Pith. sign in

REVIEW 2 major objections 4 minor 129 references

Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Simulations show Kibble-Zurek scaling governs the superfluid-to-supersolid transition in an elongated dipolar gas, with critical exponents matching mean-field theory.

desk verdict Solid numerical KZM study of the dipolar superfluid-supersolid transition, but the headline critical exponents are internally inconsistent with the paper's own scaling relations. read the letter →

arxiv 2411.18395 v2 pith:K3I3MLVO submitted 2024-11-27 cond-mat.quant-gas hep-ph

Wyatt Kirkby , Hayder Salman , Thomas Gasenzer , Lauriane Chomaz This is my paper · ORCID
classification cond-mat.quant-gashep-ph
keywords Kibble-ZurekmechanismsupersoliddipolarquantumgascriticalexponentsrotoninstabilityquenchdynamicsextendedGross-Pitaevskiiequationcorrelationlengthscaling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether the Kibble-Zurek mechanism governs how a dipolar gas forms a supersolid when the interaction strength is swept linearly across the superfluid-to-supersolid transition. Simulating an elongated gas of dipolar atoms with a quasi-one-dimensional extended Gross-Pitaevskii equation, the authors find that the formation delay (freeze-out time) and the growing crystalline correlation length scale as powers of the quench rate over several orders of magnitude. The measured exponents give critical exponents $\nu = 0.57(1)$ and $z = 1.05(2)$, close to the mean-field values $\nu = 1/2$, $z = 1$ that follow from the linear closing of the roton gap. If the paper is right, a single universal scaling description—not an exponential Berezinskii-Kosterlitz-Thouless one—captures the onset of supersolid order, and the transition belongs to a near-mean-field universality class that remains to be determined.

What carries the argument

The load-bearing object is the Kibble-Zurek scaling ansatz for a linear quench: as the control parameter approaches its critical value, the relaxation time $\tau$ and correlation length $\xi$ diverge as power laws, giving a freeze-out time $\hat{\tau}\propto \tau_Q^{z\nu/(1+z\nu)}$ and a frozen length $\hat{\xi}\propto \tau_Q^{\nu/(1+z\nu)}$. In this system the underlying critical softening is the roton minimum of the Bogoliubov excitation spectrum, which closes as $\epsilon_{\mathrm{rot}}\propto\sqrt{a_s-a_c}$; the dynamics are generated with the extended Gross-Pitaevskii equation reduced to one dimension through a variational transverse profile. The paper identifies the freeze-out time with the delay before the superfluid fraction drops below 0.98 and the correlation length with the Gaussian envelope width of the density-density correlation function at that time.

What would settle it

A direct test would repeat the same linear quenches in full three-dimensional simulations or in a uniform ring-trap experiment with $^{164}$Dy and measure the freeze-out delay and correlation length at the critical crossing over the same quench-rate range. If the power laws depart from $\hat{\tau}\propto\tau_Q^{0.35}$ and $X\propto\tau_Q^{0.34}$ beyond the quoted fit errors—for instance by showing exponential Berezinskii-Kosterlitz-Thouless scaling at slow rates—the central claim would be falsified. A complementary check is to measure how the roton gap closes as a function of $a_s$ in the full model and confirm independently that $z\nu=1/2$ and $z=1$.

Watch

Extended reading notes

Core claim

The paper simulates linear ramps of the s-wave scattering length from the uniform superfluid into the supersolid phase in an elongated tube of dipolar atoms, using the reduced extended Gross-Pitaevskii equation with stochastic initial noise and many independent realizations. It claims that the delay in the onset of density modulation after crossing the critical point—the Kibble-Zurek freeze-out time—and the width of the density-density correlation function at that moment both obey clean power laws in the quench time, $\hat{\tau} \propto \tau_Q^{0.352(3)}$ and $X \propto \tau_Q^{0.335(3)}$, over roughly three decades of quench rates. From these exponents the paper extracts $\nu = 0.57(1)$ and $z = 1.05(2)$, compatible with the Bogoliubov mean-field values $\nu = 1/2$, $z = 1$, and it finds that the number of crystal-phase defects at freeze-out also follows a power law when the phase jumps defining a defect are sufficiently large. The authors take this as evidence for a continuous transition whose universality class is near mean-field and not that of the (1+1)-dimensional XY model.

Load-bearing premise

The central assumption is that the reduced quasi-one-dimensional extended Gross-Pitaevskii equation, with its fixed variational transverse profile and approximate quantum-fluctuation term, faithfully represents the real three-dimensional many-body dynamics of the dipolar gas across the transition.

Editorial extensions

If this is right

  • The freeze-out time and correlation length of supersolid formation are predictable for any linear quench rate in this regime, up to the fast-quench breakdown where domains approach the lattice spacing.
  • The transition is consistent with a continuous second-order transition with near-mean-field exponents, which would rule out the (1+1)-dimensional XY/BKT universality class for these parameters.
  • Defects of the supersolid crystal appear as local jumps of the crystal phase; for jumps larger than $\pi/2$ their count follows the predicted KZM power law and their statistics are Poissonian, so defect counting is a viable experimental probe.
  • Experimental verification needs only the onset of density modulation, not long-lived supersolid coherence, which relaxes the lifetime requirement for ring-trap experiments.
  • Very fast quenches break the scale separation between domain size and crystal periodicity, producing a saturation that is itself a universal breakdown of Kibble-Zurek scaling.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the near-mean-field exponents survive a fully self-consistent many-body treatment, the transition may behave as if it were above its upper critical dimension; an exact many-body calculation of $\nu$ and $z$ for the same Hamiltonian would settle that without relying on the quasi-1D mean-field reduction.
  • The two correlation-length measures in the paper—the density-envelope exponent 0.335 and the crystal-phase width exponent 0.275—may indicate separate density and phase coherence lengths; tracking both after the freeze-out time would clarify whether one or two order parameters are needed.
  • Because only the onset of supersolid formation is required, the same protocol could be applied to shorter-lived supersolids and ring traps, and a reverse quench that melts the supersolid should show symmetric freeze-out if the mechanism is Kibble-Zurek rather than coarsening.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript reports a truncated-Wigner extended Gross-Pitaevskii study of linear quenches of the s-wave scattering length across the continuous superfluid-to-supersolid transition of an elongated 164Dy gas. The authors define a freeze-out time from the delay in the drop of the superfluid fraction, extract a frozen correlation length from a fit to the density-density correlation function, and count crystal-phase defects. They find power-law scalings τ̂ ∝ τ_Q^{0.352(3)}, X ∝ τ_Q^{0.335(3)}, and a defect-count exponent of 0.37(2), and from these they quote critical exponents ν = 0.57(1) and z = 1.05(2), comparing them with Bogoliubov mean-field predictions ν = 1/2, z = 1. The paper also includes checks with quantum-only noise, larger system sizes, and full 3D simulations.

