Implications of gauge freedom for nonrelativistic quantum electrodynamics

Abstract

We review gauge-freedom in quantum electrodynamics (QED) outside of textbook regimes. We emphasise that QED subsystems are defined relative to a choice of gauge. Each definition uses different gauge-invariant observables. We show that this relativity is only eliminated if a sufficient number of Markovian and weak-coupling approximations are employed. All physical predictions are gauge-invariant, including subsystem properties such as photon number and entanglement. However, subsystem properties naturally differ for different physical subsystems. Gauge-ambiguities arise not because it is unclear how to obtain gauge-invariant predictions, but because it is not always clear which physical observables are the most operationally relevant. The gauge-invariance of a prediction is necessary but not sufficient to ensure its operational relevance. We show that in controlling which gauge-invariant observables are used to define a material system, the choice of gauge affects the balance between the material system's localisation and its electromagnetic dressing. We review various implications of subsystem gauge-relativity for deriving effective models, for describing timedependent interactions, for photodetection theory, and for describing matter within a cavity.

Strong light-matter interaction effects on molecular ensembles

“…Most cavity modes are highly off-resonant with the molecular system in every case, and we checked that a smaller number of cavity modes N 0 C would suffice to obtain thermodynamic limit predictions. However, as mentioned above, N 0 C depends on various parameters and we leave for future work a detailed analysis of optimal multimode cavity representations [59] for studying the effects of photonic devices on molecules.…”

The Jaynes-Cummings model and its descendants

“…Let us discuss a problem of the TLA of more fundamental character [401,996] (see also the review article [997]). To derive the Hamiltonian (287), given in the Coulomb gauge, we projected the full dipole Hilbert space {|ϕ i } onto a truncated subspace;…”

Non-linear optical processes in cavity light-matter systems

“…We consider a matter Hamiltonian representing a noninteracting lattice model with two orbitals in each unit cell. To describe the coupling to an electromagnetic field, we employ here the Coulomb gauge 29 (similar to the velocity gauge in Ref. 30).…”

“…Using the notations and definitions of the main text, the Coulomb gauge Hamiltonian of the light-matter coupled system, obtained through the minimal-coupling procedure, 29 reads…”