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Few-Mode Geometric Description of a Driven-Dissipative Phase Transition in an Open Quantum System
Dmitry O Krimer1, Mikhail Pletyukhov2
1Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria, EU.
Physical Review Letters
|October 2, 2019
Summary
Hysteresis in driven-dissipative phase transitions can be simplified using two collective Liouvillian eigenmodes. This geometric approach enhances computational accessibility and analytical insights for nonlinear Kerr mode systems.
Area of Science:
- Quantum optics
- Nonlinear dynamics
- Condensed matter physics
Background:
- Driven-dissipative systems exhibit complex behaviors like phase transitions.
- Hysteresis is a key phenomenon in these systems, often challenging to model.
- Nonlinear Kerr media provide a relevant experimental platform for studying such transitions.
Purpose of the Study:
- To develop a simplified description of hysteresis in driven-dissipative phase transitions.
- To introduce a powerful geometric approach for analyzing these phenomena.
- To extend the computational and analytical accessibility of nonlinear system studies.
Main Methods:
- Utilizing a nonlinear Kerr mode driven by a laser as a model system.
- Employing collective, dissipative Liouvillian eigenmodes for system description.
- Applying a non-Abelian geometric connection framework.
Main Results:
- Accurate description of hysteresis using only two collective, dissipative Liouvillian eigenmodes.
- Identification of two key components of a non-Abelian geometric connection.
- Demonstration of significant simplification in describing driven-dissipative phase transitions.
Conclusions:
- A powerful geometric approach simplifies the analysis of driven-dissipative phase transitions.
- This method expands the range of computationally accessible parameter regimes.
- Provides a new foundation for experimental and analytical investigations in nonlinear optics and beyond.
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