Significance. The topic is timely and the study is in a regime of current experimental interest. The main strengths are the extended dynamical range of τ_Q, the ensemble averaging over hundreds of realizations, and the explicit checks in Appendices A–C that the exponents are robust to the noise model, system size, and, within larger error bars, the dimensionality of the simulation. If the reported scalings survive a corrected analysis, this would be one of the first quantitative Kibble-Zurek exponent extractions for a dipolar supersolid transition and would provide a useful benchmark for experiments. However, the headline exponent extraction contains an internal inconsistency that must be resolved before the quantitative claims can be accepted.

major comments (2)
  1. [§III D and Eq. (1)] The quoted exponents ν = 0.57(1) and z = 1.05(2) are not consistent with the inputs stated in the text. With ζ_KZ = 0.352(3) and ν_KZ = 0.335(3), Eq. (1) gives z = ζ_KZ/ν_KZ = 1.05(2) and ν = ν_KZ/(1 − ζ_KZ) = 0.335/(1 − 0.352) = 0.517(5). The difference from the reported 0.57 is about ten standard errors, far outside the quoted uncertainty. Because Sec. III D explicitly states that the extraction uses the results of Secs. III A and III B, this is an arithmetic inconsistency in the central result rather than an alternative fitting choice. The abstract, Sec. III D, and Sec. IV should be revised to report the corrected exponents and the correspondingly adjusted comparison with mean-field predictions.
  2. [§III C and Eq. (11)] The paper presents three mutually inconsistent estimates of the KZM correlation-length exponent for the same quenches: ν_KZ = 0.335(3) from g(2) in Sec. III B, 0.275(3) from the half-width of C(x) in Sec. III C, and 0.37(2) from the defect count with Δϕ > π/2 in Sec. III C. Equation (11) predicts that the defect-density exponent equals ν_KZ, and the three values are all presented as probes of the same frozen correlation scale; the spread between C(x) and g(2) is roughly 14σ on the quoted errors. The manuscript acknowledges these discrepancies only qualitatively. The authors should either provide a quantitative account of the systematic differences or present the headline exponents with error bars that reflect this systematic spread.
minor comments (4)
  1. [Sec. I] The sentence 'Sections III D-III C presents our observations' appears to be a typo; it should read 'Sections III A-III D present' or similar, with the sections in the correct order.
  2. [Fig. 12 caption] The caption contains the incomplete phrase 'A giving an approximate scaling'; a verb is missing and the sentence should be rewritten.
  3. [Appendix E] The text refers to a rescaling of 'the g(1) correlator', but the quantity plotted and discussed in Sec. III B and in Fig. 15 is g(2); please correct the label to avoid confusion.
  4. [Figs. 3–6] The open-symbol convention for quenches that extend past the supersolid phase boundary is used consistently, but the figures would be easier to read if the caption or the main text stated explicitly that open markers correspond to the modified fast-quench protocol described in Sec. III A.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: measured KZM exponents are inverted with Eq. (1) and compared with an independently computed Bogoliubov spectrum. The reported nu=0.57(1) is internally inconsistent with the paper's own stated inputs, but that is an arithmetic/attribution issue, not a circular reduction.

full rationale

The paper's central derivation is self-contained. Sec. III A reports the measured freeze-out scaling tau_hat ~ tau_Q^{0.352(3)}, and Sec. III B reports the correlation-length scaling X ~ tau_Q^{0.335(3)}. Sec. III D converts these into critical exponents using the standard KZM relations in Eq. (1), which is an inversion of measured power laws, not a fit to the theory being tested. The comparison with Bogoliubov mean-field theory is independent: the roton-gap scaling epsilon_rot ~ sqrt(as - ac) is stated as 'verified here in the inset to Fig. 8(a)' from the dispersion relation Eq. (15), and the dynamical exponent z=1 follows from linearization of the dispersion around the roton momentum in Eq. (17). These Bogoliubov predictions do not use the quench-simulation exponents. Self-citations such as Refs. [15, 73-75] supply the reduced model and phase-diagram framework, but the central scaling exponents are new dynamical measurements compared against parameter-free theoretical predictions, so the load-bearing argument does not reduce to a self-citation. The App. E data collapses use the already-extracted exponents and are consistency checks, not independent predictions. A separate, non-circularity concern: using the paper's own stated inputs, Eqs. (1) with zeta=0.352(3) and nu_KZ=0.335(3) give nu = nu_KZ/(1-zeta) = 0.517(7), not the reported 0.57(1); the reported value matches the Sec. III C defect-density exponent 0.37(2) via 0.37/(1-0.352)=0.57. This is an internal inconsistency in the headline numeric result, but it is not a reduction of a claimed prediction to its inputs, so it does not raise the circularity score.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central result rests on the eGPE model, the variational reduction to 1D, and the KZM scaling assumptions. The model is standard in the field, but the paper introduces empirical fitting procedures (thresholds and fit forms) that are not derived from first principles. No entirely new physical entities are introduced.

