Rise and Fall of a Bright Soliton in an Optical Lattice

Area of Science:

• Quantum physics
• Atomic physics
• Condensed matter physics

Background:

• Ultracold atomic gases are crucial for simulating complex quantum phenomena.
• One-dimensional optical lattices provide a controllable environment for studying many-body physics.

Purpose of the Study:

• To investigate the excitation spectrum of ultracold atomic gases with attractive interactions in a 1D optical lattice.
• To understand the behavior of quantum soliton bands and their interplay with continuum states.

Main Methods:

• Theoretical study of ultracold atomic gas in a 1D optical lattice.
• Analysis of the excitation spectrum, focusing on N-particle bound states (solitons) and extended states.
• Examination of the energy degeneracy and gap opening with varying interaction strength.

Main Results:

• Identification of a quantum soliton band (N-particle bound states) and a continuum band in the excitation spectrum.
• Observation of energy degeneracy for weak interactions and gap opening above a threshold interaction strength in finite systems.
• Demonstration that solitonic states are robust against spatial perturbations and disorder.

Conclusions:

• The interplay between bound and extended states significantly impacts static and dynamic properties.
• The system exhibits a crossover in quantum many-body dynamics (integrable nonergodic to nonintegrable ergodic) with varying lattice filling.
• This system serves as a model for exploring diverse quantum dynamics regimes.