Effective theory for matter in non-perturbative cavity QED
arXiv:2110.07632 · doi:10.21468/SciPostPhysLectNotes.50
Abstract
Starting from a general material system of particles coupled to a cavity, we use a coherent-state path integral formulation to produce a non-perturbative effective theory for the material degrees of freedom. We tackle the effects of image charges, the term and a multimode arbitrary-geometry cavity. The resulting (non-local) action has the photonic degrees of freedom replaced by an effective position-dependent interaction between the particles. In the large- limit, we discuss how the theory can be cast into an effective Hamiltonian where the cavity induced interactions are made explicit. The theory is applicable, beyond cavity QED, to any system where bulk material is linearly coupled to a diagonalizable bosonic bath. We highlight the differences of the theory with other well-known methods and numerically study its finite-size scaling on the Dicke model. Finally, we showcase its descriptive power with three examples: photon condensation, the 2D free electron gas in a cavity and the modification of magnetic interactions between molecular spins; recovering, condensing and extending some recent results in the literature.
Changes: 1. New section added. 2. Added citations and other minor changes
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Cited by in corpus (22)
- Cavity Quantum Materials
- Off-resonant Dicke Quantum Battery: Charging by Virtual Photons
- Cavity Quantum Electrodynamics with Hyperbolic van der Waals Materials
- A non-perturbative no-go theorem for photon condensation in approximate models
- Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems
- Nonperturbative cavity quantum electrodynamics: is the Jaynes-Cummings model still relevant?
- Cavity Induced Collective Behavior in the Polaritonic Ground State
- Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
- Cavity-induced charge transfer in periodic systems: length-gauge formalism
- Corrections to the Hamiltonian induced by finite-strength coupling to the environment
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- Cavity-enhanced Kondo effect
- Cavity-mediated superconductor$\unicode{x2013}$ferromagnetic insulator coupling
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- Electrostatic nature of cavity-mediated interactions between low-energy matter excitations
- Bound polariton states in the Dicke-Ising model
- Theory of photon condensation in an arbitrary gauge condensed matter cavity model
- General theory of cavity-mediated interactions between low-energy matter excitations
- Effective Field Theories and Finite-temperature Properties of Zero-dimensional Superradiant Quantum Phase Transitions
- Optimal Dynamical Gauge in the Quantum Rabi Model
- Amplified response of cavity-coupled quantum-critical systems