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arXiv:1701.03762 · Laser Physics Letters

Statics and dynamics of a self-bound dipolar matter-wave droplet

S K Adhikari

Published Dec 23, 2016• 12 citations
arXivHTMLPDF

Abstract

Abstract We study the statics and dynamics of a stable, mobile, self-bound three-dimensional dipolar matter-wave droplet created in the presence of a tiny repulsive three-body interaction. In frontal collision with an impact parameter and in angular collision at large velocities along all directions two droplets behave like quantum solitons. Such a collision is found to be quasi elastic and the droplets emerge undeformed after collision without any change of velocity. However, in a collision at small velocities the axisymmeric dipolar interaction plays a significant role and the collision dynamics is sensitive to the direction of motion. For an encounter along the z direction at small velocities, two droplets, polarized along the z direction, coalesce to form a larger droplet—a droplet molecule. For an encounter along the x direction at small velocities, the same droplets stay apart and never meet each other due to the dipolar repulsion. The present study is based on an analytic variational approximation and a numerical solution of the mean-field Gross–Pitaevskii equation using the parameters of 52 Cr atoms.

DOI
10.1088/1612-202x/aa532e

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Abstract We study the statics and dynamics of a stable, mobile, self-bound three-dimensional dipolar matter-wave droplet created in the presence of a tiny repulsive three-body interaction. In frontal collision with an impact parameter and in angular collision at large velocities along all directions two droplets behave like quantum solitons. Such a collision is found to be quasi elastic and the droplets emerge undeformed after collision without any change of velocity. However, in a collision at small velocities the axisymmeric dipolar interaction plays a significant role and the collision dynamics is sensitive to the direction of motion. For an encounter along the z direction at small velocities, two droplets, polarized along the z direction, coalesce to form a larger droplet—a droplet molecule. For an encounter along the x direction at small velocities, the same droplets stay apart and never meet each other due to the dipolar repulsion. The present study is based on an analytic variational approximation and a numerical solution of the mean-field Gross–Pitaevskii equation using the parameters of 52 Cr atoms.
We study the statics and dynamics of a stable, mobile, three-dimensional matter-wave spherical quantum ball created in the presence of an attractive two-body and a very small repulsive three-body interaction. The quantum ball can propagate with a constant velocity in any direction in free space and its stability under a small perturbation is established numerically and variationally. In frontal head-on and angular collisions at large velocities two quantum balls behave like quantum solitons. Such collision is found to be quasielastic and the quantum balls emerge after collision without any change of direction of motion and velocity and with practically no deformation in shape. When reflected by a hard impenetrable plane, the quantum ball bounces off like a wave obeying the law of reflection without any change of shape or speed. However, in a collision at small velocities two quantum balls coalesce to form a larger ball which we call a quantum-ball breather. We point out the similarity and difference between the collision of two quantum and classical balls. The present study is based on an analytic variational approximation and a full numerical solution of the mean-field Gross-Pitaevskii equation using the parameters of 7Li^{7}\mathrm{Li}7Li atoms.
We study self-bound quantum droplets in the regime dominated by microwave-induced non-axisymmetric dipole−dipole interactions, using the extended Gross−Pitaevskii equation with the Lee−Huang−Yang corrections. We identify the existence region through numerical simulations and employ an anisotropic Gaussian−super-Gaussian variational ansätz to capture the characteristic density profile of the droplets, with a Gaussian profile along the narrow x direction and super-Gaussian profiles in the extended (y, z) plane. Within this variational framework, we characterize the self-binding, spatial localization, and density-compression properties of the droplets and find good agreement between the variational predictions and the numerical results. Collisions between droplets moving along different directions reveal a strong directional dependence, with outcomes ranging from quasi-elastic rebound and merger to fragmentation. In addition, we explore the rotational dynamics of a single self-bound droplet about all three Cartesian axes, revealing rich and controllable three-dimensional rotational dynamics. Together, these results demonstrate how non-axisymmetric dipolar interactions provide versatile means for controlling the translational, collisional, and rotational dynamics of self-bound quantum droplets.
We study the formation and dynamics of bright solitons in a quasi-one-dimensional reduced mean-field Gross-Pitaevskii equation of a dipolar Bose-Einstein condensate with repulsive short-range interactions. The study is carried out using a variational approximation and a numerical solution. Plots of chemical potential and root mean square (rms) size of solitons are obtained for the quasi-one-dimensional model of three different dipolar condensates of 52Cr, 168Er and 164Dy atoms. The results achieved are in good agreement with those produced by the full three-dimensional mean-field model of the condensate. We also study the dynamics of the collision of a train of two solitons in the quasi-one-dimensional model of every condensate above. At small velocities (zero or close to zero) the dynamics is attractive for a phase difference δ = 0, the solitons coalesce and these oscillate forming a bound soliton molecule. For a phase difference δ = π the effect is repulsive. At large velocities the collision is independent of the initial phase difference δ. This is quasi-elastic and the result is two quasi-solitons.
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We study the stability, form, and interaction of single and multiple dark solitons in quasi-one-dimensional dipolar Bose-Einstein condensates. The solitons are found numerically as stationary solutions in the moving frame of a nonlocal Gross Pitaevskii equation and characterized as a function of the key experimental parameters, namely the ratio of the dipolar atomic interactions to the van der Waals interactions, the polarization angle, and the condensate width. The solutions and their integrals of motion are strongly affected by the phonon and roton instabilities of the system. Dipolar matter-wave dark solitons propagate without dispersion and collide elastically away from these instabilities, with the dipolar interactions contributing an additional repulsion or attraction to the soliton-soliton interaction. However, close to the instabilities, the collisions are weakly dissipative.
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