1103/revmodphys.82.1225. 19

work page doi:10.1103/revmodphys.82.1225 2010