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

Communications in Theoretical Physics

Dynamics of Spin-2 Bose–Einstein Condensates

Jing-Min Hou

Published Dec 1, 2007• 0 citations
Publisher

Abstract

We numerically simulate the dynamics of a spin-2 Bose–Einstein condensate. We find that the initial phase plays an important role in the spin component oscillations. The spin mixing processes can fully cancel out due to quantum interference when taking some initial special phase. In all the spin mixing processes, the total spin is conversed. When the initial population is mainly occupied by a component with the maximal or minimal magnetic quantum number, the oscillations of spin components cannot happen due to the total spin conversation. The presence of quadratic Zeeman energy terms suppresses some spin mixing processes so that the oscillations of spin components are suppressed in some initial spin configuration. However, the linear Zeeman energy terms have no effects on the spin mixing processes.

DOI
10.1088/0253-6102/48/6/017

Related papers

Spin mixing dynamics in a spin-orbit coupled spin-1 Bose–Einstein condensate

Nian-Sheng Wan, Zi-Fa Yu, Gi-Ming Gao +3 more

We study the spin mixing dynamics of a spin-orbit coupled spin-1 Bose–Einstein condensate. Using mean-field theory and adopting plane wave solutions, the spin mixing dynamics can be well described by an internal Josephson equation. In order to establish the role of the different terms in spin mixing dynamics clearly, we consider the equilibrium state firstly, which shows that the spin-orbit coupling can significantly modify the dispersion relation and change the property of ground state of the condensate. For the non-equilibrium state, the spin-orbit coupling plays an important role in the spin mixing dynamics. Moreover, the oscillation period of spin mixing dynamics is determined by the coupled effects of momentum, magnetization, spin-dependent atomic interaction and spin-orbit coupling. When spin-orbit coupling is less than a critical value, it can prolong the oscillation period of spin mixing dynamics. Conversely, when the spin-orbit coupling is larger than the critical value, it can shorten the oscillation period of spin mixing dynamics. Particularly, when spin-orbit coupling is equal to the critical value, the period tends to infinity. Our study provides a complete spin mixing dynamics of spin-orbit coupled spin-1 BEC, which can be used to explore the spin mixing dynamics experimentally.

Modern Physics Letters B•Nov 28, 2018•1 citation

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

Spin-mixing dynamics of a spinor Bose-Einstein condensate

Han Pu, C. K. Law, S. Raghavan +2 more

We study the spin-mixing dynamics of an $f=1$ spinor condensate. We show that the dynamics is sensitive to the relative phase and particle number distribution among the individual components of the condensate, and find that complex structures can develop in the density profiles during the time evolution. We investigate the different time scales of the spin-mixing process and their dependence on the total particle number.

Physical Review A•Aug 1, 1999•231 citations

Dynamical Zeeman resonance in spin-orbit-coupled spin-1 Bose gases

Jingtao Fan, Gang Chen, Suotang Jia

We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.

arXiv:2007.14131•Physical Review A•Dec 7, 2020•3 citations

Evolution of a spinor condensate: Coherent dynamics, dephasing, and revivals

Jochen Kronjäger, C. Becker, M. Brinkmann +4 more

We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a $F=1$ $^{87}\mathrm{Rb}$ Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.

arXiv:cond-mat/0509083•Physical Review A•Dec 27, 2005•93 citations

Josephson tunneling of binary mixtures of spinor BECs

M. Guilleumas, Bruno Juliá-Díaz, M. Melé-Messeguer +1 more

We study the dynamics of Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double well potential. Two interesting mixture genuine effects are identified. First, we find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. Secondly, in the balanced population case, the Josephson oscillations behave as if the interatomic interactions have been partially cancelled. This effect could be used as a new procedure to measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are physically interpreted in terms of an analytical description of the binary mixture using a two-mode model.

