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:0903.2541 · Physical Review A

Strong spin oscillation of small spin-1 condensates caused by an inclined weak magnetic field

Y. Z. He, Zihao Chen, Zhibing Li, Bao Cheng-guang

Published Aug 24, 2009• 2 citations
arXivHTMLPDF

Abstract

For studying the spin evolution of a condensate of spin-1 atoms, the total magnetization $M$ relative to the $Z$ axis of quantization is prepared at a given value previously. During the evolution, $M$ would not be conserved if an inclined magnetic field is applied (i.e., the direction of the field deviates from the $Z$ axis). In this case, the inclined field can cause a strong spin evolution via the linear Zeeman term even the field is very weak (say, close to 0.01 mG). An approach beyond the mean-field theory is proposed to study the evolution of small $^{87}\text{R}\text{b}$ condensates under the weak inclined fields. The time-dependent populations of spin components are given in analytical forms. The evolution is found to be highly sensitive to the magnitude and direction of the field.

DOI
10.1103/physreva.80.023620

Related papers

Effect of a Magnetic Field on the Spin Evolution of 87Rb Bose–Einstein Condensates with Zero Polarization

Zhifeng Chen, Bao Cheng-guang, Zhibing Li

The spin mixing dynamics of spin-1 Bose–Einstein condensates with zero magnetization and under an external magnetic field is investigated in a systematic way. Beyond the mean field theory, the time-dependent solutions of the Hamiltonian under the single mode approximation are obtained via a procedure of diagonalization. Thereby the time-dependent populations of spin-0 component starting from various initial states are obtained and analyzed. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field. Since the solutions are exact for the Hamiltonian, we can study the long-term behavior of the evolution, where periodicity and inherent symmetry emerge. In particular, some special cases are found in which the evolution is highly sensitive to the field, very strong oscillation in population can be thereby induced. A new mode of oscillation of the population characterized by having two frequencies, one is high and one is low, is found when the field is sufficiently strong.

Journal of the Physical Society of Japan•Oct 26, 2009•4 citations

Effect of magnetic fields on the spin evolution of non-polarized 87Rb Bose-Einstein condensates

Zhifeng Chen, Bao Cheng-guang, Zhibing Li

The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero magnetization and under an external magnetic field is investigated. The time-dependent solutions are obtained via a diagonalization of the Hamiltonian, which has a simple form under the single mode approximation. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field, which can induce strong oscillation in population of atoms in spin component 0 . A new mode of oscillation characterized by a high frequency and a low frequency, is found when the field is sufficiently strong.

arXiv:0802.0822•Feb 6, 2008•0 citations

Spin dynamics and structure formation in a spin-1 condensate in a magnetic field

Jordi Mur-Petit

We study the dynamics of a trapped spin-1 condensate in a magnetic field. First, we analyze the homogeneous system, for which the dynamics can be understood in terms of orbits in phase space. We analytically solve for the dynamical evolution of the populations of the various Zeeman components of the homogeneous system. This result is then applied via a local-density approximation to trapped quasi-one-dimensional condensates. Our analysis of the trapped system in a magnetic field shows that both the mean-field and Zeeman regimes are simultaneously realized, and we argue that the border between these two regions is where spin domains and phase defects are generated. We propose a method to experimentally tune the position of this border.

arXiv:0904.1160•Physical Review A•Jun 2, 2009•16 citations

Vortex Formation in Spin-Orbit Coupled Spin-1 Bose Condensates with Magnetic Field

Qiang Zhao

In this article, we study the vortex formation in spin-1 spin–orbit coupling rotating Bose–Einstein condensates. Numerical results are obtained by solving the spinor Gross–Pitaevskii equation. We mainly focus on the influences of external magnetic fields on vortex structures and dynamics properties. With the increase in magnetic field strength, the populations of magnetic components j=±1 reach the identical value. For the density profile, the three components present identical density structures, and the size of condensates is nearly the same. In addition, some related physical quantities, such as the time taken for the arrival of a steady population and root-mean-square size, kinetic energy, and total angular momentum, are calculated. The results show that these quantities decrease as the magnetic field strength increases. Moreover, we also investigate the time evolution of angular momentum. It is seen that the dynamic behavior of the magnetic components j=±1 is exactly consistent, and the total angular momentum reduces in the presence of the strong magnetic field. This reflects the fact that the introduction of the strong magnetic field makes it difficult to rotate the condensate, and thus, it is disadvantageous for generating more vortices.

Acta Physica Polonica A•May 1, 2024•0 citations

Mean field ground state of a spin-1 condensate in a magnetic field

Wenxian Zhang, Su Yi, Li You

Abstract. We revisit the topic of the mean field ground state of a spin-1 atomic condensate inside a uniform magnetic field (B) under the constraints that both the total number of atoms (N) and the magnetization (M) are conserved. In the presence of an internal state (spin component) independent trap, we also investigate the dependence of the so-called single spatial mode approximation (SMA) on the magnitude of the magnetic field and M. Our result indicate that the quadratic Zeeman effect is an important factor in balancing the mean field energy from elastic atom-atom collisions that are known to conserve both N and M.Mean field ground state of a spin-1 condensate in a magnetic field 2 1.