free parameters (5)
  • threshold f_s = 0.98 for freeze-out time = 0.98
    The freeze-out time tau_hat is defined as the time when f_s first drops below 0.98. This threshold is chosen empirically and is not derived from first principles; different thresholds could change the extracted zeta_KZ slightly.
  • variational parameters l = 1.08 um, eta = 4.25 = 1.08 um, 4.25
    The variational parameters (width and ellipticity) are fixed to their ground-state values at a_s = 88 a0. This is an approximation; the true parameters vary across the phase diagram, and the critical point shift is acknowledged (a_c = 91.05 vs 90.5).
  • empirical fit function parameters {A, K, X} for g(2) = varies per fit
    The correlation function g(2) is fitted to A + (1-A) cos(Kx) exp(-x^2/X^2). The width X is identified with the correlation length, but the Gaussian form is empirical.
  • defect threshold Delta phi > pi/2 = pi/2
    Defects are defined as crystal phase jumps larger than pi/2. The paper checks several thresholds and selects pi/2 based on Poisson statistics, but this selection is post hoc.
  • thermal noise temperature T = 20 nK = 20 nK
    The initial thermal noise is added at 20 nK, chosen as 'experimentally relevant'. The appendix shows the scaling is similar with quantum noise only, so this parameter is not strongly affecting the exponents.
assumptions (5)
  • domain assumption Extended Gross-Pitaevskii equation (eGPE) with LHY correction is a valid model for the dipolar gas dynamics.
    Section II.A. The paper uses the eGPE, which is a mean-field-like theory with non-self-consistent quantum fluctuations. The authors note this limitation. The KZM exponents extracted from this model may differ from the true many-body physics.
  • domain assumption The separability ansatz Psi(r,t) = phi(y,z) psi(x,t) is valid for the elongated tube geometry.
    Section II.A, Eq. (3). This reduces the 3D eGPE to a 1D equation. Appendix B compares with full 3D simulations for a few cases, but the main results rely on this reduction.
  • domain assumption Kibble-Zurek scaling relations (tau_hat ~ tau_Q^{z nu/(1+z nu)} and xi_hat ~ tau_Q^{nu/(1+z nu)}) hold for this transition.
    The entire analysis is based on these relations. The paper assumes a continuous transition and that the system is in the KZM regime. The observed power laws support this, but the derivation of these relations assumes a linear quench and a single diverging length scale.
  • domain assumption The transition at n_bar = 2500 um^-1 is continuous.
    The paper selects this density based on prior phase diagram calculations (Refs. [15,16]). The continuous nature is essential for KZM. The paper provides evidence from the smooth emergence of modulation and the roton softening, but this is a model-based prediction.
  • ad hoc to paper The g(2) correlation function can be fitted to a Gaussian envelope to extract the correlation length.
    Section III.B, Eq. (8). The Gaussian decay is empirical. The paper discusses that generally order parameters decay exponentially, but the Gaussian form is used for the fit. This is a modeling choice that affects the extracted X.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas." pith.science (2026). https://pith.science/paper/K3I3MLVO

@misc{pith2026241118395,
  author       = {Pith},
  title        = {Pith review of: Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/K3I3MLVO}},
  note         = {Machine review of arXiv:2411.18395}
}
abstract

We simulate interaction quenches crossing from a superfluid to a supersolid state in a dipolar quantum gas of ${}^{164}\mathrm{Dy}$ atoms, trapped in an elongated tube with periodic boundary conditions, via the extended Gross-Pitaevskii equation. A freeze-out time is observed through a delay in supersolid formation after crossing the critical point. We compute the density-density correlations at the freeze-out time and extract the frozen correlation length for the solid order. An analysis of the freeze-out time and correlation length versus the interaction quench rate allows us to extract universal exponents corresponding to the relaxation time and correlation length based on predictions of the Kibble-Zurek mechanism. Over several orders of magnitude, clear power-law scaling is observed for both the freeze-out time and the correlation length, and the corresponding exponents are compatible with predictions based on the excitation spectrum calculated via Bogoliubov theory. Defects due to independent local breaking of translational symmetry, contributing to globally incommensurate supersolid order, are identified, and their number at the freeze-out time is found to also scale as a power law. Our results support the hypothesis of a continuous transition whose universality class remains to be determined but appears to differ from that of the (1+1)D XY model.

Figures

Figures reproduced from arXiv: 2411.18395 by the authors.

Figure 1
Figure 1. FIG. 1. KZM in quenches across the superfluid-supersolid [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Quench across the superfluid-supersolid transition. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Delay in supersolid formation for various quenches [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Scaling of the correlation length. Panels (a)-(c) show [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Crystal phase and correlation function [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Defect density scaling. Panel (a) illustrates a crystal [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Defect counting statistics. The probability of oc [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Panel (a) show the dispersion relation and the closing [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Delay in supersolid formation , similar to Fig. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Supersolid correlation length [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Delay in supersolid formation in the reduced theory [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Universal scaling functions. Panel (a) shows the [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

129 extracted references · 61 canonical work pages

  1. [1]

    Penrose and L

    O. Penrose and L. Onsager, Bose-Einstein condensation and liquid helium, Phys. Rev. 104, 576 (1956)

    1956

  2. [2]

    E. P. Gross, Unified theory of interacting bosons, Phys. Rev. 106, 161 (1957)

    1957

  3. [3]

    Gross, Classical theory of boson wave fields, Annals of Physics 4, 57 (1958)

    E. Gross, Classical theory of boson wave fields, Annals of Physics 4, 57 (1958)

    1958

  4. [4]

    Andreev and I

    A. Andreev and I. Lifshitz, Quantum theory of defects in crystals, J. Exp. Theo. Phys. 56, 2057 (1969)

    1969

  5. [5]

    A. J. Leggett, Can a solid be ”superfluid”?, Phys. Rev. Lett. 25, 1543 (1970)

    1970

  6. [7]

    J.-R. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F. C ¸ . Top, A. O. Jamison, and W. Ketterle, A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates, Nature 543, 91 (2017)

    2017

  7. [8]

    Putra, F

    A. Putra, F. Salces-C´ arcoba, Y. Yue, S. Sugawa, and I. B. Spielman, Spatial coherence of spin-orbit-coupled Bose gases, Phys. Rev. Lett. 124, 053605 (2020)

    2020

  8. [9]

    Tanzi, E

    L. Tanzi, E. Lucioni, F. Fam` a, J. Catani, A. Fioretti, C. Gabbanini, R. N. Bisset, L. Santos, and G. Modugno, Observation of a dipolar quantum gas with metastable supersolid properties, Phys. Rev. Lett. 122, 130405 (2019)

