Avoiding gauge ambiguities in cavity quantum electrodynamics

When an optical emitter is strongly coupled to a vibrational bath the polaron transformation is often used to permit an accurate second-order Redfield master equation. However, the optical transition rates in the polaron frame are not analytic and approximations typically need to be made, which result in the loss of anything other than simple additive effects of the two baths. In this paper, we derive an intuitive analytic expression for the polaron frame optical transition rates by means of a finite-mode truncation of the vibrational bath. Using this technique, calculations of the transition rates converge for only a few modes in the truncated spectral density, and capture nonadditive effects such as population inversion of a two-level system.

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“…The optical spectral density is more subtle, depending on the gauge in which the Hamiltonian is derived [50][51][52].…”

Section: Displacement Energymentioning

confidence: 99%

Analytic expression for the optical exciton transition rates in the polaron frame

2022

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“…The former form is usually favoured semi-classically as well as in the context of macroscopic QED [5,24], whereas the latter is more common in cavity and molecular QED [21]. This has naturally caused some confusion over which field to use, resolved by Ackerhalt and Milonni [25], although it has once more come to the forefront of research as this choice (commonly controlled by a gauge choice [3] but not necessarily [26]) re-distributes the energy between matter and field components -something that can lead to gauge ambiguous predictions if energy-dependent approximations are made further along the calculation [27][28][29][30][31]. Regardless, in the context of macroscopic QED, we would like to note that the 'electric' field usually [5] referred to when writing H int = − d • E is, in fact, a type of displacement field.…”

Section: An Argument For a Dual Symmetric Couplingmentioning

confidence: 99%

Duality, decay rates, and local-field models in macroscopic QED

2022

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Any treatment of magnetic interactions between atoms, molecules and optical media must start at the form of the interaction energy. This forms the base on which predictions about any number of magnetic atom-light properties stands -spontaneous decay rates and forces included. As is well-known, the Heaviside-Larmor duality symmetry of Maxwell's equations, where electric and magnetic quantities are exchanged, is broken by the usual form of the magnetic interaction energy. We argue that this symmetry can be restored by including general local-field effects, and that local fields should be treated as a necessity for correctly translating between the microscopic world of the dipole and the macroscopic world of the measured fields. This may additionally aid in resolving a long standing debate over the form of the force on a dipole in a medium. Finally, we compute the magnetic dipole decay rate in a magneto-dielectric with local-field effects taken into account, and show that macroscopic quantum electrodynamics can be made to be dual symmetric at an operator level, instead of only for expectation values.

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Section: An Argument For a Dual Symmetric Couplingmentioning

confidence: 99%

Duality, decay rates and local-field models in macroscopic QED

Westerberg,

Messinger,

Barnett

2021

Preprint

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Any treatment of magnetic interactions between atoms, molecules and optical media must start at the form of the interaction energy. This forms the base on which predictions about any number of magnetic atom-light properties stands -spontaneous decay rates and forces included. As is well-known, the Heaviside-Larmor duality symmetry of Maxwell's equations, where electric and magnetic quantities are exchanges, is broken by the usual form of the magnetic interaction energy. We argue that this symmetry can be restored by including general local-field effects, and that local fields should be treated as a necessity for correctly translating between the microscopic world of the dipole and the macroscopic world of the measured fields. This may additionally aid in resolving a long standing debate over the form of the force on a dipole in a medium. Finally, we compute the magnetic dipole decay rate in a magneto-dielectric with local-field effects taken into account, and show that macroscopic quantum electrodynamics can be made to be dual symmetric at an operator level, instead of only for expectation values.

show abstract

Avoiding gauge ambiguities in cavity quantum electrodynamics

Cited by 10 publications

References 65 publications

Analytic expression for the optical exciton transition rates in the polaron frame

Analytic expression for the optical exciton transition rates in the polaron frame

Duality, decay rates, and local-field models in macroscopic QED

Duality, decay rates and local-field models in macroscopic QED

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