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Stability and dynamics of a two-component Bose-Einstein condensate in ring ladders

Eulàlia Nicolau Jiménez

Published Jul 19, 2018• 0 citations
OpenAlex

Abstract

We investigate the dynamics of a two-component Bose-Einstein condensate trapped in two coupled rings in ladder configuration. First, we derive from the two-component Gross-Pitaevskii equation a few state model for the angular momentum modes. Then, we analyse the stability of the stationary states by solving the Bogoliubov-de Gennes equations. Also, we study the dynamics of the system for an arbitrary population imbalance between the rings, characterizing the transition from Josephson oscillations to quantum self-trapping. We also derive the self-trapping condition for the bosonic mixture, finding simultaneous self-trapping of the two components.

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We investigate the dynamics of a two-component Bose-Einstein condensate trapped in two coupled rings in ladder configuration. First, we derive from the two-component Gross-Pitaevskii equation a few state model for the angular momentum modes. Then, we analyse the stability of the stationary states by solving the Bogoliubov-de Gennes equations. Also, we study the dynamics of the system for an arbitrary population imbalance between the rings, characterizing the transition from Josephson oscillations to quantum self-trapping. We also derive the self-trapping condition for the bosonic mixture, finding simultaneous self-trapping of the two components.
We investigate the stability and dynamics of the orbital angular momentum modes of a repulsive Bose-Einstein condensate trapped in two tunnel-coupled rings in a stack configuration. Within mean-field theory, we derive a two-state model for the system in the case in which we populate both rings equally with a single orbital angular momentum mode and include small perturbations in other modes. Analyzing the fixed-point solutions of the model and the associated classical Hamiltonian, we characterize the destabilization of the stationary states and the subsequent dynamics. By populating a single orbital angular momentum mode with an arbitrary population imbalance between the rings, we derive analytically the boundary between the regimes of Josephson oscillations and macroscopic quantum self-trapping and study numerically the stability of these solutions.
We investigate the dynamics of two-component Bose–Einstein condensates, composed of atoms in two distinct hyperfine states, which are linearly coupled by two-photon Raman transitions. The condensate is loaded into a double-well potential. A variety of dynamical behaviour, ranging from regular Josephson oscillations to mixed Rabi–Josephson oscillations and to regimes featuring increasing complexity are described in terms of a reduced Hamiltonian system with four degrees of freedoms, which are the numbers of atoms in each component in the left and right potential wells, whose canonically conjugate variables are phases of the corresponding wavefunctions. Using the system with four degrees of freedom, we study the dynamics of fractional imbalances of the two bosonic components and compare the results to direct simulations of the Gross–Pitaevskii equations describing the bosonic mixture. We perform this analysis when the fractional imbalance oscillates around a zero-time averaged value and in the self-trapping regime as well.
One-dimensional quantum tunneling dynamics between two-component Bose-Einstein condensates confined in a double-well magnetic trap is investigated. One-dimensional Gross-Pitaevskii equations for two-component Bose-Einstein condensates are derived from the three-dimensional ones. We derive Feynman equations from one-dimensional Gross-Pitaevskii equations. To study tunneling dynamics we solve Feynman equations in terms of a completely numerical procedure. In contrast to single-component condensates between two-component condensates, we find that this system can take on abundant tunneling results, the full tunneling dynamical behavior is summarized in phase portrait with constant energy lines. It is found that this system can achieve self-trapping when increase interatomic interactions exceed a critical value. We give the analytical critical expressions of interatomic interactions from the system Hamiltonian.
We consider an ultracold bosonic binary mixture confined in a quasi-one-dimensional double-well trap. The two bosonic components are assumed to be two hyperfine internal states of the same atom. We suppose that these two components are spin-orbit coupled to each other. We employ the two-mode approximation starting from two coupled Gross-Pitaevskii equations and derive a system of ordinary differential equations governing the temporal evolution of the interwell population imbalance of each component and of the polarization, which is the imbalance of the total populations of the two species. From this set of equations we disentangle the different macroscopic quantum tunneling and self-trapping scenarios occurring for both population imbalances and the polarization in terms of the interplay between the interatomic interactions and the other relevant energies in the problem, like the spin-orbit coupling or the conventional tunneling term. We find a rich dynamics in all three variables and discuss the experimental feasibility of such a system.
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