•Jan 1, 2003•51 citations

Magnetic field dependence of the dynamics of Rb87 spin-2 Bose-Einstein condensates

T. Kuwamoto, K. Araki, T. Eno +1 more

We experimentally studied the spin-dependent collision dynamics of $^{87}\mathrm{Rb}$ spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to $3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}$. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the $F=2$ manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each ${m}_{F}$ component.

Physical Review A•Jun 8, 2004•172 citations
For studying the spin evolution of a condensate of spin-1 atoms, the total magnetization MMM relative to the ZZZ axis of quantization is prepared at a given value previously. During the evolution, MMM would not be conserved if an inclined magnetic field is applied (i.e., the direction of the field deviates from the ZZZ axis). In this case, the inclined field can cause a strong spin evolution via the linear Zeeman term even the field is very weak (say, close to 0.01 mG). An approach beyond the mean-field theory is proposed to study the evolution of small 87Rb^{87}\text{R}\text{b}87Rb condensates under the weak inclined fields. The time-dependent populations of spin components are given in analytical forms. The evolution is found to be highly sensitive to the magnitude and direction of the field.
The spin mixing dynamics of spin-1 Bose–Einstein condensates with zero magnetization and under an external magnetic field is investigated in a systematic way. Beyond the mean field theory, the time-dependent solutions of the Hamiltonian under the single mode approximation are obtained via a procedure of diagonalization. Thereby the time-dependent populations of spin-0 component starting from various initial states are obtained and analyzed. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field. Since the solutions are exact for the Hamiltonian, we can study the long-term behavior of the evolution, where periodicity and inherent symmetry emerge. In particular, some special cases are found in which the evolution is highly sensitive to the field, very strong oscillation in population can be thereby induced. A new mode of oscillation of the population characterized by having two frequencies, one is high and one is low, is found when the field is sufficiently strong.
The spin mixing dynamics of spin-1 Bose-Einstein condensates with zero magnetization and under an external magnetic field is investigated. The time-dependent solutions are obtained via a diagonalization of the Hamiltonian, which has a simple form under the single mode approximation. The features of evolution are compared in detail with those with the field removed so as to emphasize the effect of the field, which can induce strong oscillation in population of atoms in spin component 0 . A new mode of oscillation characterized by a high frequency and a low frequency, is found when the field is sufficiently strong.
We study the dynamics of a trapped spin-1 condensate in a magnetic field. First, we analyze the homogeneous system, for which the dynamics can be understood in terms of orbits in phase space. We analytically solve for the dynamical evolution of the populations of the various Zeeman components of the homogeneous system. This result is then applied via a local-density approximation to trapped quasi-one-dimensional condensates. Our analysis of the trapped system in a magnetic field shows that both the mean-field and Zeeman regimes are simultaneously realized, and we argue that the border between these two regions is where spin domains and phase defects are generated. We propose a method to experimentally tune the position of this border.
In this article, we study the vortex formation in spin-1 spin–orbit coupling rotating Bose–Einstein condensates. Numerical results are obtained by solving the spinor Gross–Pitaevskii equation. We mainly focus on the influences of external magnetic fields on vortex structures and dynamics properties. With the increase in magnetic field strength, the populations of magnetic components j=±1 reach the identical value. For the density profile, the three components present identical density structures, and the size of condensates is nearly the same. In addition, some related physical quantities, such as the time taken for the arrival of a steady population and root-mean-square size, kinetic energy, and total angular momentum, are calculated. The results show that these quantities decrease as the magnetic field strength increases. Moreover, we also investigate the time evolution of angular momentum. It is seen that the dynamic behavior of the magnetic components j=±1 is exactly consistent, and the total angular momentum reduces in the presence of the strong magnetic field. This reflects the fact that the introduction of the strong magnetic field makes it difficult to rotate the condensate, and thus, it is disadvantageous for generating more vortices.
Abstract. We revisit the topic of the mean field ground state of a spin-1 atomic condensate inside a uniform magnetic field (B) under the constraints that both the total number of atoms (N) and the magnetization (M) are conserved. In the presence of an internal state (spin component) independent trap, we also investigate the dependence of the so-called single spatial mode approximation (SMA) on the magnitude of the magnetic field and M. Our result indicate that the quadratic Zeeman effect is an important factor in balancing the mean field energy from elastic atom-atom collisions that are known to conserve both N and M.Mean field ground state of a spin-1 condensate in a magnetic field 2 1.
We experimentally studied the spin-dependent collision dynamics of 87Rb^{87}\mathrm{Rb}87Rb spin-2 Bose-Einstein condensates confined in an optical trap. The condensed atoms were initially populated in the $\ensuremath{\mid}F=2,{m}_{F}=0⟩$ state, and their time evolutions in the trap were measured in the presence of external magnetic field strengths ranging from 0.1 to 3.0G3.0\phantom{\rule{0.3em}{0ex}}\mathrm{G}3.0G. The atom loss rate due to inelastic two-body collisions was found to be $1.4(2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. Spin mixing in the F=2F=2F=2 manifold developed dramatically for the first few tens of milliseconds, and the oscillations in the population distribution between different magnetic components were observed over a limited range of magnetic field strengths. The antiferromagnetic property of this system was deduced from the magnetic field dependence on the evolution of relative populations for each mF{m}_{F}mF​ component.