    2019

Show all 129 references
  1. [10]

    B¨ ottcher, J.-N

    F. B¨ ottcher, J.-N. Schmidt, M. Wenzel, J. Hertkorn, M. Guo, T. Langen, and T. Pfau, Transient super- solid properties in an array of dipolar quantum droplets, Phys. Rev. X 9, 011051 (2019)

    2019

  2. [11]

    Chomaz, D

    L. Chomaz, D. Petter, P. Ilzh¨ ofer, G. Natale, A. Traut- mann, C. Politi, G. Durastante, R. M. W. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, and F. Fer- laino, Long-lived and transient supersolid behaviors in dipolar quantum gases, Phys. Rev. X 9, 021012 (2019). 16

    2019

  3. [12]

    Sohmen, C

    M. Sohmen, C. Politi, L. Klaus, L. Chomaz, M. J. Mark, M. A. Norcia, and F. Ferlaino, Birth, life, and death of a dipolar supersolid, Phys. Rev. Lett. 126, 233401 (2021)

    2021

  4. [13]

    Bland, E

    T. Bland, E. Poli, C. Politi, L. Klaus, M. A. Nor- cia, F. Ferlaino, L. Santos, and R. N. Bisset, Two- dimensional supersolid formation in dipolar conden- sates, Phys. Rev. Lett. 128, 195302 (2022)

    2022

  5. [14]

    S. M. Roccuzzo and F. Ancilotto, Supersolid behavior of a dipolar Bose-Einstein condensate confined in a tube, Phys. Rev. A 99, 041601 (2019)

    2019

  6. [15]

    P. B. Blakie, D. Baillie, L. Chomaz, and F. Ferlaino, Supersolidity in an elongated dipolar condensate, Phys. Rev. Res. 2, 043318 (2020)

    2020

  7. [16]

    J. C. Smith, D. Baillie, and P. B. Blakie, Supersolidity and crystallization of a dipolar Bose gas in an infinite tube, Phys. Rev. A 107, 033301 (2023)

    2023

  8. [17]

    Zhang, F

    Y.-C. Zhang, F. Maucher, and T. Pohl, Supersolidity around a critical point in dipolar Bose-Einstein conden- sates, Phys. Rev. Lett. 123, 015301 (2019)

    2019

  9. [18]

    Zhang, T

    Y.-C. Zhang, T. Pohl, and F. Maucher, Phases of su- persolids in confined dipolar Bose-Einstein condensates, Phys. Rev. A 104, 013310 (2021)

    2021

  10. [19]

    B. T. E. Ripley, D. Baillie, and P. B. Blakie, Two- dimensional supersolidity in a planar dipolar Bose gas, Phys. Rev. A 108, 053321 (2023)

    2023

  11. [20]

    Zhang, T

    Y.-C. Zhang, T. Pohl, and F. Maucher, Metastable pat- terns in one- and two-component dipolar Bose-Einstein condensates, Phys. Rev. Res. 6, 023023 (2024)

    2024

  12. [21]

    M. E. Fisher, Renormalization of critical exponents by hidden variables, Phys. Rev. 176, 257 (1968)

    1968

  13. [22]

    ´Odor, Universality classes in nonequilibrium lattice systems, Rev

    G. ´Odor, Universality classes in nonequilibrium lattice systems, Rev. Mod. Phys. 76, 663 (2004)

    2004

  14. [23]

    Zinn-Justin, Quantum field theory and critical phe- nomena, 4th ed., International Series of Monographs on Physics (Clarendon Press, Oxford, England, 2002)

    J. Zinn-Justin, Quantum field theory and critical phe- nomena, 4th ed., International Series of Monographs on Physics (Clarendon Press, Oxford, England, 2002)

    2002

  15. [24]

    T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A: Math. Theor. 9, 1387 (1976)

    1976

  16. [25]

    T. W. B. Kibble, Some implications of a cosmological phase transition, Physics Reports 67, 183 (1980)

    1980

  17. [26]

    W. H. Zurek, Cosmological experiments in superfluid helium?, Nature 317, 505 (1985)

    1985

  18. [27]

    W. H. Zurek, Cosmological experiments in condensed matter systems, Physics Reports 276, 177 (1996)

    1996

  19. [28]

    del Campo and W

    A. del Campo and W. H. Zurek, Universality of phase transition dynamics: Topological defects from symme- try breaking, Int. J. Mod. Phys. A 29, 1430018 (2014)

    2014

  20. [29]

    T. W. B. Kibble, Phase-transition dynamics in the lab and the universe, Physics Today 60, 47 (2007)

    2007

  21. [30]

    Uhlmann, R

    M. Uhlmann, R. Sch¨ utzhold, and U. R. Fischer, Vor- tex quantum creation and winding number scaling in a quenched spinor bose gas, Phys. Rev. Lett. 99, 120407 (2007)

    2007

  22. [31]

    W. H. Zurek, Causality in condensates: Gray solitons as relics of BEC formation, Phys. Rev. Lett. 102, 105702 (2009)

    2009

  23. [32]

    Damski and W

    B. Damski and W. H. Zurek, Soliton creation during a Bose-Einstein condensation, Phys. Rev. Lett. 104, 160404 (2010)

    2010

  24. [33]

    del Campo, A

    A. del Campo, A. Retzker, and M. B. Plenio, The in- homogeneous Kibble–Zurek mechanism: vortex nucle- ation during Bose–Einstein condensation, New Journal of Physics 13, 083022 (2011)

    2011

  25. [34]

    A. Das, J. Sabbatini, and W. H. Zurek, Winding up superfluid in a torus via Bose Einstein condensation, Scientific Reports 2, 352 (2012)

    2012

  26. [35]

    del Campo, T

    A. del Campo, T. W. B. Kibble, and W. H. Zurek, Causality and non-equilibrium second-order phase tran- sitions in inhomogeneous systems, Journal of Physics: Condensed Matter 25, 404210 (2013)

    2013

  27. [36]

