Strict Time-Resolved Steady States via Affine-Eigenstate Mapping: A Robust Framework for Ultracold Atom-Molecule...

Area of Science:

• Quantum physics
• Ultracold atomic gases
• Quantum chemistry

Background:

• Analyzing ultracold atom-molecule conversion dynamics is crucial for quantum simulations.
• Particle loss presents a significant challenge in maintaining coherence.

Purpose of the Study:

• To develop a theoretical framework for analyzing atom-molecule conversion dynamics with particle loss.
• To identify and characterize different self-trapping regimes, particularly a robust strict self-trapping regime.

Main Methods:

• An affine-eigenstate transformation to map mean-field dynamics to an effective two-mode representation.
• Analysis of fixed points, Bloch-sphere trajectories, and linear stability within the transformed variables.
• Introduction of von Neumann and linear-entropy diagnostics for mixed-state descriptions.

Main Results:

• The framework distinguishes ordinary, pseudo, and strict self-trapping regimes.
• The strict self-trapping regime, characterized by a balanced condition (S=0), demonstrates robustness against atom- and molecule-loss imbalance.
• An inverse reconstruction procedure for preparing initial states realizing strict self-trapping is provided.

Conclusions:

• The proposed theoretical framework offers a unified approach to analyze ultracold atom-molecule conversion dynamics.
• The identified strict self-trapping regime has implications for developing decoherence-resilient quantum simulations and information processing architectures.
• Future work may involve finite-particle simulations and exploring phase-modulated control protocols.