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Contracted description of driven degenerate multilevel quantum systems
Xiangyu Xu1, Kewei Sun1, Maxim F Gelin1
1School of Science, Hangzhou Dianzi University, Hangzhou 310018, China.
The Journal of Chemical Physics
|December 13, 2023
Summary
A new contraction theorem simplifies quantum dynamics by mapping multilevel degenerate systems to lower-dimension non-degenerate systems. This method aids in understanding complex quantum system-field interactions.
Area of Science:
- Quantum mechanics
- Atomic, molecular, and optical physics
Background:
- Multilevel degenerate systems (DS) exhibit complex quantum dynamics under external fields.
- Simulating these dynamics often requires significant computational resources.
Purpose of the Study:
- To develop a theoretical framework for simplifying the study of quantum dynamics in multilevel degenerate systems.
- To establish a mapping between degenerate and non-degenerate system dynamics.
Main Methods:
- Formulation of a contraction theorem for quantum dynamics.
- Analysis of system-field interactions under arbitrary external fields.
- Consideration of transitions with identical dipole moments between degenerate levels.
Main Results:
- A theorem is established that maps quantum dynamics of a multilevel degenerate system (DS) to a contracted non-degenerate system (CNS) of lower dimension.
- The theorem holds for external fields of any strength and shape, with or without rotating wave approximation.
- Explicit relations between DS and CNS observables are derived.
Conclusions:
- The contraction theorem significantly simplifies numerical calculations for quantum dynamics.
- The theorem provides clarity on the physical origins of field-induced dynamics in degenerate systems.
- This approach offers a powerful tool for analyzing complex quantum phenomena.
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