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

TL;DR

This paper analyzes the dynamics of two weakly coupled Bose-Einstein condensates, revealing novel oscillation regimes like $ ext{pi}$-oscillations and self-trapping, using an analytical approach to the nonlinear Gross-Pitaevskii equation.

Contribution

It provides an analytical solution for BEC Josephson junctions, exploring new dynamical regimes not seen in superconducting Josephson junctions.

Findings

Identification of $ ext{pi}$-phase oscillations.

Observation of macroscopic quantum self-trapping.

Universal scaling law for oscillation periods.

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 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 $\pi$ ($\pi-phase$ 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.