Weakly linked binary mixtures ofF= 1⁸⁷Rb Bose–Einstein condensates

Abstract

We present a study of binary mixtures of Bose-Einstein condensates confined in a double-well potential within the framework of the mean field Gross-Pitaevskii equation. We reexamine both the single component and the binary mixture cases for such a potential, and we investigate in which situations a simpler two-mode approach leads to an accurate description of their dynamics. We also estimate the validity of the most usual dimensionality reductions used to solve the Gross-Pitaevskii equations. To this end, we compare both the semi-analytical two-mode approaches and the numerical simulations of the 1D reductions with the full 3D numerical solutions of the Gross-Pitaevskii equation. Our analysis provides a guide to clarify the validity of several simplified models that describe mean field non-linear dynamics, using an experimentally feasible binary mixture of an F = 1 spinor condensate with two of its Zeeman manifolds populated, m = ±1.

Dissipation effect in the double-well Bose-Einstein condensate

“…The TDGP equation provides a very good description of dynamical evolution of trapped dilute Bose gases at temperature far below the critical temperature [22,23]. The two-mode approximation for the BJJ is an extremely simplified version of the TDGP equation.…”

Josephson physics of spin-orbit-coupled elongated Bose-Einstein condensates

“…Notice that if S ± , , andδ vanish, these equations give back those of the two-component two-well problem discussed in Ref. [32]. According to its definition, Eq.…”

“…Let us note, however, that the effect of the repulsion between species has been discussed thoroughly in Refs. [25][26][27][28][29][30][31][32]47], where it was found that the conventional Josephson dynamics is crucially modified by this term, even leading to measure synchronization in some limits [48]. In particular, the interspecies interaction induces the presence of additional fixed points in the problem which are related to the repulsion between components.…”

“…that U 1 ≈ U 2 ≈ U 12 [32]. The interspecies interactions have profound and diverse effects on the Josephson dynamics of two components in double wells [25][26][27][28][29][30][31][32]47,50], and therefore an extensive discussion on this topic is out of the scope of this paper. If the interspecies interaction U 12 is similar to the intraspecies ones (U 1 and U 2 ), and for the case considered here of a polarized initial state, the dynamics of the less populated species is crucially influenced by the dynamics of the more populated one [28].…”

“…This framework represents the ideal arena to analyze the atomic counterpart of the Josephson effect which occurs in superconductoroxide-superconductor junctions [24] with bosonic binary mixtures [25][26][27][28][29][30][31][32]. It is worth noting that Josephson physics with bosonic mixtures seems within reach for a number of experimental groups which have in recent years studied single-component Josephson physics [33][34][35][36][37][38][39][40].…”