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:0705.4235 · Physical Review A

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

Published Apr 23, 2008• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.77.043625

Related papers

Interference of the evolutions of Rb and Na Bose-Einstein condensates

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 beyond the mean field theory. Both analytical expression and numerical results on the populations of spin-components are obtained. The interference is found to depend on the initial states and the inter-species interaction sensitively. A number of phenomena arising from the interference have been predicted. In particular, periodic behavior and the alternate appearances of a zone of oscillation and a long quiet zone are found.

arXiv:0808.4018•Aug 29, 2008•0 citations

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

Evolution of the average spin of spinor Bose-Einstein condensates in external fields

Lei Tan

Within the mean field approximation and the single mode approximation,the evolution of the average spin of the F=1 spinor condensate in an external magnetic field was studies and the evolution was independent of the density-density collisional interaction.When the population in each quantum state was constant,the average spin was determined by the external magnetic field and the spin-spin collisional interaction.

Journal of Lanzhou University•Jan 1, 2008•0 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

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

Y. Z. He

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 $g_0$.

arXiv:0908.2781•Aug 19, 2009•0 citations

Quenched binary Bose-Einstein condensates: Spin-domain formation and coarsening

S. De, Daniel L. Campbell, Rodney Price +3 more

We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a $\mathrm{U}(1)$ order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.

arXiv:1211.3127•Physical Review A•Mar 25, 2014•65 citations
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.
Spin evolution of a mixture of two species of spin-1 Bose-Einstein condensates (Rb and Na) has been investigated beyond the mean field theory. Both analytical expression and numerical results on the populations of spin-components are obtained. The interference is found to depend on the initial states and the inter-species interaction sensitively. A number of phenomena arising from the interference have been predicted. In particular, periodic behavior and the alternate appearances of a zone of oscillation and a long quiet zone are found.
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.
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.
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​.
We explore the time evolution of two-component Bose-Einstein condensates (BECs), quasi one dimensional with respect to their spinor dynamics, following a quench from one component BECs with a U(1)\mathrm{U}(1)U(1) order parameter into two-component condensates with a $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ order parameter. In our case, these two spin components have a propensity to phase separate, i.e., they are immiscible. Remarkably, these spin degrees of freedom can equivalently be described as a single-component attractive BEC. A spatially uniform mixture of these spins is dynamically unstable, rapidly amplifying any quantum or pre-existing classical spin fluctuations. This coherent growth process drives the formation of numerous spin-polarized domains, which are far from the system's ground state. At much longer times these domains grow in size, coarsening, as the system approaches equilibrium. The experimentally observed time evolution is consistent with our fully three-dimensional stochastic-projected Gross--Pitaevskii calculation.