Atomic Josephson junction with two bosonic species

Abstract

Abstract. We study an atomic Josephson junction (AJJ) in presence of two interacting Bose-Einstein condensates (BECs) confined in a double well trap. We assume that bosons of different species interact with each other. The macroscopic wave functions of the two components obey to a system of two 3D coupled GrossPitaevskii equations (GPE). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODE), for which the coupled pendula represent the mechanic analogous. These differential equations control the dynamical behavior of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and non zero -the macroscopic quantum self-trapping (MQST) -time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPE and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signs the onset of MQST.

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

“…The functions φ α k (x) (α = L,R) which we consider as real functions as was done for example in [29][30][31], are singleparticle wave functions tightly localized in the αth well, while the time dependence is encoded in…”

“…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].…”

Splitting dynamics of a two-species Bose-Einstein condensate in two translating traps

“…The recent achievement of condensing two-species Bose atoms has spurred much interest in theoretical investigations of their stationary properties as well as dynamic properties [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The two species can refer to the same alkali in two different internal states, two isotopes, or two different alkali.…”