Internal Josephson Effects in Spinor Dipolar Bose--Einstein Condensates

TL;DR

This paper theoretically investigates the internal Josephson effect in spin-1 Bose--Einstein condensates, revealing novel spin dynamics and phase modes driven by spin exchange and dipole-dipole interactions.

Contribution

It introduces a theoretical framework with single spatial mode approximation to derive Josephson equations and identifies unique oscillational modes in spinor dipolar Bose--Einstein condensates.

Findings

Identification of multiple novel Josephson phase modes

Derivation of Josephson equations analogous to superconducting tunneling

Prediction of these modes in real atomic Bose gas systems

Abstract

We theoretically study the internal Josephson effect, which is driven by spin exchange interactions and magnetic dipole-dipole interactions, in a three-level system for spin-1 Bose--Einstein condensates, obtaining novel spin dynamics. We introduce single spatial mode approximations into the Gross--Pitaevskii equations and derive the Josephson type equations, which are analogous to tunneling currents through three junctions between three superconductors. From an analogy with two interacting nonrigid pendulums, we identify unique varied oscillational modes, called the 0--$\pi$, 0--$running$, $running$--$running$, $2n\pi & running$--$2\pi$, $single nonrigid pendulum$, and $two rigid pendulums$ phase modes. These Josephson modes in the three states are expected to be found in real atomic Bose gas systems.