Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Research

Evolution and decay of an Alice ring in a spinor Bose-Einstein condensate

Markus Kivioja, Roberto Zamora-Zamora, Alina Blinova, Sanna Mönkölä, Tuomo Rossi, Mikko Möttönen

Published May 15, 2023• 7 citations
Publisher

Abstract

We use first-principles-derived numerical simulations to investigate the long-time evolution of a half-quantum vortex ring, an Alice ring, arising from the decay dynamics of an isolated monopole in the polar phase of a dilute spin-1 Bose-Einstein condensate. In particular, we study the lifetime and decay characteristics of the Alice ring under different experimentally relevant conditions. We observe that, in a $^{87}\mathrm{Rb}$ condensate with a homogeneous external magnetic field, a well-centered Alice ring may survive for over 160 ms, and that during its lifetime it can contract back into a monopole, which again converts into an Alice ring. Interestingly, we notice an additional Alice ring, with an opposite topological charge, to emerge during the decay dynamics within the condensate, leading to the coexistence of two Alice rings in the same cloud. Shortly after this coexistence, the original Alice ring breaks into a line-like defect referred to as an Alice string. We find that the location of the initial isolated monopole correlates with the winding direction of the scalar phase in the produced vortex ring, a phenomenon which we utilize to create two Alice rings with opposite charges and opposite winding directions. Such created Alice ring and anti-Alice ring naturally annihilate each other in the subsequent evolution.

DOI
10.1103/physrevresearch.5.023104

Related papers

Observation of an Alice ring in a Bose–Einstein condensate

Alina Blinova, Roberto Zamora-Zamora, Tuomas Ollikainen +3 more

Abstract Monopoles and vortices are fundamental topological excitations that appear in physical systems spanning enormous scales of size and energy, from the vastness of the early universe to tiny laboratory droplets of nematic liquid crystals and ultracold gases. Although the topologies of vortices and monopoles are distinct from one another, under certain circumstances a monopole can spontaneously and continuously deform into a vortex ring with the curious property that monopoles passing through it are converted into anti-monopoles. However, the observation of such Alice rings has remained a major challenge, due to the scarcity of experimentally accessible monopoles in continuous fields. Here, we present experimental evidence of an Alice ring resulting from the decay of a topological monopole defect in a dilute gaseous 87 Rb Bose–Einstein condensate. Our results, in agreement with detailed first-principles simulations, provide an unprecedented opportunity to explore the unique features of a composite excitation that combines the topological features of both a monopole and a vortex ring.

Nature Communications•Aug 29, 2023•14 citations

Decay of a Quantum Knot

Tuomas Ollikainen, Alina Blinova, Mikko Möttönen +1 more

We experimentally study the dynamics of quantum knots in a uniform magnetic field in spin-1 Bose-Einstein condensates. The knot is created in the polar magnetic phase, which rapidly undergoes a transition toward the ferromagnetic phase in the presence of the knot. The magnetic order becomes scrambled as the system evolves, and the knot disappears. Strikingly, over long evolution times, the knot decays into a polar-core spin vortex, which is a member of a class of singular SO(3) vortices. The polar-core spin vortex is stable with an observed lifetime comparable to that of the condensate itself. The structure is similar to that predicted to appear in the evolution of an isolated monopole defect, suggesting a possible universality in the observed topological transition.

arXiv:1908.01285•Physical Review Letters•Oct 16, 2019•25 citations

Decay of an isolated monopole into a Dirac monopole configuration

Konstantin Tiurev, Emmi Ruokokoski, H. Mäkelä +2 more

We study numerically the detailed structure and decay dynamics of isolated monopoles in conditions similar to those of their recent experimental discovery. We find that the core of a monopole in the polar phase of a spin-1 Bose-Einstein condensate contains a small half-quantum vortex ring. Well after the creation of the monopole, we observe a dynamical quantum phase transition that destroys the polar phase. Strikingly, the resulting ferromagnetic order parameter exhibits a Dirac monopole in its synthetic magnetic field. We observe quantitatively matching decay dynamics for both ferromagnetic and antiferromagnetic spin-spin interactions.

