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Register a new userThe dynamics of a strongly driven two component Bose-Einstein Condensate
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Grant Leonard Salmond
Publication date
2001
fields
Physics
and research's language is
English
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We consider a two component Bose-Einstein condensate in two spatially localized modes of a double well potential, with periodic modulation of the tunnel coupling between the two modes. We treat the driven quantum field using a two mode expansion and define the quantum dynamics in terms of the Floquet Operator for the time periodic Hamiltonian of the system. It has been shown that the corresponding semiclassical mean-field dynamics can exhibit regions of regular and chaotic motion. We show here that the quantum dynamics can exhibit dynamical tunneling between regions of regular motion, centered on fixed points (resonances) of the semiclassical dynamics.
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We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark and dark-dark solitons with our analytical prediction and with that of Painleve-analysis of the dynamical equation. We demonstrate that tuning the inter-species scattering length away from the predicted value (keeping the intra-species coupling fixed) breaks the stability of the soliton pairs.
The method of geometrization arises as an important tool in understanding the entanglement of quantum fields and the behavior of the many-body system. The symplectic structure of the boson operators provide a natural way to geometrize the quantum dynamics of the bosonic systems of quadratic Hamiltonians, by recognizing that the time evolution operator corresponds to a real symplectic matrix in $Sp(4,R)$ group. We apply this geometrization scheme to study the quantum dynamics of the spinor Bose-Einstein condensate systems, demonstrating that the quantum dynamics of this system can be represented by trajectories in a six dimensional manifold. It is found that the trajectory is quasi-periodic for coupled bosons. The expectation value of the observables can also be naturally calculated through this approach.
This paper deals with the study of the phase transition of the wave functions of a segregated two-component Bose-Einstein condensate under Rabi coupling. This yields a system of two coupled ODEs where the Rabi coupling is linear in the other wave function and acts against segregation. We prove estimates on the asymptotic behaviour of the wave functions, as the strength of the interaction gets strong or weak. We also derive limiting problems in both cases.
We point out that the widely accepted condition g11g22<g122 for phase separation of a two-component Bose-Einstein condensate is insufficient if kinetic energy is taken into account, which competes against the intercomponent interaction and favors phase mixing. Here g11, g22, and g12 are the intra- and intercomponent interaction strengths, respectively. Taking a d-dimensional infinitely deep square well potential of width L as an example, a simple scaling analysis shows that if d=1 (d=3), phase separation will be suppressed as Lrightarrow0 (Lrightarrowinfty) whether the condition g11g22<g122 is satisfied or not. In the intermediate case of d=2, the width L is irrelevant but again phase separation can be partially or even completely suppressed even if g11g22<g122. Moreover, the miscibility-immiscibility transition is turned from a first-order one into a second-order one by the kinetic energy. All these results carry over to d-dimensional harmonic potentials, where the harmonic oscillator length {xi}ho plays the role of L. Our finding provides a scenario of controlling the miscibility-immiscibility transition of a two-component condensate by changing the confinement, instead of the conventional approach of changing the values of the gs.
We study Bragg spectroscopy of a strongly interacting Bose-Einstein condensate using time-dependent Hartree-Fock-Bogoliubov theory. We include approximatively the effect of the momentum dependent scattering amplitude which is shown to be the dominant factor in determining the spectrum for large momentum Bragg scattering. The condensation of the Bragg scattered atoms is shown to significantly alter the observed excitation spectrum by creating a novel pairing channel of mobile pairs.
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