Field quantization for open optical cavities

Abstract

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\epsilon (\mathbf{r})$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system--and--bath Hamiltonian of quantum optics. The field dynamics is investigated using the input--output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

16 pages, added references, corrected typos

References in corpus (2)

• Field quantization for chaotic resonators with overlapping modes
• Field Quantization, Photons and Non-Hermitean Modes

Cited by in corpus (68)

• Light fields in complex media: mesoscopic scattering meets wave control
• Laser cooling of a nanomechanical resonator mode to its quantum ground state
• Intrinsic dissipation in nanomechanical resonators due to phonon tunneling
• Theory of reflectionless scattering modes
• General phase-diagram of multimodal ordered and disordered lasers in closed and open cavities
• Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer
• Temporal Switching to Extend the Bandwidth of Thin Absorbers
• Recent developments in the theory of multimode random lasers
• Implications of gauge freedom for nonrelativistic quantum electrodynamics
• Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides
• The glassy random laser: replica symmetry breaking in the intensity fluctuations of emission spectra
• Route from spontaneous decay to complex multimode dynamics in cavity QED
• Ab initio self-consistent laser theory and random lasers
• Strong coupling in chiral cavities: nonperturbative framework for enantiomer discrimination
• A recipe for Hamiltonian of system-environment coupling applicable to ultrastrong light-matter interaction regime
• The resonant dynamics of arbitrarily-shaped meta-atoms
• Few-mode Field Quantization for Multiple Emitters
• The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media
• Statistical mechanics models for multimode lasers and random lasers
• Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?
• Quantum theory of multimode fields: Applications to optical resonators
• Vacuum Rabi spectra of a single quantum emitter
• Quantum squeezing generation versus photon localization in a disordered microcavity
• Vibrational polariton transport in disordered media
• Quantum Input-Output Theory for Optical Cavities with Arbitrary Coupling Strength: Application to Two-Photon Wave-Packet Shaping
• Ericson fluctuations in an open, deterministic quantum system: theory meets experiment
• Ab initio few-mode theory for quantum potential scattering problems
• Ab initio quantum models for thin-film x-ray cavity QED
• Reflectionless excitation of arbitrary photonic structures: A general theory
• QED of lossy cavities: operator and quantum-state input-output relations
• QED with a parabolic mirror
• Quantum statistics of overlapping modes in open resonators
• System-environment coupling derived by Maxwell's boundary conditions from weak to ultrastrong light-matter coupling regime
• Certifying multi-mode light-matter interaction in lossy resonators
• Statistical physics of nonlinear wave interaction
• Gauge-invariant theory of truncated quantum light-matter interactions in arbitrary media
• Bosonic Mpemba effect with non-classical states of light
• Statistical properties of one-dimensional random lasers
• Statistical physical theory of mode-locking laser generation with a frequency comb
• Metasurface-based hybrid optical cavities for chiral sensing
• A master equation for a two-sided optical cavity
• Glassiness and Lack of Equipartition in Random Lasers: the common roots of Ergodicity Breaking in Disordered and Non-linear Systems
• Cavity-assisted spontaneous emission as a single-photon source: Pulse shape and efficiency of one-photon Fock state preparation
• Why the laser linewidth is so narrow: A modern perspective
• Quantum optics measurement scheme for quantum geometry and topological invariants
• Mode statistics in random lasers
• Cavity-waveguide interplay in lossy resonators and its role in optimal single-photon sources
• Diagrammatic semiclassical laser theory
• Photon noise in a random laser amplifier with fluctuating properties
• One-sided destructive quantum interference from an exceptional point-enabled metasurface
• Modal analysis of the scattering coefficients of an open cavity in a waveguide
• Quantum theory of a two-mode open-cavity laser
• Leaky cavities with unwanted noise
• Multi-body quenched disordered $XY$ and $p$-clock models on random graphs
• Perturbation theory of optical resonances of deformed dielectric spheres
• What is the spectral density of the reservoir for a lossy quantized cavity?
• Inference for interacting linear waves in ordered and random media
• Electromagnetic Eigenvalue Problems and Nonhermitian Effects in Linear and Saturable Scattering
• Determination of quantum-noise parameters of realistic cavities
• Two-membrane etalon
• Stochastic correction to the Maxwell-Bloch equations via the positive $P$ representation
• Gas lasers with wave-chaotic resonators
• Circuit quantum electrodynamics: A new look toward developing full-wave numerical models
• Multimode-cavity picture of non-Markovian waveguide QED
• Dissipation and non-thermal states in cryogenic cavities
• Probing the collective excitations of excitonic insulators in an optical cavity
• Generalized Maxwell projections for multi-mode network Photonics
• Position-Resolved Resonance Quantization for Lossy Cavities