Creating solitons with controllable and near-zero velocity in Bose-Einstein condensates

Dark soliton detection using persistent homology

“…The goal is to distinguish significant dark solitoninduced density depletions from local minima caused by density fluctuations of the condensate and imaging noise. If the number of solitons and their orientation is known in advance, a simple and effective way to identify their positions is by performing least squares fitting of the dips to Gaussian functions [33]. We desire a method which does not require manual identification of the number of solitons and knowledge of their orientation.…”

Deflation-based identification of nonlinear excitations of the three-dimensional Gross-Pitaevskii equation

“…Despite their complexity, such states may only be weakly unstable (thus potentially tractable experimentally) and feature long-time dynamics consisting of splittings and recombinations towards the original state. Recent experimental advances have enabled the formulation (painting) of arbitrary potentials [34], the establishment of arbitrary density [35] or imposition of controlled phase [36][37][38] patterns, and even the realization of unstable (but sufficiently long-lived) complex topological states such as vortex knots [39]. In light of all these developments and their impact on vortex ring and line dynamics [40][41][42], we expect that the states identified in this work to be within reach of current state-of-the-art experimental efforts.…”

Localized waves and mixed interaction solutions with dynamical analysis to the Gross–Pitaevskii equation in the Bose–Einstein condensate

“…As a new state of matter and a field in physics, the surge of interest in Bose-Einstein condensate (BEC) has been prompted in recent years by researchers [1][2][3][4][5][6][7]. The mean-field Gross-Pitaevskii equation (GPE) is used to describe and understand some nonlinear phenomena, interesting and important properties and characteristics of vortex states [8][9][10][11][12] and localized waves including soliton [13][14][15][16], rogue wave (RW) [17][18][19], breather [20,21] in BEC, which is also one of the main theoretical research methods, and some predictions have been exposed to agree with relevant vortex and localized wave experiments [22][23][24]. The GPE is similar to the famous nonlinear Schrödinger equation (NLSE), the former is a special variant of the latter, and the latter is widely related to applications in many fields such as optics, quantum mechanics, quantum field theory, biophysics, fluid dynamics, plasma physics and so on.…”

“…Therefore, creating nonlinear localized waves in these fields has motivated intense attention and interest in their properties and abundant structures [39][40][41][42][43]. In recent years, localized waves in BEC have also attracted the attention of researchers [13][14][15][16][17][18][19][20][21]. The exact localized wave solutions and time evolution of them in BECs are described by the GPE with abundant different external potentials.…”