    Su, S.-C

    S.-W. Su, S.-C. Gou, A. Bradley, O. Fialko, and J. Brand, Kibble-Zurek scaling and its breakdown for spontaneous generation of Josephson vortices in Bose- Einstein condensates, Phys. Rev. Lett. 110, 215302 (2013)

    2013

  28. [37]

    Beugnon and N

    J. Beugnon and N. Navon, Exploring the Kibble–Zurek mechanism with homogeneous Bose gases, J. Phys. B: At. Mol. Opt. Phys. 50, 022002 (2017)

    2017

  29. [38]

    Liu and Y

    S. Liu and Y. Zhang, Quench dynamics in a trapped Bose-Einstein condensate with spin-orbit coupling, Phys. Rev. A 99, 053609 (2019)

    2019

  30. [39]

    Comaron, F

    P. Comaron, F. Larcher, F. Dalfovo, and N. P. Proukakis, Quench dynamics of an ultracold two- dimensional Bose gas, Phys. Rev. A 100, 033618 (2019)

    2019

  31. [40]

    Jiang, S

    X. Jiang, S. Wu, Q. Ye, and C. Lee, Universality of miscible–immiscible phase separation dynamics in two- component Bose–Einstein condensates, New Journal of Physics 21, 023014 (2019)

    2019

  32. [41]

    I.-K. Liu, J. Dziarmaga, S.-C. Gou, F. Dalfovo, and N. P. Proukakis, Kibble-Zurek dynamics in a trapped ultracold Bose gas, Phys. Rev. Res. 2, 033183 (2020)

    2020

  33. [42]

    Thudiyangal and A

    M. Thudiyangal and A. del Campo, Universal vortex statistics and stochastic geometry of Bose-Einstein con- densation, Phys. Rev. Res. 6, 033152 (2024)

    2024

  34. [43]

    N. P. Proukakis, Universality of Bose–Einstein conden- sation and quenched formation dynamics, in Encyclo- pedia of Condensed Matter Physics (Elsevier, 2024) pp. 84–123

    2024

  35. [44]

    M. T. Wheeler, H. Salman, and M. O. Borgh, Dynamics of a nonequilibrium discontinuous quantum phase tran- sition in a spinor bose–einstein condensate, Commun. Phys. 8 (2025)

    2025

  36. [45]

    C. N. Weiler, T. W. Neely, D. R. Scherer, A. S. Bradley, M. J. Davis, and B. P. Anderson, Spontaneous vortices in the formation of Bose–Einstein condensates, Nature 455, 948 (2008)

    2008

  37. [46]

    Lamporesi, S

    G. Lamporesi, S. Donadello, S. Serafini, F. Dalfovo, and G. Ferrari, Spontaneous creation of Kibble–Zurek soli- tons in a Bose–Einstein condensate, Nature Physics 9, 656 (2013)

    2013

  38. [47]

    Corman, L

    L. Corman, L. Chomaz, T. Bienaim´ e, R. Desbuquois, C. Weitenberg, S. Nascimb` ene, J. Dalibard, and J. Beugnon, Quench-induced supercurrents in an annu- lar Bose gas, Phys. Rev. Lett. 113, 135302 (2014)

    2014

  39. [48]

    Navon, A

    N. Navon, A. L. Gaunt, R. P. Smith, and Z. Hadzibabic, Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas, Science 347, 167 (2015)

    2015

  40. [49]

    Chomaz, L

    L. Chomaz, L. Corman, T. Bienaim´ e, R. Desbuquois, C. Weitenberg, S. Nascimb` ene, J. Beugnon, and J. Dal- ibard, Emergence of coherence via transverse condensa- tion in a uniform quasi-two-dimensional Bose gas, Na- ture Communications 6, 6162 (2015)

    2015

  41. [50]

    Donadello, S

    S. Donadello, S. Serafini, T. Bienaim´ e, F. Dalfovo, G. Lamporesi, and G. Ferrari, Creation and counting of defects in a temperature-quenched Bose-Einstein con- densate, Phys. Rev. A 94, 023628 (2016). 17

    2016

  42. [51]

    L. W. Clark, L. Feng, and C. Chin, Universal space-time scaling symmetry in the dynamics of bosons across a quantum phase transition, Science 354, 606 (2016)

    2016

  43. [52]

    I. K. Liu, S. Donadello, G. Lamporesi, G. Ferrari, S. C. Gou, F. Dalfovo, and N. P. Proukakis, Dynamical equili- bration across a quenched phase transition in a trapped quantum gas, Commun. Phys. 1, 24 (2018)

    2018

  44. [53]

    B. Ko, J. W. Park, and Y. Shin, Kibble–Zurek univer- sality in a strongly interacting Fermi superfluid, Nature Physics 15, 1227 (2019)

    2019

  45. [54]

    J. Goo, Y. Lim, and Y. Shin, Defect saturation in a rapidly quenched Bose gas, Phys. Rev. Lett. 127, 115701 (2021)

    2021

  46. [55]

    Liu, X.-C

    X.-P. Liu, X.-C. Yao, Y. Deng, Y.-X. Wang, X.-Q. Wang, X. Li, Q. Chen, Y.-A. Chen, and J.-W. Pan, Dy- namic formation of quasicondensate and spontaneous vortices in a strongly interacting Fermi gas, Phys. Rev. Res. 3, 043115 (2021)

    2021

  47. [56]

    J. Goo, Y. Lee, Y. Lim, D. Bae, T. Rabga, and Y. Shin, Universal early coarsening of quenched Bose gases, Phys. Rev. Lett. 128, 135701 (2022)

    2022

  48. [57]

    Rabga, Y

    T. Rabga, Y. Lee, D. Bae, M. Kim, and Y. Shin, Varia- tions of the Kibble-Zurek scaling exponents of trapped Bose gases, Phys. Rev. A 108, 023315 (2023)

    2023

  49. [58]

    D. G. Allman, P. Sabharwal, and K. C. Wright, Quench- induced spontaneous currents in rings of ultracold fermionic atoms, Phys. Rev. A 109, 053320 (2024)

    2024

  50. [59]

    W. H. Zurek, U. Dorner, and P. Zoller, Dynamics of a quantum phase transition, Phys. Rev. Lett. 95, 105701 (2005)

    2005

  51. [60]

