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On gauge freedom and subsystems in quantum electrodynamics

Adam Stokes

Published Jan 1, 2014• 4 citations
OpenAlex

Abstract

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.

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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.
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.
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.
Composition of Different and of Identical Systems It is a general tendency of physics to interpret physical systems as composed of simpler, more elementary subsystems. The question “What is it made of?” is a very tempting and popular one. Though this attitude does not reflect a logical necessity, it has proved to be successful in significant circumstances: we think, e.g., of macroscopic matter as composed of atoms and molecules, of molecules as composed of atoms, of atoms as composed of nuclei and electrons, and of nuclei as composed of protons and neutrons. Loosely speaking, one might expect that this attitude will be successful whenever the interaction that packs the constituent subsystems together is not strong enough to make them lose their identity. Here, we are concerned with the problem of constructing the quantum-mechanical formalism of a compound system knowing the formalisms of the constituent subsystems. Thus our first problem is to specify the Hilbert space of the compound system. For the sake of simplicity, let us restrict ourselves to the case of a system composed of only two subsystems. The prescriptions of quantum theory vary according to whether one is faced with the composition of identical or nonidentical subsystems.
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.
We describe the physical relativity of light and matter quantum subsystems, their correlations, and energy exchanges. We examine the most commonly adopted definitions of atoms and photons, noting the significant difference in their localisation properties when expressed in terms of primitive manifestly gauge-invariant and local fields. As a result, different behaviours for entanglement generation and energy exchange occur for different definitions. We explore such differences in detail using toy models of a single photonic mode interacting with one and two dipoles.
Time-dependent light-matter interactions are a widespread means by which to describe controllable experimental operations. They can be viewed as an approximation in which a third system - the control system - is treated as external within the Hamiltonian. We demonstrate that this results in non-equivalence between gauges. We provide a physical example in which each different non-equivalent model coincides with a gauge-invariant description applied in a different experimental situation. The qualitative final-time predictions obtained from these models, including entanglement and photon number, depend on the gauge within which the time-dependent coupling assumption is made. This occurs whenever the interaction switching is sufficiently strong and non-adiabatic even if the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.