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/9706221 · Physical Review Letters

Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates

Augusto Smerzi, Stefano Fantoni, S. Giovanazzi, Subodh R. Shenoy

Published Dec 22, 1997• 1,293 citations
arXivHTMLPDF

Abstract

We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.

DOI
10.1103/physrevlett.79.4950

Related papers

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

BOSON JOSEPHSON JUNCTION WITH TRAPPED ATOMS

S. Raghavan, Augusto Smerzi, Stefano Fantoni +1 more

We consider coherent atomic tunneling between two weakly coupled Bose-Einstein condensates at T =0 in a double-well trap. The condensate dynamics of the macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevskii equations (GPE) coupled by a tunneling matrix element. Analytic elliptic function solutions are obtained for the time evolution of the inter-well fractional population imbalance z(t) (related to the condensate phase difference) of the Boson Josephson junction (BJJ). Surprisingly, the neutral-atom BJJ shows (non-sinusoidal generalizations of) effects seen in charged-electron superconductor Josephson junctions (SJJ). The BJJ elliptic-function behavior has a singular dependence on a GPE parameter ratio Λ at a critical ratio Λ=Λc, beyond which a novel 'macroscopic quantum self-trapping' effect sets in with a non-zero time-averaged imbalance <z>≠0.

International Journal of Modern Physics B•Mar 10, 1999•0 citations

Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping

S. Raghavan, Augusto Smerzi, Stefano Fantoni +1 more

We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\ensuremath{\pi} (\ensuremath{\pi}$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^{3}\mathrm{He}\ensuremath{-}B$ and the internal Josephson effect in ${}^{3}\mathrm{He}\ensuremath{-}A$ are also discussed.

Physical Review A•Jan 1, 1999•969 citations

Coherent oscillations between two weakly coupled Bose-Einstein Condensates: Josephson effects, $π$-oscillations, and macroscopic quantum self trapping

S. Raghavan, Augusto Smerzi, Stefano Fantoni +1 more

We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The Boson Josephson Junction (BJJ) dynamics is described by the two-mode non-linear Gross-Pitaevskii equation, that is solved analytically in terms of elliptic functions. The BJJ, being a $neutral$, isolated system, allows the investigations of new dynamical regimes for the phase difference across the junction and for the population imbalance, that are not accessible with Superconductor Josephson Junctions (SJJ). These include oscillations with either, or both of the following properties: 1) the time-averaged value of the phase is equal to $π$ ($π-phase$ oscillations); 2) the average population imbalance is nonzero, in states with ``macroscopic quantum self-trapping'' (MQST). The (non-sinusoidal) generalization of the SJJ `ac' and `plasma' oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and total number of condensate atoms) onto a single universal curve, for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of $^3$He-B and the internal Josephson effect in $^3$He-A are also discussed.

arXiv:cond-mat/9706220•Jun 23, 1997•2 citations

Laser-assisted coherent atomic tunneling between two trapped Bose-Einstein condensates

Noriaki Tsukada, Mitsunobu Gotoda, Y. Nomura +1 more

We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the $n\mathrm{th}$ LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.

Physical Review A•May 1, 1999•32 citations

Macroscopic quantum self-trapping and atomic tunneling in two-species Bose-Einstein condensates

Le‐Man Kuang, Zhongwen Ouyang

We present a theoretical treatment of macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunneling in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is shown that the nonlinear interactions can dramatically affect the MQST and the atomic tunneling, and lead to the collapses and revivals (CR) of the population imbalance between the two condensates. The competing effects between the self-interaction of each species and the interspecies interaction can lead to a quenching of the MQST and a suppression of the CR and the Shapiro-like steps of the atomic tunneling current. It is revealed that interatomic nonlinear interactions can induce coherent atomic tunneling between two condensates even though interspecies Josephson-like tunneling coupling does not exist.

arXiv:cond-mat/0003490•Physical Review A•Jan 11, 2000•91 citations
We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.
We consider coherent atomic tunneling between two weakly coupled Bose-Einstein condensates at T =0 in a double-well trap. The condensate dynamics of the macroscopic amplitudes in the two wells is modeled by two Gross-Pitaevskii equations (GPE) coupled by a tunneling matrix element. Analytic elliptic function solutions are obtained for the time evolution of the inter-well fractional population imbalance z(t) (related to the condensate phase difference) of the Boson Josephson junction (BJJ). Surprisingly, the neutral-atom BJJ shows (non-sinusoidal generalizations of) effects seen in charged-electron superconductor Josephson junctions (SJJ). The BJJ elliptic-function behavior has a singular dependence on a GPE parameter ratio Λ at a critical ratio Λ=Λc, beyond which a novel 'macroscopic quantum self-trapping' effect sets in with a non-zero time-averaged imbalance <z>≠0.
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to $\ensuremath{\pi} (\ensuremath{\pi}$-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of ${}^{3}\mathrm{He}\ensuremath{-}B$ and the internal Josephson effect in ${}^{3}\mathrm{He}\ensuremath{-}A$ are also discussed.
Coherent oscillations between two weakly coupled Bose-Einstein Condensates: Josephson effects, πππ-oscillations, and macroscopic quantum self trapping
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The Boson Josephson Junction (BJJ) dynamics is described by the two-mode non-linear Gross-Pitaevskii equation, that is solved analytically in terms of elliptic functions. The BJJ, being a neutralneutralneutral, isolated system, allows the investigations of new dynamical regimes for the phase difference across the junction and for the population imbalance, that are not accessible with Superconductor Josephson Junctions (SJJ). These include oscillations with either, or both of the following properties: 1) the time-averaged value of the phase is equal to πππ (π−phaseπ-phaseπ−phase oscillations); 2) the average population imbalance is nonzero, in states with ``macroscopic quantum self-trapping'' (MQST). The (non-sinusoidal) generalization of the SJJ `ac' and `plasma' oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and total number of condensate atoms) onto a single universal curve, for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3^33He-B and the internal Josephson effect in 3^33He-A are also discussed.
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
We present a theoretical treatment of macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunneling in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is shown that the nonlinear interactions can dramatically affect the MQST and the atomic tunneling, and lead to the collapses and revivals (CR) of the population imbalance between the two condensates. The competing effects between the self-interaction of each species and the interspecies interaction can lead to a quenching of the MQST and a suppression of the CR and the Shapiro-like steps of the atomic tunneling current. It is revealed that interatomic nonlinear interactions can induce coherent atomic tunneling between two condensates even though interspecies Josephson-like tunneling coupling does not exist.