    Polkovnikov, Universal adiabatic dynamics in the vicinity of a quantum critical point, Phys

    A. Polkovnikov, Universal adiabatic dynamics in the vicinity of a quantum critical point, Phys. Rev. B 72, 161201 (2005)

    2005

  52. [61]

    L. E. Sadler, J. M. Higbie, S. R. Leslie, M. Vengalat- tore, and D. M. Stamper-Kurn, Spontaneous symme- try breaking in a quenched ferromagnetic spinor Bose– Einstein condensate, Nature 443, 312 (2006)

    2006

  53. [62]

    D. Chen, M. White, C. Borries, and B. DeMarco, Quan- tum quench of an atomic mott insulator, Phys. Rev. Lett. 106, 235304 (2011)

    2011

  54. [63]

    Anquez, B

    M. Anquez, B. A. Robbins, H. M. Bharath, M. Bogus- lawski, T. M. Hoang, and M. S. Chapman, Quantum Kibble-Zurek mechanism in a spin-1 Bose-Einstein con- densate, Phys. Rev. Lett. 116, 155301 (2016)

    2016

  55. [64]

    L. Feng, L. W. Clark, A. Gaj, and C. Chin, Coher- ent inflationary dynamics for Bose–Einstein condensates crossing a quantum critical point, Nature Physics 14, 269 (2017)

    2017

  56. [65]

    Y. Chen, M. Horikoshi, K. Yoshioka, and M. Kuwata- Gonokami, Dynamical critical behavior of an attractive Bose-Einstein condensate phase transition, Phys. Rev. Lett. 122, 040406 (2019)

    2019

  57. [66]

    C.-R. Yi, S. Liu, R.-H. Jiao, J.-Y. Zhang, Y.-S. Zhang, and S. Chen, Exploring inhomogeneous Kibble-Zurek mechanism in a spin-orbit coupled Bose-Einstein con- densate, Phys. Rev. Lett. 125, 260603 (2020)

    2020

  58. [67]

    K. Lee, S. Kim, T. Kim, and Y. Shin, Universal Kibble– Zurek scaling in an atomic Fermi superfluid, Nature Physics 20, 1570 (2024)

    2024

  59. [68]

    Ferrier-Barbut, H

    I. Ferrier-Barbut, H. Kadau, M. Schmitt, M. Wenzel, and T. Pfau, Observation of quantum droplets in a strongly dipolar Bose gas, Phys. Rev. Lett. 116, 215301 (2016)

    2016

  60. [69]

    W¨ achtler and L

    F. W¨ achtler and L. Santos, Quantum filaments in dipo- lar Bose-Einstein condensates, Phys. Rev. A 93, 061603 (2016)

    2016

  61. [70]

    Chomaz, S

    L. Chomaz, S. Baier, D. Petter, M. J. Mark, F. W¨ achtler, L. Santos, and F. Ferlaino, Quantum- fluctuation-driven crossover from a dilute Bose-Einstein condensate to a macrodroplet in a dipolar quantum fluid, Phys. Rev. X 6, 041039 (2016)

    2016

  62. [71]

    Sch¨ utzhold, M

    R. Sch¨ utzhold, M. Uhlmann, Y. Xu, and U. R. Fischer, Mean-field expansion in Bose–Einstein condensates with finite-range interactions, International Journal of Mod- ern Physics B 20, 3555–3565 (2006)

    2006

  63. [72]

    A. R. P. Lima and A. Pelster, Quantum fluctuations in dipolar Bose gases, Phys. Rev. A 84, 041604 (2011)

    2011

  64. [73]

    P. B. Blakie, D. Baillie, and S. Pal, Variational the- ory for the ground state and collective excitations of an elongated dipolar condensate, Communications in The- oretical Physics 72, 085501 (2020)

    2020

  65. [74]

    S. Pal, D. Baillie, and P. B. Blakie, Excitations and number fluctuations in an elongated dipolar Bose- Einstein condensate, Phys. Rev. A 102, 043306 (2020)

    2020

  66. [75]

    e2i¯kR ei(ϕ(x)+ϕ(x′)) + ei¯ks ei(ϕ(x)−ϕ(x′)) + h.c. # , (D4) since the exponential prefactors will not change from trial to trial. ⟨n(x)n(x′)⟩ = ¯n2 + λ2 4

    for a more in-depth discussion of the emergence of this Higgs mode. In all quenches, there is a final trend towards the ground state superfluid fraction of approxi- mately f s = 0.323, settling slightly above this value with some oscillations remaining, indicating some residua...

    2023

  67. [76]

    P. B. Blakie, L. Chomaz, D. Baillie, and F. Fer- laino, Compressibility and speeds of sound across the superfluid-to-supersolid phase transition of an elongated dipolar gas, Phys. Rev. Res. 5, 033161 (2023)

    2023

  68. [77]

    A. J. Leggett, On the superfluid fraction of an arbi- trary many-body system at T=0, Journal of Statistical Physics 93, 927–941 (1998)

    1998

  69. [78]

    Ala˜ na, N

    A. Ala˜ na, N. Antolini, G. Biagioni, I. n. L. Egusquiza, and M. Modugno, Crossing the superfluid-supersolid transition of an elongated dipolar condensate, Phys. Rev. A 106, 043313 (2022)

    2022

  70. [79]

    Biagioni, N

    G. Biagioni, N. Antolini, A. Ala˜ na, M. Modugno, A. Fioretti, C. Gabbanini, L. Tanzi, and G. Mod- ugno, Dimensional crossover in the superfluid-supersolid quantum phase transition, Physical Review X 12 (2022)

    2022

  71. [80]

    Ala˜ na, I

    A. Ala˜ na, I. L. Egusquiza, and M. Modugno, Supersolid formation in a dipolar condensate by roton instability, Physical Review A 108 (2023)

    2023

  72. [81]

    Ala˜ na, Supersolid-formation-time shortcut and exci- tation reduction by manipulating the dynamical insta- bility, Phys

    A. Ala˜ na, Supersolid-formation-time shortcut and exci- tation reduction by manipulating the dynamical insta- bility, Phys. Rev. A 109, 023308 (2024)

    2024

  73. [82]

