Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2009.10662 · Reviews of Modern Physics

Implications of gauge freedom for nonrelativistic quantum electrodynamics

Adam Stokes, Ahsan Nazir

Published Nov 3, 2022• 60 citations
arXivHTMLPDF

Abstract

This article reviews the meaning of gauge freedom in quantum electrodynamics and emphasizes its consistency with examples and analyses. It thus demonstrates that ambiguities and recent controversies are resolved by proper identification of physically relevant observables of field and matter subsystems. Since these observables differ for different gauges, light and matter subsystems can only be defined relative to the choice of gauge, with implications for the identification of effective few-dimensional models, entanglement, phase transitions, and cavity quantum electrodynamics effects beyond weak-coupling regimes.

DOI
10.1103/revmodphys.94.045003

Related papers

On gauge freedom and subsystems in quantum electrodynamics

Adam Stokes

I analyse different decompositions of composite light-matter systems into constituent \nsubsystems. I show that given a single description of a composite atomfield \nsystem, many different decompositions into “atom” and “field” subsystems \ncan be made. I show that these decompositions are generally physically \ninequivalent, and that they can be understood as corresponding to different \nchoices of gauge. I discuss some of the implications this has for the ontology \nof QED, and find experimental signatures that could be used to distinguish \nbetween different theoretical subsystem decompositions.

•Jan 1, 2014•4 citations

Gauge freedom, quantum measurements, and time-dependent interactions in cavity QED

Alessio Settineri, Omar Di Stefano, David Zueco +3 more

The interaction between quantized electromagnetic fields in cavities and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interactions and quantum technologies.Recently, new regimes beyond the weak and strong light-matter coupling of cavity-QED have been explored in several settings, wherein the light-matter coupling rate becomes comparable to (ultrastrong coupling) or even exceeds (deep-strong coupling) the photon frequency.These ultrastrong coupling regimes can give rise to new physical effects and applications, and they challenge our understanding of cavity QED; fundamental issues like the proper definition of subsystems, their quantum measurements, the structure of light-matter ground states, and the analysis of time-dependent interactions are subject to gauge ambiguities that lead to even qualitatively distinct predictions.The resolution of these ambiguities is important for understanding and designing next-generation quantum devices that can operate in extreme coupling regimes.Here we discuss and provide solutions to these ambiguities by adopting an approach based on operational procedures involving measurements on the individual light and matter components of the interacting system.

arXiv:1912.08548•Physical Review Research•Apr 28, 2021•49 citations

Avoiding gauge ambiguities in cavity quantum electrodynamics

Dominic M. Rouse, Brendon W. Lovett, Erik M. Gauger +1 more

Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few low-lying energy eigenstates. This effect is particularly prominent in the ultra-strong coupling regime. Such ambiguities arise because transformations reshuffle the partition between light and matter degrees of freedom and so level truncation is a gauge dependent approximation. To avoid this gauge ambiguity, we redefine the electromagnetic fields in terms of potentials for which the resulting canonical momenta and Hamiltonian are explicitly unchanged by the gauge choice of this theory. Instead the light/matter partition is assigned by the intuitive choice of separating an electric field between displacement and polarisation contributions. This approach is an attractive choice in typical cavity quantum electrodynamics situations.

arXiv:2003.04899•Scientific Reports•Feb 19, 2021•12 citations

Gauge ambiguities in ultrastrong-coupling QED: the Jaynes-Cummings model is as fundamental as the Rabi model

Adam Stokes, Ahsan Nazir

Ultrastrong-coupling between an effective two-level system and radiation offers immense potential for advancing both fundamental and applied quantum electrodynamics (QED). Such regimes cannot be treated using the rotating-wave approximation, which applied to the quantum Rabi model yields the apparently less fundamental Jaynes-Cummings model. However, the implications of gauge-freedom for ultrastrong-coupling QED are yet to be recognised. Here we show that when truncating the material system to only two levels, each gauge gives a different effective description whose predictions can vary significantly for ultrastrong-coupling. Rabi models are obtained through specific gauge choices, but so too is a Jaynes-Cummings model without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this Jaynes-Cummings model is not only valid well beyond the rotating-wave approximation, it is often more accurate than the Rabi model. Among the many implications of this finding is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling light-matter physics.

•May 16, 2018•1 citation

Metrics and properties of optimal gauges in multimode cavity QED

Geva Arwas, Vladimir Manucharyan, Cristiano Ciuti

Multimode cavity quantum electrodynamics describes, for example, the coupling between an atom and a multimode electromagnetic resonator. The gauge choice is important for practical calculations in truncated Hilbert spaces, because the exact gauge invariance is recovered only in the whole space. An optimal gauge can be defined as the one predicting the most accurate observables for the same number of atomic levels and modes. Different metrics quantifying the gauge performance can be introduced depending on the observable of interest. In this paper we demonstrate that the optimal choice is generally mode dependent, i.e., a different gauge is needed for each cavity mode. While the choice of gauge becomes more important for increasing light-matter interaction, we also show that the optimal gauge does not correspond to the situation where the entanglement between light and matter is the smallest.

