Hamiltonian averaging for solitons with nonlinearity management

Area of Science:

• Quantum physics
• Atomic physics
• Nonlinear optics

Background:

• The nonlinear Schrödinger (NLS) equation models various wave phenomena.
• Nonlinearity management is crucial for controlling wave propagation.
• Previous averaged equations had limitations in describing long-term dynamics.

Purpose of the Study:

• To derive and validate a new Hamiltonian averaged NLS equation for extended time intervals.
• To numerically construct matter-wave solitons in Bose-Einstein condensates (BECs) using the new model.
• To investigate the existence thresholds for dark and bright solitons under Feshbach resonance management.

Main Methods:

• Revisiting and analyzing the averaged equation from Phys. Rev. Lett. 91, 240201 (2003).
• Deriving a new Hamiltonian averaged NLS equation applicable for longer time scales.
• Numerical construction of matter-wave solitons in BECs with Feshbach resonance management.

Main Results:

• The previously derived averaged equation is only valid for initial time intervals.
• The new Hamiltonian averaged NLS equation provides accurate descriptions for longer durations.
• No threshold exists for the existence of large-amplitude dark solitons.
• A threshold is identified for the existence of bright solitons.

Conclusions:

• The developed Hamiltonian averaged NLS equation is a more robust tool for studying soliton dynamics in BECs.
• The findings clarify the conditions for the existence of different types of solitons, impacting BEC research.
• This work advances the understanding of nonlinear wave phenomena in quantum systems.