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Area of Science:

  • Nonlinear physics
  • Quantum optics
  • Bose-Einstein condensates

Background:

  • Dissipative solitons are crucial in nonlinear systems.
  • Spin-orbit coupling in Bose-Einstein condensates (BECs) offers novel quantum phenomena.
  • Understanding the stability of BECs is essential for quantum technologies.

Purpose of the Study:

  • To introduce a vector form of the cubic complex Ginzburg-Landau equation for dissipative solitons in helicoidal spin-orbit coupled open BECs.
  • To theoretically investigate the stability of continuous-wave (cw) solutions using linear stability analysis.
  • To numerically explore the dynamics of modulational instability.

Main Methods:

  • Developing a vector Ginzburg-Landau equation.
  • Applying linear stability analysis to cw solutions.
  • Performing direct numerical simulations in Fourier space.

Main Results:

  • The study introduces a novel vector Ginzburg-Landau equation for dissipative solitons in BECs.
  • Linear stability analysis provides insights into the modulational instability gain spectrum.
  • Numerical simulations validate theoretical predictions and identify instability thresholds.

Conclusions:

  • The developed model accurately describes dissipative soliton dynamics in spin-orbit coupled BECs.
  • The findings contribute to understanding the stability and dynamics of BECs.
  • This research paves the way for controlling and utilizing dissipative solitons in quantum systems.