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

Chinese Physics B

Dynamics of spin–orbital-angular-momentum coupled Bose–Einstein condensates on a ring

Lin 林 Wen 文, Yihan Huang, Lei Zhao, Xu Qiu, Ming-Yue Yang

Published Apr 3, 2026• 0 citations
Publisher

Abstract

Abstract We investigate the dynamics of a two-component Bose–Einstein condensate subject to spin–orbital-angular-momentum coupling and confined to a ring, via the variational approach. Adopting a single-mode approximation by assuming that the BEC carries a single angular momentum for SU(2)-symmetric spin interactions, the equations of motion for the variational parameters are derived. The phase diagram of the ground state in the plane of the Raman coupling and detuning contains three different phases which meet at a tricritical point, and the exact phase boundaries between the three phases are determined. Linear stability analysis shows that the stationary state is dynamically stable, and there exists an oscillation eigenmode with frequency determined by detuning, angular momentum, and Raman coupling. The time-evolution results indicate that the spin vector undergoes periodic rotation along a closed orbit on the Bloch sphere, which can be interpreted as a precession of the collective spin around an effective field determined by the Raman coupling strength, the detuning, and the angular momentum.

DOI
10.1088/1674-1056/ae5b5c

Related papers

Dynamics of spin-tensor-momentum coupled Bose-Einstein condensates

Xu Qiu, Lin-Xue Wang, Guangping Chen +2 more

We investigate the dynamics of the plane wave state in one-dimensional spin-tensor-momentum coupled Bose-Einstein condensate. By using the Gaussian variational approximation, we first derive the equations of motion for the variational parameters, including the center-of-mass coordinate, momentum, amplitude, width, chirp, and relative phase. These variational parameters are coupled together nonlinearly by the spin-tensor-momentum coupling, Raman coupling, and the spin-dependent atomic interaction. By minimizing the energy with respect to the variational parameters, we find that the ground state is a biaxial nematic state, the momentum of the ground state decreases monotonically with the increase of the strength of the Raman coupling, and the parity of real part of the ground-state wave function is opposite to that of the imaginary part. The linear stability analysis shows that the ground state is dynamically stable under a perturbation, and exhibits three different oscillation excitation modes, the frequencies of which are related to the strength of the Raman coupling, the aspect ratio of the harmonic trap, and the strength of the atomic interaction. By solving the equations of motion for the variational parameters, we find that the system displays periodical oscillation in the dynamical evolution. These variational results are also confirmed by the direct numerical simulations of the Gross-Pitaevskii equations, and these findings reveal the unique properties given by the spin-tensor-momentum coupling.

Acta Physica Sinica•Jan 1, 2023•0 citations

Spin-orbit angular momentum coupling in a spin-1 Bose-Einstein condensate

Li Chen, Han Pu, Yunbo Zhang

We propose a simple model with spin and orbit angular momentum coupling in a spin-1 Bose-Einstein condensate, where three internal atomic states are Raman coupled by a pair of copropagating Laguerre-Gaussian beams. The resulting Raman transition imposes a transfer of orbital angular momentum between photons and the condensate in a spin-dependent way. Focusing on a regime where the single-particle ground state is nearly threefold degenerate, we show that the weak interatomic interaction in the condensate produces a rich phase diagram, and that a many-body Rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic Zeeman shift. We carried out our calculations using both a variational method and a full numerical method, and found excellent agreement.

arXiv:1512.06276•Physical Review A•Jan 28, 2016•49 citations

Phase separation of spin-1 spin-orbital-angular-momentum coupled Bose–Einstein condensates

Zicun Li, Jinbin Li, Daning Shi

In this study, we study the circularly-symmetric phase separation in spin-1 spin-orbit-angular-momentum coupled (SOAMC) [Formula: see text] Bose–Einstein condensate (BEC) system in the [Formula: see text]-plane using a numerical solution of the mean-field Gross–Pitaevskii equation. The increase of the coupling strength [Formula: see text] in such a system is found to generate annular structures. The phase-separated had different structures with the spin and linear momentum coupling BEC. Our results are in good agreement with the new experiment H. R. Chen, K. Y. Lin, P. K. Chen, N. C. Chiu, J. B. Wang and C.-A. Chen, Phys. Rev. Lett. 121 (2018) 113204. We also analyzed the influence of different parameters of SOAMC on coupling strength [Formula: see text], spin correlation coefficient [Formula: see text], the number of particles [Formula: see text], and the anisotropy of the potential in the three-component equations. The dynamical stability of the phase separation is demonstrated by real-time propagation numerically.

Modern Physics Letters B•Mar 20, 2022•1 citation

Orbital angular momentum dynamics of Bose-Einstein condensates trapped in two stacked rings

Eulàlia Nicolau, J. Mompart, Bruno Juliá-Díaz +1 more

We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.

arXiv:2001.04394•Physical Review A•Aug 27, 2020•16 citations

Ground States and Dynamics of Spin-Orbit-Coupled Bose--Einstein Condensates

Weizhu Bao, Yongyong Cai

We study analytically and asymptotically, as well as numerically, ground states and dynamics of two-component spin-orbit-coupled Bose--Einstein condensates (BECs) modeled by the coupled Gross--Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynamical properties become very rich and complicated. For the ground states, we establish existence and nonexistence results under different parameter regimes and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either nonperiodic or with different frequency than the trapping frequency when the external trapping potential is taken as harmonic and/or the initial data is chosen as a stationary state (e.g., ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclassical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.

arXiv:1407.5815•SIAM Journal on Applied Mathematics•Jan 1, 2015•45 citations

GROUND STATES AND DYNAMICS OF SPIN-ORBIT-COUPLED

Bose-Einstein Condensates, Yongyong Cai

We study analytically and asymptotically as well as numerically ground states and dynamics of two-component spin-orbit-coupled Bose-Einstein condensates (BECs) modeled by the coupled Gross-Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynam- ical properties become very rich and complicated. For the ground states, we establish the existence and non-existence results under different parameter regimes, and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either non-periodic or with different frequency to the trapping frequency when the external trapping potential is taken as harmonic and the initial data is chosen as a stationary state (e.g. ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclas- sical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.

