Abstract
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.
Highlights
Systems of interacting charges and fields are ubiquitous in physics
It has recently been shown that the invariance is lost in the strong light/matter coupling regime if the matter degrees of freedom are treated as quantum systems with a fixed number of energy levels[8,9,10,11,12,13,14], including the commonly used two-level truncation (2LT)
Two common gauge choices of non-relativistic quantum electrodynamics (QED) 9,10,14 are the Coulomb gauge, which has the advantage of describing photons as purely transverse radiation modes, and the multipolar gauge, which is most useful when the leading order terms are dominant in a multipole expansion of the fields[20,21,22]
Summary
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 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. Extensions to the model, and derivations in the Supplementary Material
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