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Acta Physica Sinica

One-dimensional tunneling dynamics between two-component Bose-Einstein condensates

Li Gao-Qing, Chen Hai-Jun, Xue Ju-Kui, (1)陇东学院物理与电子工程学院，庆阳 745000; (2)西北师范大学物理与电子工程学院，兰州 730070

Published Jan 1, 2010• 5 citations
Publisher

Abstract

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.

DOI
10.7498/aps.59.1449

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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.
In this paper, we study the interaction-modulated tunneling dynamics of a Bose-Fermi superfluid mixture, where a Bose-Einstein condensate (BEC) with weak repulsive interaction is confined in a symmetric deep double-well potential and an equally populated two-component Fermi gas in a harmonic potential symmetrically is positioned in the center of the double-well potential. The tunneling between the two wells is modulated by fermions trapped in a harmonic potential. When the temperature is adequately low and the bosonic particle number is adequately large, we can employ the mean-field theory to describe the evolution of the BEC in the double-well potential through the time-dependent Gross-Pitaevskii equation. For the Fermi gas in the harmonic potential trap, we consider the case where the inter-fermion interaction is tuned on the deep Bose-Einstein condensate of the inter-fermion Feshbach resonance, where two fermions of spin-up and spin-down form a two-body bound state. Within the regime, the Fermi gas is well described by a condensate of these fermionic dimers, and hence can be simulated as well by a Gross-Pitaevskii equation of dimers. The inter-species interactions couple the dynamics of the two species, which results in interesting features in the tunneling oscillations. The dynamic equations of the BEC in the double-well potential is described by a two-mode approximation. Coupling it with time-dependent Gross-Pitaevskii equation of the harmonically potential trapped molecular BEC, we numerically investigate the dynamical evolution of the Boson-Fermi hybrid system under different initial conditions. It is found that the interaction among fermions in a harmonic potential leads to strong non-linearity in the oscillations of the bosons in the double-well potential and enriches the tunneling dynamics of the bosons. Especially, it strengthens macroscopic quantum self-trapping. And the macroscopic quantum self-trapping can be expressed in three forms: the phase tends to be negative and monotonically decreases with time, the phase evolves with time, and the phase tends to be positive and increases monotonically with time. This means that it is possible the tunneling dynamics of the BEC in double-well potential is adjustable. Our results can be verified experimentally in a Bose-Fermi superfluid mixture by varying different interaction parameters via Feshbach resonance and confinement-induced resonance.
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.
Abstract We investigate the dynamical phase transition of two-component Bose–Einstein condensate with nonlinear tunneling, which is trapped inside a double-well and dispersively coupled to a single mode of a high-finesse optical cavity with one moving end mirror driven by a single mode standing field. In the mean-field approximation, the Hamiltonian of the system with nonlinear tunneling is characterized by the population difference of the particles and relative phase in double wells. The characteristics of the system’s stability points are determined by the corresponding Hessian matrices. However, the number of the system’s stability points depends on the roots of the first derivative of the energy. In the absence of the nonlinearity, the Hamiltonian of the system is a binary quadratic equation. When there is nonlinear tunneling, the Hamiltonian of the system is a binary quartic equation. Therefore, from a mathematical point of view, it can be found that the roots of the equation will increase, which means that the number of stability points in the system will increase. We also build the phase portrait from classical analysis. Considering the strong pair tunneling case, we confirm that nonlinear tunneling interaction leads to an increment of stability points and enriches the phase diagram of the system. We further analyze the phase portrait with the moving end mirror. It is shown that the semiclassical dynamics of the system undergoes a bifurcation of stability points with an increase in the coupling strength or detuning. In other words, the system experiences a phase transition.
We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.
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.