Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi></mml:math>oscillations, and macroscopic quantum self-trapping

TLDR

The boson Josephson junction, a neutral isolated system, enables exploration of dynamical regimes of phase difference and population imbalance inaccessible to superconducting junctions, and analogies with 3He‑B and 3He‑A Josephson effects are also discussed. The study discusses coherent atomic oscillations between two weakly coupled Bose‑Einstein condensates. The weak link is realized by a laser barrier in a (possibly asymmetric) double‑well trap or Raman coupling between hyperfine levels, and the dynamics are described by the two‑mode nonlinear Gross‑Pitaevskii equation solved analytically with elliptic functions. The authors find π‑phase oscillations, macroscopic quantum self‑trapping with nonzero average imbalance, generalized ac and plasma oscillations and Shapiro resonances, and predict that experimental data collapse onto a universal curve for the inverse oscillation period.

Abstract

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.