Laser Physics•Apr 2, 2010•6 citations
We numerically simulate the dynamics of a spin-2 Bose–Einstein condensate. We find that the initial phase plays an important role in the spin component oscillations. The spin mixing processes can fully cancel out due to quantum interference when taking some initial special phase. In all the spin mixing processes, the total spin is conversed. When the initial population is mainly occupied by a component with the maximal or minimal magnetic quantum number, the oscillations of spin components cannot happen due to the total spin conversation. The presence of quadratic Zeeman energy terms suppresses some spin mixing processes so that the oscillations of spin components are suppressed in some initial spin configuration. However, the linear Zeeman energy terms have no effects on the spin mixing processes.
We study the spin mixing dynamics of a spin-orbit coupled spin-1 Bose–Einstein condensate. Using mean-field theory and adopting plane wave solutions, the spin mixing dynamics can be well described by an internal Josephson equation. In order to establish the role of the different terms in spin mixing dynamics clearly, we consider the equilibrium state firstly, which shows that the spin-orbit coupling can significantly modify the dispersion relation and change the property of ground state of the condensate. For the non-equilibrium state, the spin-orbit coupling plays an important role in the spin mixing dynamics. Moreover, the oscillation period of spin mixing dynamics is determined by the coupled effects of momentum, magnetization, spin-dependent atomic interaction and spin-orbit coupling. When spin-orbit coupling is less than a critical value, it can prolong the oscillation period of spin mixing dynamics. Conversely, when the spin-orbit coupling is larger than the critical value, it can shorten the oscillation period of spin mixing dynamics. Particularly, when spin-orbit coupling is equal to the critical value, the period tends to infinity. Our study provides a complete spin mixing dynamics of spin-orbit coupled spin-1 BEC, which can be used to explore the spin mixing dynamics experimentally.
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 study the spin-mixing dynamics of an f=1f=1f=1 spinor condensate. We show that the dynamics is sensitive to the relative phase and particle number distribution among the individual components of the condensate, and find that complex structures can develop in the density profiles during the time evolution. We investigate the different time scales of the spin-mixing process and their dependence on the total particle number.
We predict a dynamical resonant effect, which is driven by externally applied linear and quadratic Zeeman fields, in a spin-orbit-coupled spin-1 Bose-Einstein condensate. The Bose-Einstein condensate is assumed to be initialized in some superposed state of Zeeman sublevels and subject to a sudden shift of the trapping potential. It is shown that the time-averaged center-of-mass oscillation and the spin polarizations of the Bose-Einstein condensate exhibit remarkable resonant peaks when the Zeeman fields are tuned to certain strengths. The underlying physics behind this resonance can be traced back to the out-of-phase interference of the dynamical phases carried by different spin-orbit states. By analyzing the single-particle spectrum, the resonant condition is summarized as a simple algebraic relation, connecting the strengths of the linear and quadratic Zeeman fields. This property is potentially applicable in quantum information and quantum precision measurement.
We present measurements and a theoretical model for the interplay of spin-dependent interactions and external magnetic fields in atomic spinor condensates. We highlight general features such as quadratic Zeeman dephasing and its influence on coherent spin mixing processes by focusing on a specific coherent superposition state in a F=1F=1F=1 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate. In particular, we observe the transition from coherent spinor oscillations to the thermal equilibration.
We study the dynamics of Josephson oscillations in a mixture of two Zeeman states of a spinor Bose-Einstein condensate in a double well potential. Two interesting mixture genuine effects are identified. First, we find that in the strongly polarized case, the less populated component exhibits a complex dynamics with an anti-Josephson behavior, i.e., oscillates in phase with the more populated one. Secondly, in the balanced population case, the Josephson oscillations behave as if the interatomic interactions have been partially cancelled. This effect could be used as a new procedure to measure the distinct scattering lengths entering in the description of a spinor condensate. Our numerical results are physically interpreted in terms of an analytical description of the binary mixture using a two-mode model.