    Sabbatini, W

    J. Sabbatini, W. H. Zurek, and M. J. Davis, Phase sep- aration and pattern formation in a binary bose-einstein condensate, Phys. Rev. Lett. 107, 230402 (2011)

    2011

  74. [83]

    Pitaevskii and S

    L. Pitaevskii and S. Stringari, Bose-Einstein Condensa- tion and Superfluidity (Oxford University Press, 2016)

    2016

  75. [84]

    Boninsegni and N

    M. Boninsegni and N. V. Prokof’ev, Colloquium: Su- persolids: What and where are they?, Rev. Mod. Phys. 84, 759 (2012)

    2012

  76. [85]

    We therefore suggest that care must be taken when us- ing a function like C(x) to determine KZM scaling re- sults, especially at quench rates where ξ begins to ap- proach Luc, and perhaps greater statistics are needed for proper convergence of this measure

  77. [86]

    Uhlmann, R

    M. Uhlmann, R. Sch¨ utzhold, and U. R. Fischer, o(n) symmetry-breaking quantum quench: Topological de- fects versus quasiparticles, Phys. Rev. D 81, 025017 (2010)

    2010

  78. [87]

    Uhlmann, R

    M. Uhlmann, R. Sch¨ utzhold, and U. R Fischer, System size scaling of topological defect creation in a second- order dynamical quantum phase transition, New Jour- nal of Physics 12, 095020 (2010). 18

    2010

  79. [88]

    Bland, Q

    T. Bland, Q. Marolleau, P. Comaron, B. Malomed, and N. Proukakis, Persistent current formation in double- ring geometries, J. Phys. B: At. Mol. Opt. Phys 53, 115301 (2020)

    2020

  80. [89]

    Zeng, C.-Y

    H.-B. Zeng, C.-Y. Xia, and A. del Campo, Univer- sal breakdown of Kibble-Zurek scaling in fast quenches across a phase transition, Phys. Rev. Lett. 130, 060402 (2023)

    2023

  81. [90]

    del Campo, F

    A. del Campo, F. J. G´ omez-Ruiz, Z.-H. Li, C.-Y. Xia, H.-B. Zeng, and H.-Q. Zhang, Universal statistics of vor- tices in a newborn holographic superconductor: beyond the kibble-zurek mechanism, Journal of High Energy Physics 2021 (2021)

    2021

  82. [91]

    Balducci, M

    F. Balducci, M. Beau, J. Yang, A. Gambassi, and A. del Campo, Large deviations beyond the kibble-zurek mech- anism, Phys. Rev. Lett. 131, 230401 (2023)

    2023

  83. [92]

    del Campo, Universal statistics of topological defects formed in a quantum phase transition, Phys

    A. del Campo, Universal statistics of topological defects formed in a quantum phase transition, Phys. Rev. Lett. 121, 200601 (2018)

    2018

  84. [93]

    F. J. G´ omez-Ruiz, J. J. Mayo, and A. del Campo, Full counting statistics of topological defects after crossing a phase transition, Phys. Rev. Lett. 124, 240602 (2020)

    2020

  85. [94]

    J.-M. Cui, F. J. G´ omez-Ruiz, Y.-F. Huang, C.-F. Li, G.-C. Guo, and A. del Campo, Experimentally test- ing quantum critical dynamics beyond the kibble–zurek mechanism, Communications Physics 3 (2020)

    2020

  86. [95]

    Bando, Y

    Y. Bando, Y. Susa, H. Oshiyama, N. Shibata, M. Ohzeki, F. J. G´ omez-Ruiz, D. A. Lidar, S. Suzuki, A. del Campo, and H. Nishimori, Probing the uni- versality of topological defect formation in a quantum annealer: Kibble-zurek mechanism and beyond, Phys. Rev. Res. 2, 033369 (2020)

    2020

  87. [96]

    Sachdev, Quantum Phase Transitions, 2nd ed

    S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cam- bridge University Press, 2011)

    2011

  88. [97]

    P. C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49, 435 (1977)

    1977

  89. [98]

    M. J. Steel, M. K. Olsen, L. I. Plimak, P. D. Drummond, S. M. Tan, M. J. Collett, D. F. Walls, and R. Graham, Dynamical quantum noise in trapped bose-einstein con- densates, Phys. Rev. A 58, 4824 (1998)

    1998

  90. [99]

    Sinatra, C

    A. Sinatra, C. Lobo, and Y. Castin, The truncated wigner method for bose-condensed gases: limits of va- lidity and applications, Journal of Physics B: Atomic, Molecular and Optical Physics 35, 3599–3631 (2002)

    2002

  91. [100]

    Blakie, A

    P. Blakie, A. Bradley, M. Davis, R. Ballagh, and C. Gar- diner, Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques, Advances in Physics 57, 363 (2008)

    2008

  92. [101]

    Jeli´ c and L

    A. Jeli´ c and L. F. Cugliandolo, Quench dynamics of the 2d XY model, J. Stat. Mech. 2011, P02032 (2011)

    2011

  93. [102]

    Dziarmaga and W

    J. Dziarmaga and W. H. Zurek, Quench in the 1d Bose- Hubbard model: Topological defects and excitations from the Kosterlitz-Thouless phase transition dynam- ics, Scientific Reports 4, 5950 (2014)

    2014

  94. [103]

    Gardas, J

    B. Gardas, J. Dziarmaga, and W. H. Zurek, Dynamics of the quantum phase transition in the one-dimensional Bose-Hubbard model: Excitations and correlations in- duced by a quench, Phys. Rev. B 95, 104306 (2017)

    2017

  95. [104]

    Z. Zuo, S. Yin, X. Cao, and F. Zhong, Scaling theory of the Kosterlitz-Thouless phase transition, Phys. Rev. B 104, 214108 (2021)

    2021

  96. [105]

    M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid- insulator transition, Phys. Rev. B 40, 546 (1989)

    1989

  97. [106]

    Huang, R

    Q. Huang, R. Yao, L. Liang, S. Wang, Q. Zheng, D. Li, W. Xiong, X. Zhou, W. Chen, X. Chen, and J. Hu, Observation of many-body quantum phase transitions beyond the Kibble-Zurek mechanism, Phys. Rev. Lett. 127, 200601 (2021)

