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Nanosecond dynamics of solitons in confined Bose-Einstein condensates

Vinitha Johny, Siddharth Ghosh

Published Jan 30, 2023• 0 citations
Publisher

Abstract

Nanoscale anisotropic dynamical systems are tedious to solve in a classical domain without any approximation techniques. In such cases, the interactive space and force are significant in defining their motions. We solve and simulate the phase transition motion of water in the interface of 3 μm × 3 μm confined water domain. We demonstrate the presence of solitons in Bose-Einstein condensate at a nanosecond time scale by solving a nonlinear partial differential equation. We find an exact solution of the 2D Gross-Pitaevskii equation with XY-model using the Heisenberg picture which creates solitons and condensate nucleation.

DOI
10.26434/chemrxiv-2023-8k3sq

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Nanoscale anisotropic dynamical systems are tedious to solve in a classical domain without any approximation techniques. In such cases, the interactive space and force are significant in defining their motions. We solve and simulate the phase transition motion of water in the interface of 3 μm × 3 μm confined water domain. We demonstrate the presence of solitons in Bose-Einstein condensate at a nanosecond time scale by solving a nonlinear partial differential equation. We find an exact solution of the 2D Gross-Pitaevskii equation with XY-model using the Heisenberg picture which creates solitons and condensate nucleation.
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Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.
We model the three-dimensional (3D) trapped Bose-Einstein condensate with the Gross-Pitaevskii equation (GPE) incorporating higher-order nonlinear interaction effects. Based on the F-expansion method and self-similar approach, we analytically derive the exact soliton solutions of the 3D GPE, identifying the oscillatory mode under certain experimental settings. The oscillatory kinetic parameter values we obtained coincide very well with those reported in previous work, which is based on the variational approach, showing the applicability of the theoretical treatment presented in this work.
A Bose-Einstein Condensate (BEC) made of alkali-metal atoms at ultra-low temperatures is well described by the three-dimensional cubic nonlinear Schrödinger equation, the so-called Gross-Pitaevskii equation (GPE). Here we consider an attractive BEC in a ring and by solving the GPE we predict the existence of bright solitons with single and multi-peaks, showing that they have a limited domain of dynamical stability. We also discuss finite-temperature effects on the transition from the uniform phase to the localized phase.
Solitons are striking manifestations of nonlinearity, encountered in diverse physical systems such as water waves, nonlinear optics, and Bose-Einstein condensates (BECs). In BECs, dark solitons emerge as exact stationary solutions of the one-dimensional Gross-Pitaevskii equation. While they can be long-lived in elongated traps, their stability is compromised in higher dimensions due to the snake instability, which leads to the decay of the soliton into vortex structures among other excitations. We investigate the dynamics of a dark soliton in a Bose-Einstein condensate confined in an anisotropic harmonic trap. Using a variational ansatz that incorporates both the transverse bending of the soliton plane and the emergence of vortices along the nodal line, we derive equations of motion governing the soliton's evolution. This approach allows us to identify stable oscillation modes as well as the growth rates of the unstable perturbations. In particular, we determine the critical trap anisotropy required to suppress the snake instability. Our analytical predictions are in good agreement with full numerical simulations of the Gross-Pitaevskii equation.