Gauge invariance of the Dicke and Hopfield models
- URL: http://arxiv.org/abs/2002.04241v1
- Date: Tue, 11 Feb 2020 07:49:16 GMT
- Title: Gauge invariance of the Dicke and Hopfield models
- Authors: Luigi Garziano, Alessio Settineri, Omar Di Stefano, Salvatore Savasta,
Franco Nori
- Abstract summary: We show that the Dicke model, which describes the dipolar coupling between N two-level atoms and a quantized electromagnetic field, seemingly violates gauge invariance in the presence of ultrastrong light-matter coupling.
We express the Hopfield model, a general description based on the quantization of a linear dielectric medium, in a manifestly gauge invariant form, and show that the Dicke model in the dilute regime can be regarded as a particular case of the more general Hopfield model.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The Dicke model, which describes the dipolar coupling between N two-level
atoms and a quantized electromagnetic field, seemingly violates gauge
invariance in the presence of ultrastrong light-matter coupling, a regime that
is now experimentally accessible in many physical systems. Specifically, it has
been shown that, while the two-level approximation can work well in the dipole
gauge, the Coulomb gauge fails to provide the correct spectra in the
ultrastrong coupling regime. Here we show that, taking into account the
nonlocality of the atomic potential induced by the two-level approximation,
gauge invariance is fully restored for arbitrary interaction strengths, even in
the limit of N going to infinity. Finally, we express the Hopfield model, a
general description based on the quantization of a linear dielectric medium, in
a manifestly gauge invariant form, and show that the Dicke model in the dilute
regime can be regarded as a particular case of the more general Hopfield model.
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