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Register a new userAn $Sp(4, R)$ geometrization on the quantum dynamics of two-component Bose-Einstein condensate
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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.
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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.
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.
We theoretically show that the topology of a non-simply-connected annular atomic Bose-Einstein condensate enforces the inner surface waves to be always excited with outer surface excitations and that the inner surface modes are associated with induced vortex dipoles unlike the surface waves of a simply-connected one with vortex monopoles. Consequently, under stirring to drive an inner surface wave, a peculiar population oscillation between the inner and outer surface is generated regardless of annulus thickness. Moreover, a new vortex nucleation process by stirring is observed that can merge the inner vortex dipoles and outer vortex into a single vortex inside the annulus. The energy spectrum for a rotating annular condensate with a vortex at the center also reveals the distinct connection of the Tkachenko modes of a vortex lattice to its inner surface excitations.
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.
The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterised by a `miscibility parameter, based on the ratio of intra- to inter-species interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.
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