Elimination of the A-square problem from cavity QED
András Vukics1, Tobias Griesser2, Peter Domokos1
1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
Physical Review Letters
|March 4, 2014
Summary
We generalized a transformation to create a new quantum electrodynamics Hamiltonian, simplifying cavity quantum electrodynamics models and resolving issues with phase transition arguments.
Area of Science:
- Quantum physics
- Cavity quantum electrodynamics
- Atomic physics
Background:
- Cavity quantum electrodynamics (QED) models like Dicke, Tavis-Cummings, and Jaynes-Cummings are foundational but rely on approximations.
- The standard formulation often includes complex terms like the A-square term and instantaneous Coulomb interactions.
- Understanding phase transitions in these systems is crucial but can be hindered by model limitations.
Purpose of the Study:
- To generalize the Power-Zineau-Woolley transformation for cavity quantum electrodynamics.
- To derive a canonical Hamiltonian applicable to arbitrary boundary geometries.
- To provide a rigorous microscopic foundation for common single-mode cavity QED models.
Main Methods:
- Generalization of the Power-Zineau-Woolley transformation.
- Derivation of a canonical Hamiltonian for cavity quantum electrodynamics.
- Term-by-term mapping of the new Hamiltonian to established single-mode models.
Main Results:
- A generalized canonical Hamiltonian for cavity quantum electrodynamics is obtained, valid for arbitrary boundary geometries.
- The derived Hamiltonian is free from the A-square term and instantaneous Coulomb interactions between distinct atoms.
- The single-mode models (Dicke, Tavis-Cummings, Jaynes-Cummings) are rigorously justified through direct mapping.
Conclusions:
- The generalized Hamiltonian offers a more fundamental description of cavity quantum electrodynamics.
- This work resolves theoretical obstacles, such as the basis for no-go arguments regarding the Dicke phase transition.
- The findings pave the way for more accurate theoretical investigations in cavity QED and related quantum phenomena.
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