    2021

  98. [107]

    van Otterlo, K.-H

    A. van Otterlo, K.-H. Wagenblast, R. Baltin, C. Bruder, R. Fazio, and G. Sch¨ on, Quantum phase transitions of interacting bosons and the supersolid phase, Phys. Rev. B 52, 16176 (1995)

    1995

  99. [108]

    Roychowdhury, R

    K. Roychowdhury, R. Moessner, and A. Das, Dynamics and correlations at a quantum phase transition beyond kibble-zurek, Phys. Rev. B 104, 014406 (2021)

    2021

  100. [109]

    R. J. Nowak and J. Dziarmaga, Quantum kibble-zurek mechanism: Kink correlations after a quench in the quantum ising chain, Phys. Rev. B 104, 075448 (2021)

    2021

  101. [110]

    Kou and P

    H.-C. Kou and P. Li, Interferometry based on the quan- tum kibble-zurek mechanism, Phys. Rev. B 106, 184301 (2022)

    2022

  102. [111]

    Kou and P

    H.-C. Kou and P. Li, Varying quench dynamics in the transverse ising chain: The kibble-zurek, saturated, and presaturated regimes, Phys. Rev. B 108, 214307 (2023)

    2023

  103. [112]

    Bray, Theory of phase-ordering kinetics, Advances in Physics 43, 357–459 (1994)

    A. Bray, Theory of phase-ordering kinetics, Advances in Physics 43, 357–459 (1994)

    1994

  104. [113]

    Mukherjee, A

    V. Mukherjee, A. Dutta, and D. Sen, Defect generation in a spin- 1 2 transverse xy chain under repeated quench- ing of the transverse field, Phys. Rev. B 77, 214427 (2008)

    2008

  105. [114]

    Divakaran and A

    U. Divakaran and A. Dutta, Reverse quenching in a one-dimensional kitaev model, Phys. Rev. B 79, 224408 (2009)

    2009

  106. [115]

    H. T. Quan and W. H. Zurek, Testing quantum adia- baticity with quench echo, New Journal of Physics 12, 093025 (2010)

    2010

  107. [116]

    Bloch, Superfluidity in a ring, Phys

    F. Bloch, Superfluidity in a ring, Phys. Rev. A 7, 2187 (1973)

    1973

  108. [117]

    Amico, A

    L. Amico, A. Osterloh, and F. Cataliotti, Quantum many particle systems in ring-shaped optical lattices, Phys. Rev. Lett. 95, 063201 (2005)

    2005

  109. [118]

    Amico, D

    L. Amico, D. Anderson, M. Boshier, J.-P. Brantut, L.-C. Kwek, A. Minguzzi, and W. von Klitzing, Colloquium: Atomtronic circuits: From many-body physics to quan- tum technologies, Rev. Mod. Phys. 94, 041001 (2022)

    2022

  110. [119]

    C. Ryu, M. F. Andersen, P. Clad´ e, V. Natarajan, K. Helmerson, and W. D. Phillips, Observation of per- sistent flow of a Bose-Einstein condensate in a toroidal trap, Phys. Rev. Lett. 99, 260401 (2007)

    2007

  111. [120]

    Ramanathan, K

    A. Ramanathan, K. C. Wright, S. R. Muniz, M. Ze- lan, W. T. Hill, C. J. Lobb, K. Helmerson, W. D. Phillips, and G. K. Campbell, Superflow in a toroidal Bose-Einstein condensate: An atom circuit with a tun- able weak link, Phys. Rev. Lett. 106, 130401 (2011)

    2011

  112. [121]

    K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Driving phase slips in a superfluid atom circuit with a rotating weak link, Phys. Rev. Lett. 110, 025302 (2013)

    2013

  113. [122]

    Eckel, J

    S. Eckel, J. G. Lee, F. Jendrzejewski, N. Murray, C. W. Clark, C. J. Lobb, W. D. Phillips, M. Edwards, and G. K. Campbell, Hysteresis in a quantized superfluid ‘atomtronic’ circuit, Nature 506, 200 (2014)

    2014

  114. [123]

    Henderson, C

    K. Henderson, C. Ryu, C. MacCormick, and M. G. Boshier, Experimental demonstration of painting arbi- trary and dynamic potentials for Bose–Einstein conden- sates, New J. Phys. 11, 043030 (2009). 19

    2009

  115. [124]

    B. E. Sherlock, M. Gildemeister, E. Owen, E. Nugent, and C. J. Foot, Time-averaged adiabatic ring potential for ultracold atoms, Phys. Rev. A 83, 043408 (2011)

    2011

  116. [125]

    Moulder, S

    S. Moulder, S. Beattie, R. P. Smith, N. Tammuz, and Z. Hadzibabic, Quantized supercurrent decay in an annular Bose-Einstein condensate, Phys. Rev. A 86, 013629 (2012)

    2012

  117. [126]

    C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, Experimental realization of Josephson junc- tions for an atom squid, Phys. Rev. Lett. 111, 205301 (2013)

    2013

  118. [127]

    Beattie, S

    S. Beattie, S. Moulder, R. J. Fletcher, and Z. Hadz- ibabic, Persistent currents in spinor condensates, Phys. Rev. Lett. 110, 025301 (2013)

    2013

  119. [128]

    G. E. Marti, R. Olf, and D. M. Stamper-Kurn, Col- lective excitation interferometry with a toroidal Bose- Einstein condensate, Phys. Rev. A 91, 013602 (2015)

    2015

  120. [129]

    Nilsson Tengstrand, D

    M. Nilsson Tengstrand, D. Boholm, R. Sachdeva, J. Bengtsson, and S. M. Reimann, Persistent currents in toroidal dipolar supersolids, Phys. Rev. A 103, 013313 (2021)

    2021

  121. [130]

    Nilsson Tengstrand, P

    M. Nilsson Tengstrand, P. St¨ urmer, J. Ribbing, and S. M. Reimann, Toroidal dipolar supersolid with a ro- tating weak link, Phys. Rev. A 107, 063316 (2023)

    2023

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.