Hybrid matter-wave - microwave solitons on the lattice

Zhihuan Luo*, Weiwen Luo, Wei Pang, Zhijie Mai, Yongyao Li, Boris A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a two-component system which models a pseudospinor Bose–Einstein condensate (BEC), with a microwave field coupling its two components. The feedback of BEC onto the field (the local-field effect) is taken into account by dint of the respective Poisson equation, which is solved using the Green's function. This gives rise to an effective long-range self-trapping interaction, which may act alone, or be combined with the contact cubic nonlinearity. The system is made discrete by loading the BEC into a deep optical-lattice potential. Numerical solutions of the discrete system demonstrate that onsite-centered fundamental solitons are stable in the cases of attractive or zero contact interactions, while offsite-centered solitons are unstable. In the case of the repulsive onsite nonlinearity, offsite solitons are stable, while their onsite-centered counterparts are stable only at sufficiently small values of the norm, where bistability between the off- and onsite-centered mode takes place. The shape of the onsite-centered solitons is very accurately predicted by a variational approximation (which includes essential technical novelties), and their super-exponentially decaying tails are found by means of direct analytical consideration. Spatially-antisymmetric (“twisted”) solitons are stable at small values of the norm, being unstable at larger norms. In the strongly asymmetric version of the two-component system, which includes the Zeeman splitting, the system is reduced to a single discrete Gross–Pitaevskii equation, by eliminating the small higher-energy component.

Original languageEnglish
Pages (from-to)168-180
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Oct 2019


  • Bose-Einstein condensate
  • Hybrid solitons
  • Local-field effect
  • Microwave field coupling


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