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:2506.15104

Coherent tunneling of collective excitation of Bose-Einstein condensate in a double-well potential

Yao-Jun Ying, Wang, Haoyu, Zhang, Ming, Haibin Li

Published Jun 18, 2025• 0 citations
arXivHTMLPDF

Abstract

The Josephson effect can be observed in a Bose-Einstein condensate in a double-well potential, which is attributed to the tunneling of bosons between two wells. We propose a multi-mode theory to investigate the dynamics of local excitations in a one-dimensional condensate in a double-well potential. We show that the system can be described by two independent two-mode models. The Josephson oscillation and the self-trapping of local collective excitations are predicted analytically and confirmed by numerical simulation.

DOI
10.48550/arxiv.2506.15104

Related papers

Josephson tunnelling of dark solitons in a double-well potential

H Susanto, Jesús Cuevas–Maraver, P. Krüger

We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.

arXiv:1006.3024•Journal of Physics B Atomic Molecular and Optical Physics•Apr 21, 2011•15 citations

Dynamics of Bose-Einstein condensation in an asymmetric double-well potential

Yao-Jun Ying, Haibin Li

Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.

Acta Physica Sinica•Jan 1, 2023•1 citation

Tunneling of condensate magnetization in a double-well potential

Özgür Esat Müstecaplıoğlu, Mei Zhang, Li You

We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.

arXiv:quant-ph/0501165•Physical Review A•May 31, 2005•20 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

Symmetry-breaking and symmetry-restoring dynamics of a mixture of Bose-Einstein condensates in a double well

Indubala I. Satija, Radha Balakrishnan, Phillip Naudus +3 more

We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the ``swapping'' of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\ensuremath{\pi}$ modes.

arXiv:0811.1921•Physical Review A•Mar 16, 2009•74 citations

Collective Excitations of Bose–Einstein Condensates in a Double-Well Potential

Ippei Danshita, Kyota Egawa, Nobuhiko Yokoshi +1 more

We investigate collective excitations of Bose-Einstein condensates at absolute zero in a double-well trap. We solve the Bogoliubov equations with a double-well trap, and show that the crossover from the dipole mode to the Josephson plasma mode occurs in the lowest energy excitation. It is found that the anomalous tunneling property of low energy excitations is crucial to the crossover.

arXiv:cond-mat/0508027•Journal of the Physical Society of Japan•Dec 1, 2005•11 citations
The Josephson effect can be observed in a Bose-Einstein condensate in a double-well potential, which is attributed to the tunneling of bosons between two wells. We propose a multi-mode theory to investigate the dynamics of local excitations in a one-dimensional condensate in a double-well potential. We show that the system can be described by two independent two-mode models. The Josephson oscillation and the self-trapping of local collective excitations are predicted analytically and confirmed by numerical simulation.
We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.
Josephson effect of Bose-Einstein condensate in double-well potential is an obvious manifestation of macroscopic quantum coherence. Most of researches focus on the symmetric double-well potential. In this work, we investigate the dynamic of Bose-Einstein condensates in an asymmetric double-well potential by using two-mode theory and computer simulation. In the absence of the interaction between atoms, the dynamic equation of condensate can be solved analytically. The amplitude as a function of energy difference of two wells is obtained. We can find that the change of energy difference will lead to the different dynamic behaviors of condensate. If the energy difference is relatively large, the condensate will primarily occupy the well that is occupied more than the other well at the beginning time. It is interesting that such a trap phenomenon is not dependent on the position of the high energy potential well nor the position of low energy potential well. If the energy difference becomes small, the tunneling and oscillation of condensate will be enhanced. When the interaction between atoms is present, our numerical calculations show that as the nonlinear interaction increases, the dynamic behavior of condensate exhibits different characteristics, such as trapping in a well, enhancing the tunneling and oscillation between two wells, and enhancing the trapping in a well at large nonlinear interaction, which is similar to the dynamic change caused by the energy difference in the case of ideal condensate. That is to say, on the one hand, the nonlinear interaction can lead to the trap of condensate as well as the dynamic trap to happen in symmetric double-well potential. On the other hand, the nonlinearity can promote the tunneling of condensate, counteracting the effect of the asymmetry of potential. And, this counteracting effect is related to the difference in energy between asymmetric potential wells. To understand the underlying mechanism, the full dynamic behavior of two-mode model is illustrated and the dynamic transition can be seen clearly. Combining the results obtained with and without interaction, regarding nonlinear interaction as effective potential provides a clear way to explain dynamic transition of condensate in an asymmetric double-well potential. In addition, we also perform the numerical simulations of the Gross-Pitaevskii equation, and the results are consistent with the conclusions obtained by using the two-mode theory.
We study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
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
We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the ``swapping'' of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\ensuremath{\pi}$ modes.