arXiv:1504.07770•Physical Review A•Mar 21, 2016•14 citations

Composite cores of monopoles and Alice rings in spin-2 Bose-Einstein condensates

Giuseppe Baio, Magnus O. Borgh

We show that energy relaxation causes a point defect in the uniaxial-nematic phase of a spin-2 Bose-Einstein condensate to deform into a spin-Alice ring that exhibits a composite core structure with distinct topology at short and long distances from the singular line. An outer biaxial-nematic core exhibits a spin half-quantum vortex structure with a uniaxial-nematic inner core. By numerical simulation, we demonstrate a dynamical oscillation between the spin-Alice ring and a split-core hedgehog configuration via the appearance of ferromagnetic rings with associated vorticity inside an extended core region. We further show that a similar dynamics is exhibited by a spin-Alice ring surrounding a spin-vortex line resulting from the relaxation of a monopole situated on a spin-vortex line in the biaxial-nematic phase. In the cyclic phase, similar states are shown instead to form extended phase-mixing cores containing rings with fractional mass circulation or cores whose spatial shape reflects the order-parameter symmetry of a cyclic inner core, depending on the initial configuration. Published by the American Physical Society 2024

arXiv:2401.04103•Physical Review Research•May 13, 2024•0 citations

Creation of a Dirac monopole-antimonopole pair in a spin-1 Bose-Einstein condensate

Konstantin Tiurev, Pekko Kuopanportti, Mikko Möttönen

We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number $\ensuremath{\kappa}$. It is shown that if $\ensuremath{\kappa}=\ensuremath{-}1$, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For $\ensuremath{\kappa}=\ensuremath{-}2$, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For $\ensuremath{\kappa}=0$, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For $\ensuremath{\kappa}=\ensuremath{-}1$ and $\ensuremath{\kappa}=\ensuremath{-}2$, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.

arXiv:1810.03725•Physical Review A•Feb 19, 2019•9 citations

Existence, stability, and dynamics of monopole and Alice ring solutions in antiferromagnetic spinor condensates

Thudiyangal Mithun, R. Carretero-González, E. G. Charalampidis +2 more

In this paper. we study the existence, stability, and dynamics of select topological points and line defects in antiferromagnetic, polar phase, $F=1$ $^{23}\mathrm{Na}$ spinor condensates. Specifically, we leverage fixed-point and numerical continuation techniques in three spatial dimensions to identify solution families of monopole and Alice rings as the chemical potential (number of atoms) and trapping strengths are varied within intervals of realizable experimental parameters. We are able to follow the monopole from the linear limit of small atom number all the way to the Thomas-Fermi regime of large atom number. Additionally, and importantly, our studies reveal the existence of two Alice ring solution branches, corresponding to, relatively, smaller and larger ring radii, that bifurcate from each other in a saddle-center bifurcation as the chemical potential is varied. We find that the monopole solution is always dynamically unstable in the regimes considered. In contrast, we find that the larger Alice ring is indeed stable close to the bifurcation point until it destabilizes from an oscillatory instability bubble for a larger value of the chemical potential. We also report on the possibility of dramatically reducing, yet not completely eliminating, the instability rates for the smaller Alice ring by varying the trapping strengths. The dynamical evolution of the different unstable waveforms is also probed via direct numerical simulations.

