Gauge invariance of the Dicke and Hopfield models

Garziano, Luigi; Settineri, Alessio; Stefano, Omar Di; Savasta, Salvatore; Nori, Franco

doi:10.1103/physreva.102.023718

Cited by 42 publications

(35 citation statements)

References 68 publications

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“…As emphasized recently [49], a straightforward projection of the Coulomb gauge Hamiltonian (9) obtained through minimal coupling misses the contribution to lightmatter interaction coming from this nonlocal potential. To overcome this problem it has been recently suggested to proceed differently [49,50], namely first project the matter Hamiltonian and then perform the minimal coupling substitution through the action of the unitary transformation (13), which is itself consistently projected onto the selected manifold of degrees of freedom.…”

Section: Gauge Invariant Light-matter Coupling In a Projected Electronic Basismentioning

confidence: 99%

“…As discussed before (see also Refs. [49,50,64]), this is obtained by applying the projected unitary operator, Eq. ( 27), to the projected electronic Hamiltonian H el , Eq.…”

Section: Projected Hamiltonian In the Coulomb Gaugementioning

confidence: 99%

“…In the context of cavity-controlled chemistry [48] it has been emphasized the importance of ab initio approaches preserving the gauge invariance of the full microscopic theory. The resolution of these gauge ambiguities has been recently demonstrated for Rabi and Dicke models, leading to a consistent strategy to write down a projected quantum light-matter Hamiltonian which preserves gauge equivalence [40,41,49,50].…”

Section: Introductionmentioning

confidence: 99%

“…Following the general idea of Refs. [49,50], we present a formalism that allows us to write down the Hamiltonian of correlated electrons coupled to photons in the dipole and Coulomb gauges which remain fully equivalent, i.e., related by a unitary transformation, even after projection. We discuss the relation between our approach and the so called Peierls substitution, often used to describe light-matter coupling in tight-binding models.…”

Section: Introductionmentioning

confidence: 99%

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Gauge fixing for strongly correlated electrons coupled to quantum light

Dmytruk

Schiró

2021

Phys. Rev. B

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We discuss the problem of gauge fixing for strongly correlated electrons coupled to quantum light, described by projected low-energy models such as those obtained within tight-binding methods. Drawing from recent results in the field of quantum optics, we present a general approach to write down a quantum light-matter Hamiltonian in either dipole or Coulomb gauge which is explicitly connected by a unitary transformation, thus ensuring gauge equivalence even after projection. The projected dipole gauge Hamiltonian features a linear light-matter coupling and an instantaneous self-interaction for the electrons, similar to the structure in the full continuum theory. On the other hand, in the Coulomb gauge the photon field enters in a highly nonlinear way, through phase factors that dress the electronic degrees of freedom. We show that our approach generalizes the well-known Peierls approximation, to which it reduces when only local, on-site orbital contributions to lightmatter coupling are taken into account. As an application we study a two-orbital model of interacting electrons coupled to a uniform cavity mode, recently studied in the context of excitonic superradiance and associated no-go theorems. Using both gauges we recover the absence of a superradiant phase in the ground state and show that excitations on top of it, described by polariton modes, contain instead nontrivial light-matter entanglement. Our results highlight the importance of treating the nonlinear light-matter interaction of the Coulomb gauge nonperturbatively, to obtain a well-defined ultrastrong coupling limit and to not spoil gauge equivalence.

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Section: Gauge Invariant Light-matter Coupling In a Projected Electronic Basismentioning

confidence: 99%

“…As discussed before (see also Refs. [49,50,64]), this is obtained by applying the projected unitary operator, Eq. ( 27), to the projected electronic Hamiltonian H el , Eq.…”

Section: Projected Hamiltonian In the Coulomb Gaugementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gauge fixing for strongly correlated electrons coupled to quantum light

Dmytruk

Schiró

2021

Phys. Rev. B

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“…Several recent works [155,[168][169][170][171] have identified important issues arising in the USC when performing the two-level approximation in different gauges. A systematic study of the two-level approximation in the dipole and Coulomb gauge was performed by De Bernardis et al [168].…”

Section: A Gauge Non-invariance Of the Two-level Approximationmentioning

confidence: 99%

Theoretical Methods for Ultrastrong Light–Matter Interactions

Boité

2020

Adv Quantum Tech

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This article reviews theoretical methods developed in the last decade to understand cavity quantum electrodynamics in the ultrastrong-coupling regime, where the strength of the light-matter interaction becomes comparable to the photon frequency. Along with profound modifications of fundamental quantum optical effects giving rise to a rich phenomenology, this regime introduces significant theoretical challenges. One of the most important is the break-down of the rotating-wave approximation which neglects all non-resonant terms in lightmatter interaction Hamiltonians. Consequently, a large part of the quantum optical theoretical framework has to be revisited in order to accurately account for all interaction terms in this regime. We give in this article a broad overview of the recent progress, ranging from analytical estimates of ground-state properties to proper derivations of master equations and computation of photodetection signals. For each aspect of the theory, the basic principles of the methods are illustrated on paradigmatic models such as quantum Rabi and spin-boson models. In this spirit, most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached, such as semiconductor microcavities and superconducting circuits. The validity of these models is discussed in the last part of the article, where we address recent debates on fundamental issues related to gauge invariance in the ultrastrong-coupling regime.

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