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

Journal of Modern Optics

Bistability and macroscopic quantum coherence in BECs: the two cases of attractive and repulsive interactions

A. Montina, F. T. Arecchi

Published Jan 1, 2002• 3 citations
Publisher

Abstract

We consider Bose-Einstein condensates (BECs) in situations where the density undergoes a symmetry breaking, either in real space or in momentum space. This occurs for a suitable number of condensed atoms in a double well potential, obtained in real space for a BEC of lithium atoms by adding a standing wave light field to the trap potential, or in momentum space for rubidium atoms by Raman coupling two BECs in different magnetic states with two tilted light fields. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schrödinger cat (SC) and we evaluate the macroscopic quantum coherence between the two SC states.

DOI
10.1080/09500340110077562

Related papers

Bistability and macroscopic quantum coherence in a Bose-Einstein condensate of 7Li

A. Montina, F. T. Arecchi

We consider a Bose-Einstein condensate of ${}^{7}\mathrm{Li}$ in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double-well potential, obtained by adding a standing-wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation leads, in fact, to a macroscopic quantum superposition or Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called macroscopic quantum coherence (MQC); we study the effects of losses on MQC.

arXiv:cond-mat/0202234•Physical Review A•Jul 18, 2002•15 citations

Macroscopic quantum coherence in a repulsive Bose-Einstein condensate

A. Montina, F. T. Arecchi

We consider a Bose-Einstein bicondensate of ${}^{87}\mathrm{Rb},$ trapped in two different internal levels, in a situation where the density undergoes a symmetry breaking in momentum space. This occurs for a suitable number of condensed atoms within a double-well dispersion curve, obtained by Raman coupling two internal states with two tilted and detuned light fields. Evidence of bistability results from the Gross-Pitaevskii equation. By second quantization, we evaluate the tunneling rate between the two asymmetric states; the effects of losses on coherence are negligible.

arXiv:cond-mat/0206041•Physical Review A•Feb 28, 2003•5 citations

Coupled-mode theory for Bose-Einstein condensates

Elena A. Ostrovskaya, Yuri S. Kivshar, M. Lisak +3 more

We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by direct numerical solution of the Gross-Pitaevskii-equation.

arXiv:cond-mat/9910185•Physical Review A•Feb 7, 2000•184 citations

Strong-coupling dynamics of Bose–Einstein condensate in a double-well trap

Valentin O. Nesterenko, A N Novikov, E. Suraud

Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.

arXiv:1205.3687•Journal of Physics B Atomic Molecular and Optical Physics•Oct 24, 2012•5 citations

Macroscopic quantum tunneling of two-component Bose-Einstein condensates

Kenichi Kasamatsu, Yukinori Yasui, Makoto Tsubota

We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.

arXiv:cond-mat/0103374•Physical Review A•Oct 3, 2001•28 citations

Macroscopic self-trapping in Bose-Einstein condensates: Analysis of a dynamical quantum phase transition

Bruno Juliá-Díaz, Daniel Dagnino, Maciej Lewenstein +2 more

We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.

arXiv:0912.1239•Physical Review A•Feb 18, 2010•86 citations
We consider Bose-Einstein condensates (BECs) in situations where the density undergoes a symmetry breaking, either in real space or in momentum space. This occurs for a suitable number of condensed atoms in a double well potential, obtained in real space for a BEC of lithium atoms by adding a standing wave light field to the trap potential, or in momentum space for rubidium atoms by Raman coupling two BECs in different magnetic states with two tilted light fields. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation is in fact a Schrödinger cat (SC) and we evaluate the macroscopic quantum coherence between the two SC states.
We consider a Bose-Einstein condensate of 7Li{}^{7}\mathrm{Li}7Li in a situation where the density undergoes a symmetry breaking in real space. This occurs for a suitable number of condensed atoms in a double-well potential, obtained by adding a standing-wave light field to the trap potential. Evidence of bistability results from the solution of the Gross-Pitaevskii equation. By second quantization, we show that the classical bistable situation leads, in fact, to a macroscopic quantum superposition or Schr\"odinger cat (SC) and evaluate the tunneling rate between the two SC states. The oscillation between the two states is called macroscopic quantum coherence (MQC); we study the effects of losses on MQC.
We consider a Bose-Einstein bicondensate of 87Rb,{}^{87}\mathrm{Rb},87Rb, trapped in two different internal levels, in a situation where the density undergoes a symmetry breaking in momentum space. This occurs for a suitable number of condensed atoms within a double-well dispersion curve, obtained by Raman coupling two internal states with two tilted and detuned light fields. Evidence of bistability results from the Gross-Pitaevskii equation. By second quantization, we evaluate the tunneling rate between the two asymmetric states; the effects of losses on coherence are negligible.
We apply the concepts of nonlinear guided-wave optics to a Bose-Einstein condensate (BEC) trapped in an external potential. As an example, we consider a parabolic double-well potential and derive coupled-mode equations for the complex amplitudes of the BEC macroscopic collective modes. Our equations describe different regimes of the condensate dynamics, including the nonlinear Josephson effect for any separation between the wells. We demonstrate macroscopic self-trapping for both repulsive and attractive interactions, and confirm our results by direct numerical solution of the Gross-Pitaevskii-equation.
Dynamics of the repulsive Bose–Einstein condensate (BEC) in a double-well trap is explored within the 3D time-dependent Gross–Pitaevskii equation. The model avoids numerous common approximations (two-mode treatment, time-space factorization, fixed values of the chemical potential and barrier penetrability, etc) and thus may provide a realistic description of BEC dynamics, including both weak-coupling (sub-barrier) and strong-coupling (above-barrier) regimes and their crossover. The strong coupling regime is achieved by increasing the number N of BEC atoms and thus the chemical potential. The evolution with N of Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) is examined and the crucial impact of the BEC interaction is demonstrated. At weak coupling, the calculations well reproduce the JO/MQST experimental data. At strong coupling with a significant overlap of the left and right BECs, we observe a remarkable persistence of the Josephson-like dynamics: the JO and MQST converge to a high-frequency JO-like mode where both population imbalance and phase difference oscillate around the zero averages.
We show theoretically the existence of a metastable state and the possibility of decay to the ground state through macroscopic quantum tunneling in two-component Bose-Einstein condensates with repulsive interactions. Numerical analysis of the coupled Gross-Pitaevskii equations clarifies the metastable states whose configuration preserves or breaks the symmetry of the trapping potential, depending on the interspecies interaction and the particle number. We calculate the tunneling decay rate of the metastable state by using the collective coordinate method under the WKB approximation. Then the height of the energy barrier is estimated by the saddle point solution. It is found that macroscopic quantum tunneling is observable in a wide range of particle numbers. Macroscopic quantum coherence between two distinct states is discussed; this might give an additional coherent property of two-component Bose condensed systems. Thermal effects on the decay rate are estimated.
We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.