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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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The quantum-optics Hamiltonian in the Multipolar gauge
Emmanuel Rousseau1, Didier Felbacq2
1Université de Montpellier, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France. emmanuel.rousseau@umontpellier.fr.
Scientific Reports
|September 13, 2017
Summary
This study questions the validity of the Power-Zienau-Woolley Hamiltonian for light-matter interaction in quantum electrodynamics. It demonstrates this Hamiltonian is not equivalent to the minimal-coupling Hamiltonian, predicting different physical results.
Area of Science:
- Quantum electrodynamics
- Quantum theory
- Light-matter interaction
Background:
- The Power-Zienau-Woolley Hamiltonian is proposed as an alternative to the vector potential formulation in quantum electrodynamics.
- This Hamiltonian focuses on electric and magnetic fields, potentially simplifying light-matter interaction descriptions.
Purpose of the Study:
- To critically evaluate the validity and applicability of the Power-Zienau-Woolley Hamiltonian.
- To compare the Power-Zienau-Woolley Hamiltonian with the standard minimal-coupling Hamiltonian in quantum electrodynamics.
- To derive a correct quantum theory for light-matter interaction in the multipolar gauge.
Main Methods:
- Analysis of gauge transformations between Hamiltonians.
- Investigation of gauge fixing constraints.
- Derivation of a unitary transformation relating the two Hamiltonians.
Main Results:
- The Power-Zienau-Woolley Hamiltonian is not equivalent to the minimal-coupling Hamiltonian.
- The Power-Zienau-Woolley Hamiltonian lacks fixed gauge conditions, with interaction terms in one gauge and other terms in a different gauge.
- The Hamiltonians are related by a unitary transformation that violates gauge fixing constraints, leading to differing physical predictions.
Conclusions:
- The Power-Zienau-Woolley Hamiltonian is shown to be physically inequivalent to the minimal-coupling Hamiltonian.
- A corrected quantum theory is presented using the multipolar gauge with a Hamiltonian dependent only on physical fields.
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