arXiv:2304.02436•Physical Review A•Aug 16, 2023•9 citations

Noncovariant gauge fixing in the quantum Dirac field theory of atoms and molecules

Adam Stokes

Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincar\'e gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss important implications for the ontology of noncovariant canonical QED due to the gauge freedom that remains present in our formulation.

arXiv:1207.3196•Physical Review A•Jul 23, 2012•11 citations
This article reviews the meaning of gauge freedom in quantum electrodynamics and emphasizes its consistency with examples and analyses. It thus demonstrates that ambiguities and recent controversies are resolved by proper identification of physically relevant observables of field and matter subsystems. Since these observables differ for different gauges, light and matter subsystems can only be defined relative to the choice of gauge, with implications for the identification of effective few-dimensional models, entanglement, phase transitions, and cavity quantum electrodynamics effects beyond weak-coupling regimes.
I analyse different decompositions of composite light-matter systems into constituent \nsubsystems. I show that given a single description of a composite atomfield \nsystem, many different decompositions into “atom” and “field” subsystems \ncan be made. I show that these decompositions are generally physically \ninequivalent, and that they can be understood as corresponding to different \nchoices of gauge. I discuss some of the implications this has for the ontology \nof QED, and find experimental signatures that could be used to distinguish \nbetween different theoretical subsystem decompositions.
The interaction between quantized electromagnetic fields in cavities and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interactions and quantum technologies.Recently, new regimes beyond the weak and strong light-matter coupling of cavity-QED have been explored in several settings, wherein the light-matter coupling rate becomes comparable to (ultrastrong coupling) or even exceeds (deep-strong coupling) the photon frequency.These ultrastrong coupling regimes can give rise to new physical effects and applications, and they challenge our understanding of cavity QED; fundamental issues like the proper definition of subsystems, their quantum measurements, the structure of light-matter ground states, and the analysis of time-dependent interactions are subject to gauge ambiguities that lead to even qualitatively distinct predictions.The resolution of these ambiguities is important for understanding and designing next-generation quantum devices that can operate in extreme coupling regimes.Here we discuss and provide solutions to these ambiguities by adopting an approach based on operational procedures involving measurements on the individual light and matter components of the interacting system.
Systems of interacting charges and fields are ubiquitous in physics. Recently, it has been shown that Hamiltonians derived using different gauges can yield different physical results when matter degrees of freedom are truncated to a few low-lying energy eigenstates. This effect is particularly prominent in the ultra-strong coupling regime. Such ambiguities arise because transformations reshuffle the partition between light and matter degrees of freedom and so level truncation is a gauge dependent approximation. To avoid this gauge ambiguity, we redefine the electromagnetic fields in terms of potentials for which the resulting canonical momenta and Hamiltonian are explicitly unchanged by the gauge choice of this theory. Instead the light/matter partition is assigned by the intuitive choice of separating an electric field between displacement and polarisation contributions. This approach is an attractive choice in typical cavity quantum electrodynamics situations.
Ultrastrong-coupling between an effective two-level system and radiation offers immense potential for advancing both fundamental and applied quantum electrodynamics (QED). Such regimes cannot be treated using the rotating-wave approximation, which applied to the quantum Rabi model yields the apparently less fundamental Jaynes-Cummings model. However, the implications of gauge-freedom for ultrastrong-coupling QED are yet to be recognised. Here we show that when truncating the material system to only two levels, each gauge gives a different effective description whose predictions can vary significantly for ultrastrong-coupling. Rabi models are obtained through specific gauge choices, but so too is a Jaynes-Cummings model without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this Jaynes-Cummings model is not only valid well beyond the rotating-wave approximation, it is often more accurate than the Rabi model. Among the many implications of this finding is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling light-matter physics.
Multimode cavity quantum electrodynamics describes, for example, the coupling between an atom and a multimode electromagnetic resonator. The gauge choice is important for practical calculations in truncated Hilbert spaces, because the exact gauge invariance is recovered only in the whole space. An optimal gauge can be defined as the one predicting the most accurate observables for the same number of atomic levels and modes. Different metrics quantifying the gauge performance can be introduced depending on the observable of interest. In this paper we demonstrate that the optimal choice is generally mode dependent, i.e., a different gauge is needed for each cavity mode. While the choice of gauge becomes more important for increasing light-matter interaction, we also show that the optimal gauge does not correspond to the situation where the entanglement between light and matter is the smallest.
Starting from the Weyl gauge formulation of quantum electrodynamics (QED), the formalism of quantum-mechanical gauge fixing is extended using techniques from nonrelativistic QED. This involves expressing the redundant gauge degrees of freedom through an arbitrary functional of the gauge-invariant transverse degrees of freedom. Particular choices of functional can be made to yield the Coulomb gauge and Poincar\'e gauge representations. The Hamiltonian we derive therefore serves as a good starting point for the description of atoms and molecules by means of a relativistic Dirac field. We discuss important implications for the ontology of noncovariant canonical QED due to the gauge freedom that remains present in our formulation.