Binary mixture of Bose-Einstein condensates in a double-well potential: Berry phase and two-mode entanglement

Abstract

A binary mixtures of Bose-Einstein condensate (BEC) structures exhibit an incredible richness in terms of holding different kinds of phases. Depending on the ratio of the inter-and intra-atomic interactions, the transition from mixed to separated phase, which is also known as the miscibilityimmiscibility transition, has been reported in different setups and by different groups. Here, we describe such type of quantum phase transition (QPT) in an effective Hamiltonian approach, by applying Holstein-Primakoff transformation in the limit of large number of particles. We demonstrate that non-trivial geometric phase near the critical coupling is present, which confirms the connection between Berry phase and QPT. We also show that, by using the spin form of Hillery & Zubairy criterion, a two mode entanglement accompanies this transition in the limit of large, but not infinite number of particles. APPENDIXHere we show the derivations of Eqs. (29) and (30). By inserting displaced operators defined in Eq. (12) into the

Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential

“…Additionally, the adaptation of such optimal control methodologies to low-dimensional truncated Galerkin dynamics is a technique that could find significant potential for further applications. Some possibilities include multi-component and spinor condensates [18] where few-mode approximations have proven useful [11,40,42]. Moreover, extending such control strategies beyond the mean-field framework and into the realm of many-body effects [27,31], is of particular interest in its own right; for a review of the latter, see, e.g., the recent preprint of [29].…”

“…Some more mathematical examples include the analysis of the double-well bifurcation structure [3,14], the low-dimensional representation of the associated dynamical problem (and its fidelity) [23,26], and the effect of changing the nonlinear exponent on the bifurcation [22,35]. Among the many more physical examples are the interactions of multiple dispersive (e.g., atomic) species [11,40,42], incorporating beyond-mean-field (i.e., manybody) effects [27,31], and the effect of larger spatial dimension (and possibly four wells) [43], among others.…”

Ground-State Properties and Phase Separation of Binary Mixtures in Mesoscopic Ring Lattices

“…The critical condition for which the interplay of tunneling parameter, boson–boson interactions and boson numbers of the two components links demixing effect and spectral collapse has been analytically investigated in the double-well system [ 23 , 24 ] in the case of both repulsive and attractive components, while the role of inhomogeneity on demixing, due to the trapping effect, has been evidenced by using multiconfigurational time-dependent Hartree method [ 25 ]. Purely quantum indicators, such as entanglement and residual entropies [ 26 ], and a nontrivial geometric phase [ 27 ] have further confirmed the critical behavior distinguishing spatial separation, while the impact of a chaotic dynamical behavior on the robustness of spatial separation has been explored in both lattice structures [ 28 ] and in a harmonic trap [ 29 ].…”