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:0908.2781

The spin evolution of spin-3 $^{52}$Cr Bose-Einstein condensate

Y. Z. He

Published Aug 19, 2009• 0 citations
arXivHTMLPDF

Abstract

The spin evolution of a Bose-Einstein condensate starting from a mixture of two or three groups of $^{52}$Cr (spin-3) atoms in an optical trap has been studied theoretically. The initial state is so chosen that the system does not distinguish up and down. In this choice, the deviation caused by the single-mode approximation is reduced. Moreover, since the particle number is given very small (N=20), the deviation caused by the neglect of the long-range dipole force is also reduced. Making use of these two simplifications, a theoretical calculation beyond the mean field theory is performed. The numerical results are help to evaluate the unknown strength $g_0$.

DOI
10.48550/arxiv.0908.2781

Related papers

The spin evolution of spin-3 52 Cr Bose—Einstein condensate

Shuping Situ, Y. Z. He

This paper studies theoretically the spin evolution of a Bose—Einstein condensate starting from a mixture of two or three groups of 52 Cr (spin-3) atoms in an optical trap. The initial state is so chosen that the condensate has total magnetization zero so that the system does not distinguish up and down. It is assumed that the system is very dilute (particle number is very small), the temperature is very low, and the frequency of the harmonic trap is large enough. In these situations, the deviation caused by the neglect of the dipole—dipole interaction and by using the single-mode approximation is reduced. A theoretical calculation beyond the mean field theory is performed and the numerical results are helpful for the evaluation of the unknown strength g 0 .

Chinese Physics B•Jan 1, 2011•3 citations

Spin evolution of a mixture of Rb and Na Bose–Einstein condensates: an exact approach under the single-mode approximation

Ma Luo, Bao Cheng-guang, Zhibing Li

Spin evolution of a mixture of two species of spin-1 Bose–Einstein condensates (Rb and Na) has been investigated rigorously. The Hamiltonian under the single-mode approximation (which is the only approximation in the present theory) has been solved exactly. Both analytical expressions and numerical results on the populations of spin components are obtained. Interference between the two species is found to depend sensitively on the initial states and the inter-species interaction. A number of phenomena arising from the interference have been predicted. In particular, periodic behaviour and the alternate appearances of a zone of oscillation and a long quiet zone are found.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 2, 2008•9 citations

Energy level-splitting of ground state in spinor Bose-Einstein condensate with large number of atoms

Yan Xu, Jia Duo-Je, Zhaoxin Li +4 more

We study the mode deviation effect of a spin-1 Bose-Einstein condensate with large number of atoms in optical trap beyond the single-mode approximation. Based on the effective Hamiltonian with nondegenerate level of the collective spin states, we get the mode deviation factor and explicitly calculate the level splitting energy as function of the atom number N.

Acta Physica Sinica•Jan 1, 2009•3 citations

Evolution of the average populations of spin components of spin-1 Bose-Einstein condensates beyond mean-field theory

Ma Luo, Bao Cheng-guang, Zhibing Li

With full consideration given to symmetry, we derive an exact analytical formula governing the evolution of the average populations of the spin components for spin-1 condensates. Based on the formula, a number of peculiarities of the evolution can be better understood. Our numerical results are consistent with existing experimental data. A special initial state is found; starting from this state, the average populations remain constant during a very long time, much longer than the duration observed during experiments.

arXiv:0705.4235•Physical Review A•Apr 23, 2008•9 citations

Theoretical and experimental study of spin-1 antiferromagnetic Bose-Einstein Condensates

Shao, Lingxuan

In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field $B$. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field $B_c$, asymptotic values of $n_0$ (relative atom number in $m_F=0$ state) at large $B$ and the phase diagram of $n_0$. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of $n_0$. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature" $T_s$ and the ``kinetic temperature" $T_k$ with $T_s\ll T_k$, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.

•Jul 4, 2014•1 citation

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
The spin evolution of spin-3 52^{52}52Cr Bose-Einstein condensate
The spin evolution of a Bose-Einstein condensate starting from a mixture of two or three groups of 52^{52}52Cr (spin-3) atoms in an optical trap has been studied theoretically. The initial state is so chosen that the system does not distinguish up and down. In this choice, the deviation caused by the single-mode approximation is reduced. Moreover, since the particle number is given very small (N=20), the deviation caused by the neglect of the long-range dipole force is also reduced. Making use of these two simplifications, a theoretical calculation beyond the mean field theory is performed. The numerical results are help to evaluate the unknown strength g0g_0g0​.
This paper studies theoretically the spin evolution of a Bose—Einstein condensate starting from a mixture of two or three groups of 52 Cr (spin-3) atoms in an optical trap. The initial state is so chosen that the condensate has total magnetization zero so that the system does not distinguish up and down. It is assumed that the system is very dilute (particle number is very small), the temperature is very low, and the frequency of the harmonic trap is large enough. In these situations, the deviation caused by the neglect of the dipole—dipole interaction and by using the single-mode approximation is reduced. A theoretical calculation beyond the mean field theory is performed and the numerical results are helpful for the evaluation of the unknown strength g 0 .
Spin evolution of a mixture of two species of spin-1 Bose–Einstein condensates (Rb and Na) has been investigated rigorously. The Hamiltonian under the single-mode approximation (which is the only approximation in the present theory) has been solved exactly. Both analytical expressions and numerical results on the populations of spin components are obtained. Interference between the two species is found to depend sensitively on the initial states and the inter-species interaction. A number of phenomena arising from the interference have been predicted. In particular, periodic behaviour and the alternate appearances of a zone of oscillation and a long quiet zone are found.
With full consideration given to symmetry, we derive an exact analytical formula governing the evolution of the average populations of the spin components for spin-1 condensates. Based on the formula, a number of peculiarities of the evolution can be better understood. Our numerical results are consistent with existing experimental data. A special initial state is found; starting from this state, the average populations remain constant during a very long time, much longer than the duration observed during experiments.
In this thesis, we study theoretically and in experimentally the properties of spin-1 Bose-Einstein condensates with antiferromagnetic interactions realized in the ultra-cold sodium gases confined in optical dipole traps. We present in detail how to realize, diagnose and control the spinor Bose-Einstein condensates in our experiment. In order to describe the condensate, a mean-field theory is first adopted. This theory predicts a phase transition when changing the magnetic field BBB. The predictions of the mean-field theory agree very well with most of our experimental results, including the values of the critical magnetic field BcB_cBc​, asymptotic values of n0n_0n0​ (relative atom number in mF=0m_F=0mF​=0 state) at large BBB and the phase diagram of n0n_0n0​. However, for small magnetization and small magnetic fields, we find abnormally large fluctuations (super-Poissonian) of n0n_0n0​. In order to describe these large fluctuations, we develop a full quantum statistical description for the spinor condensate at finite temperature. To describe uncondensed thermal atoms (also present in the same trap), we use the ``semi-ideal" Hartree-Fock approximation to deal with the interactions between the condensate atoms and the thermal ones. The experimental results lead us to introduce two kinds of temperatures, the ``spin temperature" TsT_sTs​ and the ``kinetic temperature" TkT_kTk​ with Ts≪TkT_s\ll T_kTs​≪Tk​, characterizing respectively the fluctuaitons of the condensate spin and the thermal gas. We conclude that the system is reaching a quasi-equilibrium states, where different degrees of freedom reach equilibrium by separate mechanisms but where the mutual thermalization does not occur over the lifetime of the cloud.
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.