The Two-Mode Approximation in a Realistic Bose-Josephson Junction in a $^{85}$Rb/$^{87}$Rb BEC Mixture*

We have studied the behavior of an experimentally realistic Bose- Einstein condensate (BEC) mixture subjected to a double-well potential. The mixture studied consists of $^{87}$Rb and $^{85} $Rb held in an optical trap with an external magnetic field that enables tuning of the $^{85}$Rb--$^{85}$Rb scattering length. This system, without the external double--well potential, has been implemented at JILA [S.B.\ Papp, et al, Phys.Rev.Lett.\ {\bf 101}, 040402 (2008)]. A double--well potential can be added to this system by applying another pair of lasers as was done in a previous experiment for single condensates [M.\ Albiez, et al, Phys.\ Rev.\ Lett.\ {\bf 95}, 010402 (2005)]. We have used the Variable Tunneling Model (VTM) within the two--mode approximation to search for novel condensate mixture behavior in this experimentally accessible system. Possible behaviors include Bose--Josephson oscillations and macroscopic quantum self--trapping as described in a recent paper [I.\ Satija, et al, arXiv:0811.1921v1 [quant-ph]]. We compare the behavior as predicted by the two--mode VTM with the solution obtained by integrating the coupled Gross--Pitaevskii equations. We propose some new experiments designed to observe these novel phenomena.