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arXiv:2305.12697 · The European Physical Journal Plus

Dynamics of bright soliton under cubic-quartic interactions in quasi-one-dimensional geometry

Argha Debnath, Ayan Khan, Prasanta Kumar Panigrahi

Published Oct 27, 2023• 4 citations
arXivHTMLPDF
DOI
10.1140/epjp/s13360-023-04554-5

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Recent observations of droplets in dipolar and binary Bose-Einstein condensate (BEC) motivates us to study the theory of droplet formation in details. Precisely, we are interested in investigating the possibility of droplet formation in a quasi one dimensional geometry. The recent observation have concluded that the droplets are stabilized by the competition between effective mean-filed and beyond mean-field interaction. Hence, it is possible to map the effective equation of motion to a cubic-quartic nonlinear Schr\odinger equation (CQNLSE). We obtain two analytical solutions of the modified Gross-Pitaevskii equation or CQNLSE and based on their stability we investigate the parameter regime for which droplets can form. The effective potential allows us to conclude about the regions of soliton domination and self bound droplet formations.
Abstract We present analytical solution, which is periodic in nature, for a driven cubic–quartic nonlinear Schrödinger equation (DCQNLSE) is placed in a bi-chromatic optical lattice. The solution indicates the creation of density wave. Since, beyond mean-field contribution in quasi one dimensional and one dimensional geometry differs on the even exponents of the nonlinearity thus we extend our analysis toward quadratic–cubic–quartic and quadratic–cubic nonlinearities as well. Later, we study the dynamics of DCQNLSE. Our study indicates the existence of stripe phase along with considerable phase coherence. These findings allow us to comment on the possible emergence of supersolid phase in a condensate.
We demonstrate the formation of bright solitons in coupled defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type.