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Register a new userEffect of scattering lengths on the dynamics of a two-component Bose-Einstein condensate
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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.
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We use collective oscillations of a two-component Bose-Einstein condensate (2CBEC) of Rb atoms prepared in the internal states $ket{1}equivket{F=1, m_F=-1}$ and $ket{2}equivket{F=2, m_F=1}$ for the precision measurement of the interspecies scattering length $a_{12}$ with a relative uncertainty of $1.6times 10^{-4}$. We show that in a cigar-shaped trap the three-dimensional (3D) dynamics of a component with a small relative population can be conveniently described by a one-dimensional (1D) Schr{o}dinger equation for an effective harmonic oscillator. The frequency of the collective oscillations is defined by the axial trap frequency and the ratio $a_{12}/a_{11}$, where $a_{11}$ is the intra-species scattering length of a highly populated component 1, and is largely decoupled from the scattering length $a_{22}$, the total atom number and loss terms. By fitting numerical simulations of the coupled Gross-Pitaevskii equations to the recorded temporal evolution of the axial width we obtain the value $a_{12}=98.006(16),a_0$, where $a_0$ is the Bohr radius. Our reported value is in a reasonable agreement with the theoretical prediction $a_{12}=98.13(10),a_0$ but deviates significantly from the previously measured value $a_{12}=97.66,a_0$ cite{Mertes07} which is commonly used in the characterisation of spin dynamics in degenerate Rb atoms. Using Ramsey interferometry of the 2CBEC we measure the scattering length $a_{22}=95.44(7),a_0$ which also deviates from the previously reported value $a_{22}=95.0,a_0$ cite{Mertes07}. We characterise two-body losses for the component 2 and obtain the loss coefficients ${gamma_{12}=1.51(18)times10^{-14} textrm{cm}^3/textrm{s}}$ and ${gamma_{22}=8.1(3)times10^{-14} textrm{cm}^3/textrm{s}}$.
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.
We study the collapse of an attractive atomic Bose-Einstein condensate prepared in the uniform potential of an optical-box trap. We characterise the critical point for collapse and the collapse dynamics, observing universal behaviour in agreement with theoretical expectations. Most importantly, we observe a clear experimental signature of the counterintuitive weak collapse, namely that making the system more unstable can result in a smaller particle loss. We experimentally determine the scaling laws that govern the weak-collapse atom loss, providing a benchmark for the general theories of nonlinear wave phenomena.
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 propose a scheme to control quantum coherence of a two-component Bose-Einstein condensate (BEC) by a single impurity atom immersed in the BEC. We show that the single impurity atom can act as a single atom valve (SAV) to control quantum coherence of the two-component BEC. It is demonstrated that the SAV can realize the on-demand control over quantum coherence at an arbitrary time. Specially, it is found that the SAV can also control higher-order quantum coherence of two-component BEC. We investigate the long-time evolution of quantum coherence of the two-component BEC. It is indicated that the single impurity atom can induce collapse and revival phenomenon of quantum coherence of the two-component BEC. Collapse-revival configurations of quantum coherence can be manipulated by the initial-state parameters of the impurity atom and the impurity-BEC interaction strengths.
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