arXiv:2112.12723•Physical Review A•May 11, 2022•16 citations
We use first-principles-derived numerical simulations to investigate the long-time evolution of a half-quantum vortex ring, an Alice ring, arising from the decay dynamics of an isolated monopole in the polar phase of a dilute spin-1 Bose-Einstein condensate. In particular, we study the lifetime and decay characteristics of the Alice ring under different experimentally relevant conditions. We observe that, in a 87Rb^{87}\mathrm{Rb}87Rb condensate with a homogeneous external magnetic field, a well-centered Alice ring may survive for over 160 ms, and that during its lifetime it can contract back into a monopole, which again converts into an Alice ring. Interestingly, we notice an additional Alice ring, with an opposite topological charge, to emerge during the decay dynamics within the condensate, leading to the coexistence of two Alice rings in the same cloud. Shortly after this coexistence, the original Alice ring breaks into a line-like defect referred to as an Alice string. We find that the location of the initial isolated monopole correlates with the winding direction of the scalar phase in the produced vortex ring, a phenomenon which we utilize to create two Alice rings with opposite charges and opposite winding directions. Such created Alice ring and anti-Alice ring naturally annihilate each other in the subsequent evolution.
Abstract Monopoles and vortices are fundamental topological excitations that appear in physical systems spanning enormous scales of size and energy, from the vastness of the early universe to tiny laboratory droplets of nematic liquid crystals and ultracold gases. Although the topologies of vortices and monopoles are distinct from one another, under certain circumstances a monopole can spontaneously and continuously deform into a vortex ring with the curious property that monopoles passing through it are converted into anti-monopoles. However, the observation of such Alice rings has remained a major challenge, due to the scarcity of experimentally accessible monopoles in continuous fields. Here, we present experimental evidence of an Alice ring resulting from the decay of a topological monopole defect in a dilute gaseous 87 Rb Bose–Einstein condensate. Our results, in agreement with detailed first-principles simulations, provide an unprecedented opportunity to explore the unique features of a composite excitation that combines the topological features of both a monopole and a vortex ring.
We experimentally study the dynamics of quantum knots in a uniform magnetic field in spin-1 Bose-Einstein condensates. The knot is created in the polar magnetic phase, which rapidly undergoes a transition toward the ferromagnetic phase in the presence of the knot. The magnetic order becomes scrambled as the system evolves, and the knot disappears. Strikingly, over long evolution times, the knot decays into a polar-core spin vortex, which is a member of a class of singular SO(3) vortices. The polar-core spin vortex is stable with an observed lifetime comparable to that of the condensate itself. The structure is similar to that predicted to appear in the evolution of an isolated monopole defect, suggesting a possible universality in the observed topological transition.
We study numerically the detailed structure and decay dynamics of isolated monopoles in conditions similar to those of their recent experimental discovery. We find that the core of a monopole in the polar phase of a spin-1 Bose-Einstein condensate contains a small half-quantum vortex ring. Well after the creation of the monopole, we observe a dynamical quantum phase transition that destroys the polar phase. Strikingly, the resulting ferromagnetic order parameter exhibits a Dirac monopole in its synthetic magnetic field. We observe quantitatively matching decay dynamics for both ferromagnetic and antiferromagnetic spin-spin interactions.
We show that energy relaxation causes a point defect in the uniaxial-nematic phase of a spin-2 Bose-Einstein condensate to deform into a spin-Alice ring that exhibits a composite core structure with distinct topology at short and long distances from the singular line. An outer biaxial-nematic core exhibits a spin half-quantum vortex structure with a uniaxial-nematic inner core. By numerical simulation, we demonstrate a dynamical oscillation between the spin-Alice ring and a split-core hedgehog configuration via the appearance of ferromagnetic rings with associated vorticity inside an extended core region. We further show that a similar dynamics is exhibited by a spin-Alice ring surrounding a spin-vortex line resulting from the relaxation of a monopole situated on a spin-vortex line in the biaxial-nematic phase. In the cyclic phase, similar states are shown instead to form extended phase-mixing cores containing rings with fractional mass circulation or cores whose spatial shape reflects the order-parameter symmetry of a cyclic inner core, depending on the initial configuration. Published by the American Physical Society 2024
We theoretically demonstrate that a pair of Dirac monopoles with opposite synthetic charges can be created within a single spin-1 Bose-Einstein condensate by steering the spin degrees of freedom by external magnetic fields. Although the net synthetic magnetic charge of this configuration vanishes, both the monopole and the antimonopole are accompanied by vortex filaments carrying opposite angular momenta. Such a Dirac dipole can be realized experimentally by imprinting a spin texture with a nonlinear magnetic field generated by a pair of coils in a modified Helmholtz configuration. We also investigate the case where the initial state for the dipole-creation procedure is pierced by a quantized vortex line with a winding number $\ensuremath{\kappa}$. It is shown that if $\ensuremath{\kappa}=\ensuremath{-}1$, the resulting monopole and antimonopole lie along the core of a singly quantized vortex whose sign is reversed at the locations of the monopoles. For $\ensuremath{\kappa}=\ensuremath{-}2$, the monopole and antimonopole are connected by a vortex line segment carrying two quanta of angular momentum, and hence the dipole as a whole is an isolated configuration. In addition, we simulate the long-time evolution of the dipoles in the magnetic field used to create them. For $\ensuremath{\kappa}=0$, each of the semi-infinite doubly quantized vortices splits into two singly quantized vortices, as in the case of a single Dirac monopole. For $\ensuremath{\kappa}=\ensuremath{-}1$ and $\ensuremath{\kappa}=\ensuremath{-}2$, the initial vortices deform into a vortex with a kink and a vortex ring, respectively.
In this paper. we study the existence, stability, and dynamics of select topological points and line defects in antiferromagnetic, polar phase, F=1F=1F=1 23Na^{23}\mathrm{Na}23Na spinor condensates. Specifically, we leverage fixed-point and numerical continuation techniques in three spatial dimensions to identify solution families of monopole and Alice rings as the chemical potential (number of atoms) and trapping strengths are varied within intervals of realizable experimental parameters. We are able to follow the monopole from the linear limit of small atom number all the way to the Thomas-Fermi regime of large atom number. Additionally, and importantly, our studies reveal the existence of two Alice ring solution branches, corresponding to, relatively, smaller and larger ring radii, that bifurcate from each other in a saddle-center bifurcation as the chemical potential is varied. We find that the monopole solution is always dynamically unstable in the regimes considered. In contrast, we find that the larger Alice ring is indeed stable close to the bifurcation point until it destabilizes from an oscillatory instability bubble for a larger value of the chemical potential. We also report on the possibility of dramatically reducing, yet not completely eliminating, the instability rates for the smaller Alice ring by varying the trapping strengths. The dynamical evolution of the different unstable waveforms is also probed via direct numerical simulations.