Modulation instability of two-dimensional Bose-Einstein condensates with helicoidal and a mixture of Rashba-Dresselhaus spin-orbit couplings

• Published in: Physics letters. A Vol. 449; p. 128334
• Main Authors: Tabi, Conrad Bertrand, Otlaadisa, Phelo, Kofané, Timoléon Crépin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 14-10-2022
• Subjects: Helicoidal gauge potential; Helicoidal spin-orbit coupling; Modulational instability; Rashba-Dresselhaus spin-orbit coupling; Vector BECs; Rashba-Dresselhaus spin-orbit coupling; Helicoidal gauge potential; Modulational instability; Vector BECs; Helicoidal spin-orbit coupling
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2022.128334

The modulational instability (MI) process is exclusively studied in a two-component Bose-Einstein condensate (BEC) which includes Rashba-Dresselhaus (RD) spin-orbit (SO) and helicoidal SO couplings. A generalized set of two-dimensional (2D) Gross-Pitaevskii (GP) equations is derived. The tunability of the helicoidal gauge potential is exploited to address BECs dynamics in a square lattice. The MI growth rate is derived, and parametric analyses of MI show the dependence of the instability on interatomic interaction strengths, the RD SO coupling, and helicoidal SO coupling, which combines the gauge amplitude and the helicoidal gauge potential. Direct numerical simulations are carried out to confirm the analytical predictions. Trains of solitons are obtained, and their behaviors are debated when the RD SO parameters are varied under different combinations between the gauge amplitude and the helicoidal gauge potential. The latter gives a potential way to manipulate the trapping capacities of the proposed BEC model.
•A vector 2D Gross-Pitaevskii model with Rashba-Dresselhaus and helicoidal spin-orbit couplings is derived.•The tunability of the helicoidal gauge potential allows us to study dynamics in free space and a square lattice.•The modulational instability growth rate is derived and discussed for each case.•Direct numerical simulations confirm the existence of trains of solitons due to different combinations of the spin-orbit couplings.