•Jan 1, 2014•0 citations
Abstract We investigate the dynamics of a two-component Bose–Einstein condensate subject to spin–orbital-angular-momentum coupling and confined to a ring, via the variational approach. Adopting a single-mode approximation by assuming that the BEC carries a single angular momentum for SU(2)-symmetric spin interactions, the equations of motion for the variational parameters are derived. The phase diagram of the ground state in the plane of the Raman coupling and detuning contains three different phases which meet at a tricritical point, and the exact phase boundaries between the three phases are determined. Linear stability analysis shows that the stationary state is dynamically stable, and there exists an oscillation eigenmode with frequency determined by detuning, angular momentum, and Raman coupling. The time-evolution results indicate that the spin vector undergoes periodic rotation along a closed orbit on the Bloch sphere, which can be interpreted as a precession of the collective spin around an effective field determined by the Raman coupling strength, the detuning, and the angular momentum.
We investigate the dynamics of the plane wave state in one-dimensional spin-tensor-momentum coupled Bose-Einstein condensate. By using the Gaussian variational approximation, we first derive the equations of motion for the variational parameters, including the center-of-mass coordinate, momentum, amplitude, width, chirp, and relative phase. These variational parameters are coupled together nonlinearly by the spin-tensor-momentum coupling, Raman coupling, and the spin-dependent atomic interaction. By minimizing the energy with respect to the variational parameters, we find that the ground state is a biaxial nematic state, the momentum of the ground state decreases monotonically with the increase of the strength of the Raman coupling, and the parity of real part of the ground-state wave function is opposite to that of the imaginary part. The linear stability analysis shows that the ground state is dynamically stable under a perturbation, and exhibits three different oscillation excitation modes, the frequencies of which are related to the strength of the Raman coupling, the aspect ratio of the harmonic trap, and the strength of the atomic interaction. By solving the equations of motion for the variational parameters, we find that the system displays periodical oscillation in the dynamical evolution. These variational results are also confirmed by the direct numerical simulations of the Gross-Pitaevskii equations, and these findings reveal the unique properties given by the spin-tensor-momentum coupling.
We propose a simple model with spin and orbit angular momentum coupling in a spin-1 Bose-Einstein condensate, where three internal atomic states are Raman coupled by a pair of copropagating Laguerre-Gaussian beams. The resulting Raman transition imposes a transfer of orbital angular momentum between photons and the condensate in a spin-dependent way. Focusing on a regime where the single-particle ground state is nearly threefold degenerate, we show that the weak interatomic interaction in the condensate produces a rich phase diagram, and that a many-body Rabi oscillation between two quantum phases can be induced by a sudden quench of the quadratic Zeeman shift. We carried out our calculations using both a variational method and a full numerical method, and found excellent agreement.
In this study, we study the circularly-symmetric phase separation in spin-1 spin-orbit-angular-momentum coupled (SOAMC) [Formula: see text] Bose–Einstein condensate (BEC) system in the [Formula: see text]-plane using a numerical solution of the mean-field Gross–Pitaevskii equation. The increase of the coupling strength [Formula: see text] in such a system is found to generate annular structures. The phase-separated had different structures with the spin and linear momentum coupling BEC. Our results are in good agreement with the new experiment H. R. Chen, K. Y. Lin, P. K. Chen, N. C. Chiu, J. B. Wang and C.-A. Chen, Phys. Rev. Lett. 121 (2018) 113204. We also analyzed the influence of different parameters of SOAMC on coupling strength [Formula: see text], spin correlation coefficient [Formula: see text], the number of particles [Formula: see text], and the anisotropy of the potential in the three-component equations. The dynamical stability of the phase separation is demonstrated by real-time propagation numerically.
We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.
We study analytically and asymptotically, as well as numerically, ground states and dynamics of two-component spin-orbit-coupled Bose--Einstein condensates (BECs) modeled by the coupled Gross--Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynamical properties become very rich and complicated. For the ground states, we establish existence and nonexistence results under different parameter regimes and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either nonperiodic or with different frequency than the trapping frequency when the external trapping potential is taken as harmonic and/or the initial data is chosen as a stationary state (e.g., ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclassical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.
We study analytically and asymptotically as well as numerically ground states and dynamics of two-component spin-orbit-coupled Bose-Einstein condensates (BECs) modeled by the coupled Gross-Pitaevskii equations (CGPEs). In fact, due to the appearance of the spin-orbit (SO) coupling in the two-component BEC with a Raman coupling, the ground state structures and dynam- ical properties become very rich and complicated. For the ground states, we establish the existence and non-existence results under different parameter regimes, and obtain their limiting behaviors and/or structures with different combinations of the SO and Raman coupling strengths. For the dynamics, we show that the motion of the center-of-mass is either non-periodic or with different frequency to the trapping frequency when the external trapping potential is taken as harmonic and the initial data is chosen as a stationary state (e.g. ground state) with a shift, which is completely different from the case of a two-component BEC without the SO coupling, and obtain the semiclas- sical limit of the CGPEs in the linear case via the Wigner transform method. Efficient and accurate numerical methods are proposed for computing the ground states and dynamics, especially for the case of box potentials. Numerical results are reported to demonstrate the efficiency and accuracy of the numerical methods and show the rich phenomenon in the SO-coupled BECs.