TRK Sum Rule for Interacting Photons
arXiv:2002.02139 · doi:10.1515/nanoph-2020-0433
Abstract
The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Here we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light-matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light-matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light-matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.
22 pages, 4 figures
References in corpus (8)
- Quantum fluids of light
- Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
- Deep Strong Coupling Regime of the Jaynes-Cummings model
- Polaritonic Coupled-Cluster Theory
- Nonlinear interaction between two heralded single photons
- Gauge invariance of the Dicke and Hopfield models
- Dynamical Casimir Effect in Quantum Information Processing
- Collective Radiance Effects in the Ultrastrong Coupling Regime
Cited by in corpus (14)
- Hot carriers in graphene -- fundamentals and applications
- Gauge invariance of the Dicke and Hopfield models
- Gauge freedom, quantum measurements, and time-dependent interactions in cavity and circuit QED
- Gauge Principle and Gauge Invariance in Quantum Two-Level Systems
- Gauge Principle and Gauge Invariance in Two-Level Systems
- Gauge-Independent Emission Spectra and Quantum Correlations in the Ultrastrong Coupling Regime of Open System Cavity-QED
- Quantum Phase Transitions in Optomechanical Systems
- Regimes of Cavity-QED under Incoherent Excitation: From Weak to Deep Strong Coupling
- Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media
- Generalized Dicke model and gauge-invariant master equations for two atoms in ultrastrongly-coupled cavity quantum electrodynamics
- Plasmon-Polaritons in Nanoparticle Supercrystals: Microscopic Quantum Theory Beyond the Dipole Approximation
- Reconciling quantum and classical spectral theories of ultrastrong coupling: Role of cavity bath coupling and gauge corrections
- Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics
- From Few to Many Emitters Cavity QED: Energy Levels and Emission Spectra From Weak to Deep-Strong Coupling