Lee-Huang-Yang correction for bright soliton solutions of single and two component Bose-Einstein condensates

The Lee-Huang-Yang(LHY)correction refers to the self trapping state in the Bose Einstein condensates, which is stabilized through effective self repulsion caused by quantum fluctuations around the mean field(MF)state. However, the LHY correction may affect the ground state of bright solitons in Bose Einstein condensates, leading to a certain range of applicability for the experimental solution of bright solitons. This study utilized variational approximation and numerical simulation methods based on the Gross Pitaevskii equation. By incorporating LHY corrections to the ground state models of quasi one-dimensional Bose Einstein condensates with single and two components, the experimental and numerical simulation solutions of the two systems were calculated. The calculation shows that for quasi one-dimensional single component and two component Bose Einstein condensates with LHY terms, good static approximate solutions can be obtained through the variational method under certain conditions for the LHY coefficient G of the system. The research in this article provides theoretical support for obtaining the ground state analytical solutions of single and two component Bose Einstein condensates with LHY terms in the quasi one-dimensional case, and provides assistance for future research on the properties and physical connotations of the system.