A universal gauge structure in the photon content of light-matter systems
Abstract
After truncating the matter Hilbert space of a single-mode light-matter model, gauge transformations leave the spectrum invariant whereas the ground-state photon number is gauge dependent, hence, its meaning remains disputed. We show that this gauge dependence obeys an exact algebraic law whenever the gauge transformation acts as a displacement of the field coupled to a matter operator G. Namely, the ground-state photon number is a quadratic polynomial in the gauge parameter λ, ⟨ a† a⟩λ = ⟨ a† a⟩0 + Cλ + Qλ2. Here the coefficients are the correlator C=⟨ G p⟩ of G and the field momentum p, and Q=⟨ G2⟩. Its minimum over all gauges is naturally gauge-invariant, and for the quantum Rabi model it is determined by the ground-state energy alone. We show that it is strictly positive for the quantum Rabi and Dicke models with level splitting, so that a residual photon content survives in every gauge. At weak coupling the gauge of minimal photon number is the Jaynes-Cummings gauge, and for the Dicke model it remains so at all couplings in the thermodynamic limit.
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BibTeX
@misc{dutta2026universal,
title = {{A universal gauge structure in the photon content of light-matter systems}},
author = {Arka Dutta and Marcus Kollar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40446},
eprint = {2610.40446},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40446},
}
RIS
TY - UNPB
TI - A universal gauge structure in the photon content of light-matter systems
AU - Arka Dutta
AU - Marcus Kollar
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40446
UR - https://arxiv.org/abs/2610.40446
AB - After truncating the matter Hilbert space of a single-mode light-matter model, gauge transformations leave the spectrum invariant whereas the ground-state photon number is gauge dependent, hence, its meaning remains disputed. We show that this gauge dependence obeys an exact algebraic law whenever the gauge transformation acts as a displacement of the field coupled to a matter operator G. Namely, the ground-state photon number is a quadratic polynomial in the gauge parameter λ, ⟨ a^† a⟩_λ = ⟨ a^† a⟩_0 + Cλ + Qλ^2. Here the coefficients are the correlator C=⟨ G p⟩ of G and the field momentum p, and Q=⟨ G^2⟩. Its minimum over all gauges is naturally gauge-invariant, and for the quantum Rabi model it is determined by the ground-state energy alone. We show that it is strictly positive for the quantum Rabi and Dicke models with level splitting, so that a residual photon content survives in every gauge. At weak coupling the gauge of minimal photon number is the Jaynes-Cummings gauge, and for the Dicke model it remains so at all couplings in the thermodynamic limit.
ER -