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/0406182 · Low Temperature Physics

Diagnostics of macroscopic quantum states of Bose–Einstein condensate in double-well potential by nonstationary Josephson effect

E. D. Vol

Published Feb 1, 2005• 0 citations
arXivHTMLPDF

Abstract

We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double-well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn=n1−n2 measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.

DOI
10.1063/1.1820536

Related papers

Diagnostics of macroscopic quantum states of Bose–Einstein condensate in double-well potential by nonstationary Josephson effect

E. D. Vol

We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double- well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn = n₁ - n₂ measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.

•Jan 1, 2005•0 citations

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

Yao-Jun Ying, Wang, Haoyu, Zhang, Ming +1 more

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.

arXiv:2506.15104•Jun 18, 2025•0 citations

Bose-Einstein Condensates in a Single Double Well Potential

Rudolf Gati

The subject of this work is the experimental implementation of a single bosonic Josephson junction and the discussion of the performed investigations. To generate this new kind of Josephson junction a 87-Rubidium Bose-Einstein condensate is split in a double well potential into two matter wave packets, which are coupled coherently to each other via quantum mechanical tunneling of atoms through the barrier. The state of the system can be described by two dynamical variables, the population imbalance of the two wells and their phase difference. The investigation of the dynamical response of the Josephson junction shows, that two dynamical regimes can be identified, the plasma oscillation regime, where atoms tunnel back and forth between the wells, and the self trapping regime, where no tunneling is found. Furthermore, the investigation at finite temperature reveals, that the relative phase in steady state is not locked to zero but fluctuates according to its temperature and the tunneling coupling. By measuring the fluctuations and calculating the tunneling coupling it is possible to deduce the temperature of the atomic cloud. With this a new method for thermometry is realized, which also works in a regime, where the standard methods can not be applied.

•Jan 1, 2007•9 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

Macroscopic quantum tunnelling in rotating Bose Einstein condensates

Yuan-Xiu Miao, Hui Zhai, Hong-Yu Yang +1 more

In this paper we investigate various macroscopic quantum tunnelling phenomena and the phase coherence property of rotating Bose–Einstein condensates. Based on the two-mode approximation, three different cases are studied. When the rotating frequency is independent of time t , by using the SU (2) coherent state path integral method, we discuss two cases: a superposition of two macroscopic states and a Josephson-type ground state. In addition, the specific conditions to reach the two cases are obtained. We also discuss the nonlinear Landau–Zener effect in the dynamic case in which the rotating frequency varies with time t .

arXiv:cond-mat/0204219•Journal of Physics B Atomic Molecular and Optical Physics•Apr 14, 2003•1 citation

Bose -Einstein Condensation and Condensate Tunneling

Siegfried Großmann, Martin Holthaus

Abstract We consider Bose-Einstein condensation in a small cube and describe effects induced by the con­ finement. We also sketch an analogue of the Josephson effect for neutral particles, which can be realized when two almost degenerate states in a double well potential are occupied by a macroscopic number of Bosons. PACS number: 05.30.Jp

Zeitschrift für Naturforschung A•May 1, 1995•50 citations
We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double-well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn=n1−n2 measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.
We propose a method of diagnostics of a degenerate ground state of Bose condensate in a double- well potential. The method is based on the study of the one-particle coherent tunneling under switching of the time-dependent weak Josephson coupling between the wells. We obtain a simple expression that allows one to determine the phase of the condensate and the total number of the particles in the condensate from the relative number of particles in the two wells Δn = n₁ - n₂ measured before the Josephson coupling is switched on and after it is switched off. The specifics of the application of the method in the cases of the external and the internal Josephson effect are discussed.
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.
The subject of this work is the experimental implementation of a single bosonic Josephson junction and the discussion of the performed investigations. To generate this new kind of Josephson junction a 87-Rubidium Bose-Einstein condensate is split in a double well potential into two matter wave packets, which are coupled coherently to each other via quantum mechanical tunneling of atoms through the barrier. The state of the system can be described by two dynamical variables, the population imbalance of the two wells and their phase difference. The investigation of the dynamical response of the Josephson junction shows, that two dynamical regimes can be identified, the plasma oscillation regime, where atoms tunnel back and forth between the wells, and the self trapping regime, where no tunneling is found. Furthermore, the investigation at finite temperature reveals, that the relative phase in steady state is not locked to zero but fluctuates according to its temperature and the tunneling coupling. By measuring the fluctuations and calculating the tunneling coupling it is possible to deduce the temperature of the atomic cloud. With this a new method for thermometry is realized, which also works in a regime, where the standard methods can not be applied.
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.
In this paper we investigate various macroscopic quantum tunnelling phenomena and the phase coherence property of rotating Bose–Einstein condensates. Based on the two-mode approximation, three different cases are studied. When the rotating frequency is independent of time t , by using the SU (2) coherent state path integral method, we discuss two cases: a superposition of two macroscopic states and a Josephson-type ground state. In addition, the specific conditions to reach the two cases are obtained. We also discuss the nonlinear Landau–Zener effect in the dynamic case in which the rotating frequency varies with time t .