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

arXiv:cond-mat/0607184 · Physical Review A

Broken-axisymmetry phase of a spin-1 ferromagnetic Bose-Einstein condensate

Keiji Murata, Hiroki Saito, Masahito Ueda

Published Jan 5, 2007• 99 citations
arXivHTMLPDF

Abstract

A spin-1 ferromagnetic Bose-Einstein condensate subject to a certain magnetic field exhibits a broken-axisymmetry phase in which the magnetization tilts against the applied magnetic field due to the competition between ferromagnetism and linear and quadratic Zeeman effects. The Bogoliubov analysis shows that in this phase two Goldstone modes associated with U(1) and SO(2) symmetry breakings exist, in which phonons and magnons are coupled to restore the two broken symmetries.

DOI
10.1103/physreva.75.013607

Related papers

Spontaneously axisymmetry-breaking phase in a binary mixture of spinor Bose-Einstein condensates

Zhi-Fang Xu, Jia‐Wei Mei, Rong Lü +1 more

We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic ($B$) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.

arXiv:1011.0505•Physical Review A•Nov 24, 2010•16 citations

Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

M. S. Bulakhov, A. S. Peletminskii, S. V. Peletminskiǐ +1 more

Abstract We theoretically study a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also reexamine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential. We also obtain three-branch excitation spectrum of the broken-axisymmetry state. We show that this state can be prepared at three different regimes of applied magnetic field. Finally, we present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.

arXiv:2112.03128•Journal of Physics A Mathematical and Theoretical•Sep 8, 2022•2 citations

Phase diagram of spin-1 antiferromagnetic Bose-Einstein condensates

David Jacob, Lingxuan Shao, Vincent Le Corre +5 more

We study experimentally the equilibrium phase diagram of a spin-1 Bose-Einstein condensate with antiferromagnetic interactions, in a regime where spin and spatial degrees of freedom are decoupled. For a given total magnetization ${m}_{z}$, we observe for low magnetic fields an ``antiferromagnetic'' phase where atoms condense in the $m=\ifmmode\pm\else\textpm\fi{}1$ Zeeman states, and occupation of the $m=0$ state is suppressed. Conversely, for large enough magnetic fields, a phase transition to a ``broken-axisymmetry'' phase takes place: The $m=0$ component becomes populated and rises sharply above a critical field ${B}_{c}({m}_{z})$. This behavior results from the competition between antiferromagnetic spin-dependent interactions (dominant at low fields) and the quadratic Zeeman energy (dominant at large fields). We compare the measured ${B}_{c}$ as well as the global shape of the phase diagram with mean-field theory, and find good quantitative agreement.

arXiv:1209.2533•Physical Review A•Dec 5, 2012•80 citations

Magnetization of a half-quantum vortex in a spinor Bose-Einstein condensate

Shoichi Hoshi, Hiroki Saito

Magnetization dynamics of a half-quantum vortex in a spin-1 Bose-Einstein condensate with a ferromagnetic interaction are investigated by mean-field and Bogoliubov analyses. The transverse magnetization is shown to break the axisymmetry and form threefold domains. This phenomenon originates from the topological structure of the half-quantum vortex and spin conservation.

arXiv:0808.3315•Physical Review A•Nov 12, 2008•9 citations

Phase Diagram of Solitons in the Polar Phase of a Spin-1 Bose-Einstein Condensate

I-Kang Liu, SC Gou, H. Takeuchi

We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose-Einstein condensate in the presence of quadratic Zeeman effect at zero temperature. The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase. The states are assorted into normal, anti-ferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the number and spin densities in the core. The order of phase transitions between different solitons and the critical behaviour of relevant continuous transitions are proved within the mean-field theory.

•Sep 1, 2020•0 citations

Phase diagram of solitons in the polar phase of a spin-1 Bose-Einstein condensate

I-Kang Liu, Shih-Chuan Gou, Hiromitsu Takeuchi

We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose-Einstein condensate in the presence of quadratic Zeeman effect at zero temperature.The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase.The states are assorted into normal, antiferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the particle and spin densities in the core.The order of phase transitions between different solitons and the critical behavior of relevant continuous transitions are proved within the mean-field theory.

arXiv:2002.06088•Physical Review Research•Sep 28, 2020•13 citations
A spin-1 ferromagnetic Bose-Einstein condensate subject to a certain magnetic field exhibits a broken-axisymmetry phase in which the magnetization tilts against the applied magnetic field due to the competition between ferromagnetism and linear and quadratic Zeeman effects. The Bogoliubov analysis shows that in this phase two Goldstone modes associated with U(1) and SO(2) symmetry breakings exist, in which phonons and magnons are coupled to restore the two broken symmetries.
We study the ground-state phases for a mixture of two atomic spin-1 Bose-Einstein condensates in the presence of a weak magnetic (BBB) field. The ground state is found to contain a broken-axisymmetry (BA) phase due to competitions among intraspecies and interspecies spin-exchange interactions and the linear Zeeman shifts. This is in contrast to the case of a single-species spin-1 condensate, where the axisymmetry breaking results from competitions among the linear and quadratic Zeeman shifts and the intraspecies ferromagnetic interaction. All other remaining ground-state phases for the mixture are found to preserve axisymmetry. We further elaborate on the ground-state phase diagram and calculate the Bogoliubov excitation spectra of the phases. For the BA phase, there exist three Goldstone modes that attempt to restore the broken U(1) and SO(2) symmetries.
Abstract We theoretically study a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also reexamine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential. We also obtain three-branch excitation spectrum of the broken-axisymmetry state. We show that this state can be prepared at three different regimes of applied magnetic field. Finally, we present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.
We study experimentally the equilibrium phase diagram of a spin-1 Bose-Einstein condensate with antiferromagnetic interactions, in a regime where spin and spatial degrees of freedom are decoupled. For a given total magnetization mz{m}_{z}mz​, we observe for low magnetic fields an ``antiferromagnetic'' phase where atoms condense in the $m=\ifmmode\pm\else\textpm\fi{}1$ Zeeman states, and occupation of the m=0m=0m=0 state is suppressed. Conversely, for large enough magnetic fields, a phase transition to a ``broken-axisymmetry'' phase takes place: The m=0m=0m=0 component becomes populated and rises sharply above a critical field Bc(mz){B}_{c}({m}_{z})Bc​(mz​). This behavior results from the competition between antiferromagnetic spin-dependent interactions (dominant at low fields) and the quadratic Zeeman energy (dominant at large fields). We compare the measured Bc{B}_{c}Bc​ as well as the global shape of the phase diagram with mean-field theory, and find good quantitative agreement.
We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose-Einstein condensate in the presence of quadratic Zeeman effect at zero temperature. The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase. The states are assorted into normal, anti-ferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the number and spin densities in the core. The order of phase transitions between different solitons and the critical behaviour of relevant continuous transitions are proved within the mean-field theory.
We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose-Einstein condensate in the presence of quadratic Zeeman effect at zero temperature.The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase.The states are assorted into normal, antiferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the particle and spin densities in the core.The order of phase transitions between different solitons and the critical behavior of relevant continuous transitions are proved within the mean-field theory.