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:cond-mat/0210253 · Journal of Physics B Atomic Molecular and Optical Physics

Dynamics of a two-component atomic Bose Einstein condensate

Ping Zhang, C K Chan, Xiang‐Gui Li, Xian-Geng Zhao

Published Nov 4, 2002• 10 citations
arXivHTMLPDF

Abstract

The dynamical population oscillations between two internal states of a Bose–Einstein condensate are investigated within the rotating wave approximation. Analytical expressions for the population imbalance in the number states and coherent states have been derived, which predict different revival periods. Thus the true quantum state of the condensates may be unambiguously determined by detecting the atom intensity evolution for one internal state.

DOI
10.1088/0953-4075/35/22/307

Related papers

Dynamics and Berry phase of two-species Bose-Einstein condensates

Z.-D. Chen, J.-Q. Liang, Shun-Qing Shen +1 more

In terms of exact solutions of the time-dependent Schr\"odinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2) coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.

arXiv:cond-mat/0403570•Physical Review A•Feb 18, 2004•69 citations

Josephson Oscillations of Bose-Einstein Condensate in Double-Well Potential: Two-Mode Model and Beyond

Haoyu Wang, Guangyu Liu, Lizhen Sun +1 more

Abstract The Josephson oscillation of a Bose-Einstein condensate (BEC) in a double-well potential is typically characterized by the population imbalance between the two wells. Within the two-mode approximation, the dynamics of the center of mass of the condensate is predicted to coincide with that of the population imbalance. However, numerical simulations reveal a discrepancy between the dynamics of the center of mass and that of the population imbalance, indicating that the two-mode model fails to fully capture the dynamics of BEC Josephson oscillations. To address this limitation, a four-mode approximation is employed to describe the dynamics of the system. The four-mode model not only describes the dynamics of the population imbalance but also accounts for the oscillation of the center of mass, thereby explaining the origin of the discrepancy between the two-mode model and the simulation results. Moreover, we find that although higher-order excitation modes are always present in Josephson oscillations, the two-mode model can still describe the dynamics of the population imbalance. This phenomenon is explained by the interference of population oscillations between local states. PACS: 03.75.Lm, 03.75.Kk, 67.85.De

Journal of Low Temperature Physics•Sep 18, 2026•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

Quantum coherent oscillations between two coupled bose-einstein condensates

Ai-Xi Chen, Deng Li

The theoretical investigation of quantum coherent atomic oscillations between two coupled Bose-Einstein condensates(BECs) is studied.We apply the inseparable wave function of time-space to describe two trapped BECs in a double-well magnetic trap.According to Thomas-Fermi approximation,dynamical equations of the interwell phase difference and population imbalance are obtained.Using numerical method,coherent atomic tunneling and macroscopic quantum self-trapping(MQST) effect are investigated.

Journal of Atomic and Molecular Physics•Jan 1, 2006•0 citations

The interaction of atomic Bose -Einstein condensates with electromagnetic fields.

Christopher P. Search

We study the dynamics of weakly interacting Bose-Einstein condensates consisting of alkali atoms with two or more internal eigenstates. Three separate problems are examined in this thesis, which look at the behavior of the condensates in the presence of electromagnetic fields, which couple the internal states of the atoms. First, we examine the ground state and quasiparticle excitations for a condensate with a spatially uniform and time independent field, which couples two of the internal states. In particular, we address the nature of the instabilities that have been predicted in these systems. Second, we look at the time evolution of small condensates with a time dependent field, which couples two states. It is shown that the atomic population in the two components, as a function of time, is very different for a condensate with a precisely defined number of atoms and one that exhibits spontaneous symmetry breaking. Finally, we propose two methods for mapping information about the quantum state of the condensate to a mode of an electromagnetic cavity. The first method, which is irreversible, is only able to transfer the population statistics of the condensate to the cavity field. The second method involves the adiabatic transfer of the quantum state of the condensate to the cavity field.

•Jan 1, 2002•0 citations

Self-Trapping of Two Bose–Einstein Condensates with a Coupling Drive

Qiu Jian-guo

We present an approximate analytical solution to the population imbalance of two-component Bose–Einstein condensate with the coupling drive. The dependence of the time evolution of self-trapping upon the radio frequency wave, the Rabi coupling frequency, the initial atom number and relative phase between two condensates are investigated. The lower radio frequency wave, the same atom number and initial relative phase between condensates are beneficial to observe the self-trapping.

Chinese Physics Letters•May 30, 2006•1 citation
The dynamical population oscillations between two internal states of a Bose–Einstein condensate are investigated within the rotating wave approximation. Analytical expressions for the population imbalance in the number states and coherent states have been derived, which predict different revival periods. Thus the true quantum state of the condensates may be unambiguously determined by detecting the atom intensity evolution for one internal state.
In terms of exact solutions of the time-dependent Schr\"odinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2) coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.
Abstract The Josephson oscillation of a Bose-Einstein condensate (BEC) in a double-well potential is typically characterized by the population imbalance between the two wells. Within the two-mode approximation, the dynamics of the center of mass of the condensate is predicted to coincide with that of the population imbalance. However, numerical simulations reveal a discrepancy between the dynamics of the center of mass and that of the population imbalance, indicating that the two-mode model fails to fully capture the dynamics of BEC Josephson oscillations. To address this limitation, a four-mode approximation is employed to describe the dynamics of the system. The four-mode model not only describes the dynamics of the population imbalance but also accounts for the oscillation of the center of mass, thereby explaining the origin of the discrepancy between the two-mode model and the simulation results. Moreover, we find that although higher-order excitation modes are always present in Josephson oscillations, the two-mode model can still describe the dynamics of the population imbalance. This phenomenon is explained by the interference of population oscillations between local states. PACS: 03.75.Lm, 03.75.Kk, 67.85.De
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.
We study the dynamics of weakly interacting Bose-Einstein condensates consisting of alkali atoms with two or more internal eigenstates. Three separate problems are examined in this thesis, which look at the behavior of the condensates in the presence of electromagnetic fields, which couple the internal states of the atoms. First, we examine the ground state and quasiparticle excitations for a condensate with a spatially uniform and time independent field, which couples two of the internal states. In particular, we address the nature of the instabilities that have been predicted in these systems. Second, we look at the time evolution of small condensates with a time dependent field, which couples two states. It is shown that the atomic population in the two components, as a function of time, is very different for a condensate with a precisely defined number of atoms and one that exhibits spontaneous symmetry breaking. Finally, we propose two methods for mapping information about the quantum state of the condensate to a mode of an electromagnetic cavity. The first method, which is irreversible, is only able to transfer the population statistics of the condensate to the cavity field. The second method involves the adiabatic transfer of the quantum state of the condensate to the cavity field.