Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

Savasta, Salvatore; Stefano, Omar Di; Nori, Franco

doi:10.1515/nanoph-2020-0433

Cited by 14 publications

(8 citation statements)

References 79 publications

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“…This result comes from considering spectral weight conservation, 137 which is related to the Thomas-Reiche-Kuhn sum rule for light-matter interaction. 140 For the graphene conductivity, this sum rule indicates that the broadening of the interband conductivity (see previous subsection, and Fig. 18) implies that, in the "doped" regime, the spectrally integrated weight of interband transitions increases.…”

Section: Linear Conductivitymentioning

confidence: 81%

Hot carriers in graphene – fundamentals and applications

et al. 2021

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Section: Linear Conductivitymentioning

confidence: 81%

Hot carriers in graphene – fundamentals and applications

et al. 2021

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“…This fact not only leads to the useful relation in Eq. ( 6), but it also allows to obtain a Thomas-Reiche-Kuhn (TRK) sum rule for the electromagnetic field [69].…”

Section: Discussionmentioning

confidence: 99%

“…( 1) with eigenvalues ω j ordered so that k > j for ω k > ω j . Using the following relationship [69]…”

Section: A Quantum Rabi Model In the Coulomb Gaugementioning

confidence: 99%

Regimes of Cavity-QED under Incoherent Excitation: From Weak to Deep Strong Coupling

Mercurio¹,

Macrì²,

Gustin³

et al. 2021

Preprint

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The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) the appears to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength, and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurence of light-matter decoupling in the deep strong coupling regime, and show how all of the obtained results are gauge invariant.

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“…38 Recently, a generalized sum rule was obtained for the strong coupling regime. 39 It is written in terms of the eigenstates of the full Hamiltonian and cannot be directly applied to simplify our calculations. However, the existence of such a rule indicates that even in the strong coupling regime, the second-order terms perfectly balance out the first-order interactions.…”

Section: A Plasmonic Nanoparticle Crystalsmentioning

confidence: 99%

Plasmon-Polaritons in Nanoparticle Supercrystals: Microscopic Quantum Theory Beyond the Dipole Approximation

Barros,

Vieira,

Mueller

et al. 2021

Preprint

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Crystals of plasmonic metal nanoparticles have intriguing optical properties. They reach the regimes of ultrastrong and deep strong light-matter coupling, where the photonic states need to be included in the simulation of material properties. We propose a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticle building blocks and their coupling to photons. Our model excellently reproduces results of finite difference time domain simulations. It provides detailed insight into the emergence of the polariton states. Using the example of a face centered cubic crystals we show that the dipole and quadrupole states mix in many high symmetry directions of the Brilouin zone. A proper description of the plasmon and plasmon-polariton band structure is only possible when including the quadrupole-derived states. Our model leads to an expression of the reduced coupling strength in nanoparticle supercrystals that we show to enter the deep strong coupling regime for metal fill fractions above 0.8. In addition to the plasmon-polariton energies we analyse the relative contributions of the dipole, quadrupole, and photonic states to their eigenfunctions and are able to demonstrate the decoupling of light in the deep strong coupling regime. Our results pave the way for a better understanding of the quantum properties of metallic nanoparticle supercrystals in the ultrastrong and deep-strong coupling regime.

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Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons

Cited by 14 publications

References 79 publications

Hot carriers in graphene – fundamentals and applications

Hot carriers in graphene – fundamentals and applications

Regimes of Cavity-QED under Incoherent Excitation: From Weak to Deep Strong Coupling

Plasmon-Polaritons in Nanoparticle Supercrystals: Microscopic Quantum Theory Beyond the Dipole Approximation

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