This work presents a derivation of generalized input-output relations and the output electric field operator for quantized quasinormal modes, and applications towards the weak and strong light-matter coupling regime for a dielectric-metallic hybrid resonator coupled to a quantum emitter in the nonlinear cavity-QED regime.
Phenomenological approaches to photon loss have long been the workhorse of cavity-QED, but prove inadequate in the presence of sufficiently broadband light-matter interactions. We present a rigorous and ab initio derivation of a quantum master equation for a quantized optical cavity mode coupled to a dipole, using a quasinormal mode (QNM) quantization procedure for plasmonic and dielectric open-system cavity-QED, which is valid in broadband light-matter interaction regimes, including ultrastrong coupling (USC). The theory supports general three-dimensional resonators with arbitrary dispersion and loss, and thus can be applied to a wide range of realistic open cavities. Our ab initio and gauge-invariant approach fully recovers a recent result for the spectral density of a quantized cavity with a single dipole and reveals important departures from previous heuristic assumptions about system-reservoir coupling. We identify a new criterion for what we term the "broadband dissipative" regime of cavity-QED, where phenomenological models require corrections in accordance with the intrinsic and spatially-dependent complex phase of the QNM, and also shed light on fundamental limits to single-mode models in extreme coupling regimes. Using experimentally motivated plasmonic and dielectric cavity examples, we show validity ranges of our QNM master equation and spectral USC calculations, and discuss prospects for near-term experimental observation of the broadband dissipative effects.
We introduce a second quantization scheme based on quasinormal modes, which are the dissipative modes of leaky optical cavities and plasmonic resonators with complex eigenfrequencies. The theory enables the construction of multiplasmon or multiphoton Fock states for arbitrary three-dimensional dissipative resonators and gives a solid understanding to the limits of phenomenological dissipative Jaynes-Cummings models. In the general case, we show how different quasinormal modes interfere through an off-diagonal mode coupling and demonstrate how these results affect cavity-modified spontaneous emission. To illustrate the practical application of the theory, we show examples using a gold nanorod dimer and a hybrid dielectric-metal cavity structure.
Open optical or plasmonic resonators are placed on and connected through surfaces or via waveguides, forming complex lightguiding nanostructures, e.g. for integrated photonic quantum devices. We derive general boundary conditions for quasinormal modes that account for the structure's specific geometry. We then present a general quantization scheme for multiple, interacting quasinormal-mode cavities coupled to quantum emitters and to a non-bosonic bath of propagating photons on waveguides or a surface. We derive a system-bath Hamiltonian with rigorously defined coupling elements that can be computed using Maxwell solvers, including light-matter coupling between the electromagnetic field and quantum emitters. We define system-bath correlation functions for an effective, bath-mediated, and time-delayed interaction between the quasinormal modes and quantum emitters, which is a main ingredient commonly used to simulate open quantum system dynamics.
The unprecedented pace of evolution in nanoscale architectures for cavity quantum electrodynamics (cQED) has posed crucial challenges for theory, where the quantum dynamics arising from the non-perturbative dressing of matter by cavity electric and magnetic fields as well as the fundamentally non-Hermitian character of the system are to be treated without significant approximation. The lossy electromagnetic resonances of photonic, plasmonic, or magnonic nanostructures are described as quasinormal modes (QNMs), whose properties and interactions with quantum emitters and spin qubits are central to the understanding of dissipative nano-optics and magnetodielectric cQED. Despite recent advancements toward a fully quantum framework for QNMs, a general and universally accepted approach to QNM quantization for arbitrary linear media remains elusive. In this work, we introduce a unified theoretical framework, based on macroscopic QED and complex coordinate transformations, which achieves QNM quantization for a wide class of spatially inhomogeneous, dissipative and dispersive, linear, magnetodielectric resonators. The complex coordinate transformations equivalently convert the radiative losses into non-radiative material dissipation, and via a suitable transformation that reflects all the losses of the resonator, we define creation and annihilation operators that allow the construction of modal Fock states for the joint excitations of field-dressed matter. By directly addressing the intricacies of modal loss in a fully quantum theory of magnetodielectric cQED, our approach enables the exploration of modern, quantum nano-optical experiments utilizing dielectric, plasmonic, magnetic, or hybrid cQED architectures and paves the way toward a rigorous assessment of room-temperature, quantum nanophotonic technologies without recourse to ad hoc quantization schemes.
We present a quantized pseudomode theory for solving system-level cavity quantum electrodynamics with quantum emitters coupled to plasmonic resonators. Exploiting the Green function response of a silver nanoparticle and an exact solution for the input-output coupling, we study the non-Markovian coupling regimes of multi-mode vacuum Rabi oscillations and coherently pumped multi-photon resonances from the higher lying ladder states of collective plasmon modes. The nonlinear pumping regime also facilitates pronounced population inversion of a single two-level atom through multiphoton resonances dominated by dark plasmons.
Cavity quantum magnonics has ushered in an unprecedented era of hybrid light-matter interfaces in which microwave photons, collective spin excitations, and superconducting or spin qubits can be coupled within a single device architecture, facilitating a versatile platform for quantum information processing. Realizing their full potential, however, requires a theory that can treat non-reciprocal magnetic media, material dissipation and open-cavity radiation losses, as well as finite-temperature fluctuations rigorously and without significant approximation. The dissipative magnonic resonances of such systems are described as quasinormal modes (QNMs), yet a consistent quantization procedure for lossy gyrotropic resonators has remained elusive. In this work, we present a finite-temperature quantum QNM theory, based on macroscopic quantum electrodynamics for non-reciprocal media and complex coordinate transformations, that achieves QNM quantization for a wide class of spatially inhomogeneous, dissipative and dispersive, cavity magnonic systems. We demonstrate the predictive capabilities of our theory via applications to hybrid dielectric-magnonic resonators interacting with both spin and superconducting qubits, evidencing modal interference effects, a continuous transition from coherent to dissipative coupling, spatiotemporal quantum field dynamics, and magnon-mediated qubit synchronization, at both zero and finite temperatures. By addressing the intricacies of modal loss and non-reciprocity in a fully quantum theory of cavity magnonics, our approach enables the quantitative design of hybrid quantum devices that operate under realistic open-system and thermal conditions, without recourse to ad hoc quantization schemes.